Term 3 Maths year 5 (PUCD) (1)

1

2

Content 1. Probability

3

2. Two-Dimensional Shapes

19

3. Problem Solving

33

4. Pre-Algebra

49

5. Measuring

65

6. Whole Numbers

77

7. Average

89

8. Data

101

9. Circle

115

10. Speed

129

3

4

Determine Probability

5

Identifying Certain and Impossible Events

6

Identifying Likely, Unlikely and Equally Likely Events

7

Making Decisions with Probability Directions: The terms you learned on page 4 to help explain you decisions for the following situations.

8

Show Probability

9

Showing Probability with Fractions

10

Showing Probability with Decimals and Percent

11

Showing Probability in Three Ways

12

Compare Outcomes

13

Comparing Probabilities

14

Multiplying to Determine Probability

15

Drawing a Tree Diagram or Making a List

16

Make Prediction with Probability and Data

17

Make Prediction with Probability

18

Make Prediction with Data

19

20

Learning about Angles

21

22

23

Types of Angles

24

25

1. Find

Answer:________________ 2. Find

Answer:________________ 3. In the figure (not drawn to scale), AB and CD are straight lines. Find x.

Answer:________________

26

4. In the figure (not drawn to scale), ABCD is a trapezium with AB parallel to DC. Find x

Answer:________________

5. In the figure (not drawn to scale), ABCD is a rhombus. Find x

Answer:________________ 6. In the figure (not drawn to scale), ABCD is a square and EFGH is a parallelogram.

Find x

Answer:________________

27

7. In the figure (not drawn to scale), ABCD is a trapezium with AB parallel to DC. ADB is a right angle.

(a) Find x _______________________

(b) Find y _______________________

8. In the figure (not drawn to scale), ABCD is a parallelogram, EFCD is a rhombus and GEF is a straight line.

(a) Find x _______________________

(b) Find y _______________________

28

9. In the figure (not drawn to scale), ABCD is a trapezium with AB parallel to DC and ABE is an isosceles triangle with BA = BE.

(a) Find x _______________________

(b) Find y _______________________

10. In the figure (not drawn to scale), ABCD is a parallelogram and AFE is an isosceles triangle with FA = FE.

(a) Find x _______________________ (b) Find y _______________________

29

11. In the figure (not drawn to scale), ABCD is a rhombus and AECF is a rectangle.

(a) Find x _______________________

(b) Find y _______________________

12. In the figure (not drawn to scale), ABCD is a trapezium with AB parallel to DC, ADE is an isosceles triangle with AD = AE.

(a) Find x _______________________

(b) Find y _______________________

30

13. In the figure (not drawn to scale), ABCD is a rectangle and BEFG is a parallelogram.

(a) Find x _______________________

(b) Find y _______________________

14. In the figure (not drawn to scale), ACD is a right-angled triangle, ABC is an isosceles triangle with AB =AC, ACG, EAB and FAD are straight lines.

(a) Find x _______________________

(b) Find y _______________________

31

15. In the figure (not drawn to scale), ABCD is a parallelogram and GBEF is a rectangle.

(a) Find x _______________________

(b) Find y _______________________

16. Answer the questions next to each drawing. a. What angle is vertical to k? _____________ b. What angle is vertical to h? _____________ c. How many degrees is g?

_____________

d. How many degrees is h?

_____________

e. How many degrees is f ?

_____________

f. f + k =

_____________

g. f + h + g + k =

_____________

32

17.

a. How many degrees are in JNM’s supplement? _________ b. How many degrees are in JNL?

_____________

c. How many degrees are in LNK? ____________ d. How many degrees are in MNK? ____________

18.

19.

33

34

The story: Mr. Roake keeps track of students’ average test scores by averaging percents in each subject. Use the table below to answer the questions.

Directions Carefully read each question and decide what is being asked. Write the equations needed to solve each problem along with your complete answer.

1.

Name

Reading

Math

Spelling

Science

Social Studies

Nicole

88%

90%

92%

86%

99%

Jasmine

99%

99%

99%

82%

70%

Anna

99%

88%

96%

89%

95%

Isaiah

97%

98%

98%

79%

98%

Cameron

88%

92%

99%

95%

94%

Justin

99%

98%

92%

92%

90%

Find the median of Nicole’s test averages in all five subjects. ___________________________________________________________________ ___________________________________________________________________

2.

What is the mode of Jasemine’s test averages for all five subjects? ___________________________________________________________________ ___________________________________________________________________

3.

In all five subjects, Anna’s median test average is what? ___________________________________________________________________ ___________________________________________________________________

35

4.

What is the mode of Isaiah’s test averages in all five subjects? ___________________________________________________________________ ___________________________________________________________________

5.

Find the mean for the social studies test averages. ___________________________________________________________________ ___________________________________________________________________

6.

The mean score for spelling test averages is what? ___________________________________________________________________ ___________________________________________________________________

7.

Which student has a median test average of 92% for all five subjects? ___________________________________________________________________ ___________________________________________________________________

36

The story: Four women, Mrs. Brown, Mrs. Green, Mrs. White and Mrs. Black each bought a new dress. One of the new dresses is brown, one is green, one is white and one is black.

Directions Carefully read each clue and decide what is being said. On the chart, record the information given in each clue. To find the answers, check to see what possibilities are left.

Brown

Green

White

Black

Mrs. Brown Mrs. Green Mrs. White Mrs. Black Clues: 1.

Mrs. Green is wearing the black or white dress.

2.

Mrs. Brown is wearing the brown or white dress.

3.

Mrs. Black is wearing the brown or black dress.

4.

Mrs. White is wearing the brown or green dress.

5.

Mrs. Green is not wearing the black dress.

Which woman is wearing which dress?

Brown dress

___________________________________

Green dress

___________________________________

White dress

___________________________________

Black dress

___________________________________

37

The story: Five boys went to lunch: Tyler, Darius, Joseph, Andrew, and Chiyong. One boy had pepperoni pizza, one had a hot dog, one had a hamburger, one had a salad, and one had fish ‘n’ chips.

Directions

Carefully read each clue and decide what is being said. On the chart, record the information given in each clue. To find the answers, check to see what possibilities are left.

Pizza

Hotdog

Hamburger

Salad

Tyler Darius Joseph Andrew Chiyong

Clues: 1.

Tyler had a hot dog or a salad

2.

Joseph had pepperoni pizza or a hot dog.

3.

Chiyong didn’t have pepperoni pizza or a hot dog.

4.

Andrew had a salad or fish and chips.

5.

Darius is vegetarian.

Fish ‘n’ chips

38

Which boy ate which lunch?

Pizza:

___________________________________

Hot dog:

___________________________________

Hamburger:

___________________________________

Salad:

___________________________________

Fish ‘n’ chips

___________________________________

The story: Five children have pets including birds, fish, horse, dogs, and cats. Each child has only one kind of pet but some have more than one of that kind of pet. Each child has a different kind of pet from the other children. Two children have 1 pet; 1 child has 2 pets; 1 child has 3 pets; and 1 child has 5 pets.

Directions Carefully read each clue and decide what is being said. On the chart, record the information given in each clue. To find the answers, check to see what possibilities are left.

Dog (s) Becky James Alonzo Cherise Terrel

Cat (s)

Horse (s)

Fish

Bird (s)

1

1

2

3

5

39

Clues: 1.

Becky has two pets, and they aren’t dogs or fish.

2.

Terrel has more than two pets, and they aren’t horses or fish.

3.

James has only one pet, and it’s a dog or cat.

4.

Cherise has only one pet, and it isn’t a bird or cat.

5.

Alonzo doesn’t have the most pets but he has more than Becky.

6.

Terrel keeps his pets in a cage.

7.

Alonzo can ride one of his pets in a parade.

How many and what kind of pet does each child have?

Becky:

___________________________________

James:

___________________________________

Alonzo:

___________________________________

Cherise:

___________________________________

Terrel:

___________________________________

40

The story: Animals vary in their speeds. Chickens can run 9 km/h, domestic pigs can run 11 km/h, squirrels can run 12 km/h, a black mamba snake can travel 20 km/h, a pet cat can run 30 km/h, and a giraffe can run 32 km/h.

1.

If a chicken could maintain its fastest speed, how far could it run in six hours? a.

2.

36 km

b.

54 km

c.

90 km

d.

600 km

If all of the animals were on a relay team and each ran for an hour, altogether, how far would they travel? ___________________________________________________________________ ___________________________________________________________________

3.

In half an hour, how much farther can a cat travel than a squirrel? ___________________________________________________________________ ___________________________________________________________________

4.

The average speed of animals is a.

5.

10 km/h

b.

12 km/h

c.

16 km/h

d.

19 km/h

A mamba snake can travel as far in three hours as a cat can run in two hours. True or false? ___________________________________________________________________ ___________________________________________________________________

41

The story: Grace baked a huge chocolate sheet cake and cut into 20 pieces.

6.

What fractional part of the cake is represented by five pieces? a.

7.

1/5

b.

½

c.

¼

d.

1/10

Ten pieces of cake represent 50 % of the whole cake. True or false? ___________________________________________________________________ ___________________________________________________________________

8.

What decimal does six pieces of the cake represent? a.

9.

0.6

b.

0.3

c.

0.10

d.

3.33

Four tenths of the cake is how many pieces of cake? ___________________________________________________________________ ___________________________________________________________________

10.

If Grace served 17 pieces of her cake, what fractional part of the cake is left? ___________________________________________________________________ ___________________________________________________________________

42

The story: For her birthday party, Mcakenzie baked two pies, cherry and apple. She cut cherry pie into eight pieces. She cut the apple pie into six pieces.

11.

What fraction represents six pieces of the cherry pie? a.

12.

1/8

b.

¼

c.

½

d.

¾

If Julia ate half of an apple pie, she ate 2/6 of the pie. True or false? ___________________________________________________________________ ___________________________________________________________________

13.

If Mackenzie bakes two cherry pies, cuts them the same way, and sells each piece for 50 cents, how much money can she make in all? a.

14.

$4.00

b.

$6.00

c.

$8.00

d.

$16.00

What decimal is represented by two pieces of apple pie? ___________________________________________________________________ ___________________________________________________________________

15.

What fractional part of a whole pie is represented by two pieces of cherry pie and three pieces of apple pie? ___________________________________________________________________ ___________________________________________________________________

43

The story: Coach David kept track of the points made by the first-string basketball players in the first five games. Brandon scored 1, 8, 3, 0 and 8 points. Zach scored 8, 4, 4, 4 and 6 points. Tony scored 8, 10, 6, 2 and 4 points. Chris scored 4, 6, 6, 12 and 10 points. Darrel scored 8, 12, 10, 8 and 12 points.

16.

The mean score for Brandon’s game is a.

17.

4 points

b.

8 points

c.

5 points

d.

2 points

What is the mode of Zach’s scores? ___________________________________________________________________ ___________________________________________________________________

18.

Tony has a median score of six. True or False? ___________________________________________________________________ ___________________________________________________________________

19.

The mode score for the first game was a.

20.

9 points

b.

8 points

c.

6 points

d.

2 points

What is the median of Chris’s scores? ___________________________________________________________________ ___________________________________________________________________

44

Red Hot Chili Recipe (Serves 20) 300 grams hamburger

40 ml chili pepper

500 grams beans

60 ml hot sauce

400 grams tomatoes

20 ml tomato sauce

200 grams macaroni

160 ml water

Directions: Use the information in the recipe above to help you solve these problems. (Hint: Making a fraction of a recipe involves multiplication. Determining how many times a fraction fits into another number involves division).

1.

2.

3.

Maria wanted to make only ¼ of the recipe. How much did she need for each ingredient? ______________ grams hamburger

______________ ml chili pepper

______________ grams beans

______________ ml hot sauce

______________ grams tomatoes

______________ ml tomato sauce

______________ grams macaroni

______________ ml water

Crystal wanted to make only 1/3 of the recipe. How much did she need of each ingredient? ______________ grams hamburger

______________ ml chili pepper

______________ grams beans

______________ ml hot sauce

______________ grams tomatoes

______________ ml tomato sauce

______________ grams macaroni

______________ ml water

Patti made exactly ½ of the recipe. How much did she need of each ingredient? ______________ grams hamburger

______________ ml chili pepper

______________ grams beans

______________ ml hot sauce

______________ grams tomatoes

______________ ml tomato sauce

______________ grams macaroni

______________ ml water

4.

Chili beans came in 10 grams bags. How much bag of chili beans would Julie need to make the original recipe? ______________

5.

Tomatoes can be purchased in 100 grams packet. How many packets of tomatoes would Julie need to make the original recipe? ______________

6.

Macaroni can be bought in 50 grams packets. How many packets of macaroni would Julie need to make the original recipe? ______________

7.

Hamburger can be bought in 50 grams packet. How many packets of hamburger would Julie need to make the original recipe? ______________

45

Directions: The fifth grade at Garfield Public School is growing a garden as a class science project.

They are keeping a careful record of exactly how much water they are using for each plant. Help the class solve these word problems.

1.

Doreen poured ¼ of a litre of water near each corn plant. How much water did she give to all 20 corn plants?

2.

______________

James gave 1/3rd of a litre of water to the marigold and one whole litre to the sunflower. How much more water did he give to the sunflower?

3.

Alison divided 7/8th of a litre of water evenly among the 14 green bean plants. How much water did she use for each plant?

4.

______________

Melissa split 2/3rd of a litre of water evenly among 6 pumpkin plants. How much water did she distribute to each pumpkin plant?

5.

______________

George used 2/3rd of a litre of water for each of 30 cherry tomatoes. How much water did he use for all 30 cherry tomato plants?

6.

______________

______________

Eleanor gave 5/12th of a litre of water to a squash plant and 1/3rd of a litre to a cucumber plant.

How much more water did she give to the squash plant?

7.

Frank split 5/6th of a litre of water evenly among his 15 radishes. How much water did he give to each radish?

8.

______________

______________

Corine gave 5/12th of a litre of water to her pole bean plant and 3/8th of a litre to her lima bean plant. How much water did she use for both plants? ______________

9.

Robert divided 2 full litres of water by giving each of his sweet peas 1/9th of a litre. How many sweet peas did he water?

10.

______________

Elaine used 11/12th of a litre of water on her plants. Amanda used 5/6th of a litre on her plants.

How much less water did Amanda use?

______________

46

Directions: Birds have hollow bones which help keep them light. Use your knowledge of decimals to help you solve these problems.

1.

An Australian quail weighs 0.180 kilograms. How much would 3 Australian quail weigh? ______________

2.

A sky lark weighs 1.4 kilograms. How much would say 20 sky larks weigh? ______________

3.

A mallard duck weighs 2.4 kilograms. How much would 12 mallard ducks weigh? ______________

4.

A snow goose weighs 7.4 kilograms. What is the weight of 15 snow geese? ______________

5.

A green heron weighs 0.87 kilograms. What is the weight of 30 green herons? ______________

6.

The golden eagle weighs 4.575 kilograms. What is the weight of 21 golden eagles? ______________

7.

A crow weighs 0.45 kilograms. What is the weight of 100 crows? ______________

8.

A robin weighs 0.077 kilograms. What is the weight of 40 robins? ______________

9.

A hummingbird weighs 0.11 ounces. How much do 50 hummingbirds weigh? ______________

10.

The great horned owl weighs 3.1 kilograms. What is the weight of 25 great horned owls? ______________

47

Directions: Dr. Dooley D. Vision is known as “The Great Divider.” He is very famous for his ability to divide things fairly and evenly. He is often hired by families and companies to avoid disputes. Help him do the problems below.

1.

Dr. D Vision has a stick of licorice 105.25 metres long. He intends to split it evenly among 5 of his nephews. How much licorice will each nephew receive? ______________

2.

The Forty-One Flavours ice cream store asked Dr. Vision to help a teacher divide 108.4 grams of ice-cream among his 20 students. How much grams of ice cream did each child receive? ______________

3.

Dr. D. Vision decided to divide the money in his piggy bank among 7 of his grandchildren, He had $122.01. How much money did each grandchild receive? ______________

4.

The Candy Is Dandy factory hired Dr. D. Vision to help them divide 340.08 grams of chocolate among 80 chocolate bars. How much chocolate was in each bar? ______________

5.

Dr. D. Vision helped the school custodian cut a 183.6 metres rope into 9 even jump ropes. How much long was each jump rope? ______________

6.

Dr. D. Vision has hired to make sure that everyone at a party got the same amount of cake. The cake weighed 107.75 grams and there were 25 guests. How much cake did each guest receive? ______________

7.

Dr. D. Vision was hired to place 10 markers at even intervals along a public road which was 563.9 feet long. How long was each interval? ______________

8.

Dooley had a bag with 18.81 grams of gold dust which he intended to split evenly among his 9 favourite neighbours. How much gold dust did each neighbour receive? ______________

9.

The Great Divider was hired to divide to divide a vat of 896.4 grams of chocolate fudge into 90 jars. How much fudge went into each jar? ______________

10.

Dooley marked a 88.78 kilometres long state highway into 100 even sections. How long was each. ______________

48

1. David has thrice as many storybooks as Kenny. Kenny has 4 times more storybooks than Jack. If David has 42 more storybooks than Jack, how many storybooks does Kenny have?

______________

2. Jason had $38 and Megan had $14. After each of them bought a book at the same price, Jason had 5 times as much money as Megan. How much did the book cost?

______________

3. 38 children were given a packet of sweets to share equally. When 12 of them gave up their share of the sweets, the rest of the children had 6 extra sweets each. How many sweets were in the packet at first?

______________

49

50

51

52

53

54

55

56

57

58

59

Work out the following problems carefully.

1. I think of a whole number. I multiply it by 17 and then add 48 to the result. My answer is 269. Find the number that I think of.

Answer:_____________ __ 2. A watch and 3 identical shirts cost $354. If each shirt costs $202 less than the watch, find the cost of the watch.

Answer:_____________ __ 3. Mr. Clarke bought 2 dozen packets of sweets. There were 256 sweets in each packet. He repacked all the sweets into packets of 3 sweets each. How many packets of sweets did he repack?

Answer:_____________ __

60

4. Tony spent the same amount of money as Kathy. He had $248 left while she had $380 left. If they had $3458 altogether at first, how much did each of them spend?

Answer:_____________ __ 5. The product of two number is 75 360. One of the numbers is 96. Find the other number.

Answer:_____________ __ 6. When Nathan received $1368 from his mother, he had 4 times as much money as the amount he had at first. How much did he have at first?

Answer:_____________ __

61

7. Sharon had 36 more dresses than Wendy, Wendy had half as many dresses as Sharon. If Wendy had 120 dresses, how many dresses did the three girls have altogether?

Answer:_______________ 8. Mrs. Wang bought 12 similar chairs and 4 tables for $5344. Each table cost $568. Find the cost of each chair.

Answer:_____________ __ 9. George bought 6 pairs of shoes and 3 shirts for $348. If two pairs of shoes cost 3 times as much as a shirt, find the cost of 25 such shirts.

Answer:_____________ __

62

10. 1855 children were at a concert. There were 387 more boys than girls. If there were 209 more obese boys than thin boys, how many obese boys were at the concert?

Answer:_____________ __ 11. Johnny had 60 stamps more than Dave. Helen had five times as many stamps as Johnny.

If Helen had 1200 more stamps than Johnny, how many stamps did Dave have?

Answer:_____________ __ 12. If Greg packed 50 tarts into each box, what was the minimum number boxes he needed to pack 357 tarts?

Answer:_______________

63

Work out the following problems carefully. Show your working and statements clearly.

1. There were 4 rows of 16 students. The students were told to rearrange themselves to form a square with the same number of students along each side of the square. a) How many students were there altogether?

Answer:_______________ b) How many students were there along each side of the square?

Answer:_____________ __ 2. Every week, Richard earns $16 less than Andy. Each of them spends $48 per week on food and saves the rest. When Andy has saved $80, Richard has only saved $64. a) How long does Andy take to save $144?

__

Answer:_____________

b) What is Richard’s weekly earnings?

Answer:_____________ __

64

3. Ms. Walsh went to the supermarket with some money. If she bought 8kg of fish, she would need another $12. However, if she bought 5kg of fish, she would have $15 left.

What was the cost of 1 kg of fish?

__

Answer:_____________

4. At a certain coffeehouse, the charge for high tea per person is $20. For every group of 10 people, one of them does not have to pay. a) What will be the total charge for a party of 24 people?

Answer:_____________ b) How many people are there in the group if the bill comes up to $700?

Answer:_______________

65

66

1. The solid is made up of 1-cm cubes. What is the volume of the solid?

Answer :_______________ 2. The solid is made up of 1-cm cubes. What is the volume of the solid?

Answer :_______________ 3. The solid is made up of 1-cm cubes. What is the volume of the solid?

Answer :_______________ 4. The solid is made up of 1-cm cubes. What is the volume of the solid?

Answer :_______________

67

5. The solid is made up of 1-cm cubes. What is the volume of the solid?

Answer :_______________ 6. What is the volume of the cuboid?

Answer :_______________ 7. What is the volume of the cuboid?

Answer :_______________ 8. What is the volume of the cuboid?

Answer :_______________

68

9. What is the volume of the cuboid

Answer :_______________ 10. What is the volume of the cuboid?

Answer :_______________ 11. What is the volume of the cube?

Answer :_______________ 12. What is the volume of the cube?

Answer:_______________

69

13. Find the volume of water in the rectangular container.

Answer :_______________ 14. Sarah has 8 rectangular blocks of wood, each measuring 4 cm by 5 cm by 6 cm. She wants to stack up the 8 blocks of wood one on top of another. What is the lowest possible height of the stack of 8 blocks of wood?

Answer :_______________ 15. The volume of the cuboid is 688 cm3. What is the area of the shaded face of the cuboid?

Answer :_______________

70

16. The volume of the cuboid is 54 cm3. What is the area of the shaded face of the cuboid?

Answer :_______________ 17. The volume of the cuboid is 2233 cm3. What is the area of the shaded face of the cuboid?

Answer :_______________ 18. The volume of the cuboid is 650 cm3. What is the length of the cuboid?

Answer :_______________ 19. The volume of the cuboid is 240 cm3. What is the height of the cuboid?

Answer :_______________

71

20. The volume of the cuboid is 800 cm3. What is the breadth of the cuboid?

Answer :_______________

21. The volume of the cuboid is 500 cm3. What is the length of the cuboid?

Answer :_______________ 22.The volume of the cuboid is 1200 cm3. What is the height of the cuboid?

Answer :_______________

72

23. The volume of a cube is 8 cm3. What is the length of one side of the cube?

Answer :_______________ 24. The volume of a cube is 125 cm3. What is the length of one side of the cube?

Answer :_______________ 25. The volume of a cube is 1000 cm3. What is the length of one side of the cube?

Answer:_______________

73

Work out the following problems carefully. Show your working and statements clearly.

1. A carpenter made a wooden bench with 3 rectangular pieces of wood. The bottom 2 pieces are of identical dimensions. Find the total volume of the 3 pieces of wood.

Answer :_______________ 2. A carpenter made a wooden chair with 3 rectangular pieces of wood. Find the total volume of the 3 pieces of wood.

Answer :_______________

74

3. Tom has a rectangular piece of wood. What is the most number of 2-cm cubes that he can cut?

Answer :_______________ 4. Jerry had a rectangular block of wood measuring 28 cm by 20 cm by 15 cm. After he cut as many 6-cm cubes as possible from the block of wood, he was left with the block of wood as shown in the figure.

(a) How many 6-cm cubes did he get?

Answer :_______________ (b) What was the volume of the block of wood left?

Answer :_______________

75

5. A cube of side 4 cm is placed in a rectangular tank Water is then poured into the tank.

How much water is needed to fill up the tank?

Answer :_______________ 6. Tom has some cubes each of side 2 cm. He uses some of them to build the following big cube.

(a) Find the volume of the big cube.

Answer :_______________ (b) How many more cubes does he need to use to build a cube of side 8 cm?

Answer :________________

76

7. Water was poured into a rectangular tank to a height of 5 cm. Alvin found that heneeded another 1440 cm3 of water of fill up the tank. What was the height of the rectangular tank given that the area is 480 cm2?

Answer :________________ 8. The cuboid measures 5 cm by 5 cm by 17 cm. (a) What is the volume of the cuboid?

Answer :________________ (b) What is the maximum number of 2-cm cubes that can be cut from the cuboid?

Answer :________________

77

78

1. What is 7000000 in word? __________________________________________________ ________________________________________________________________________ 2. What is 8542000 in word? __________________________________________________ ________________________________________________________________________ 3. What is 9407000 in word? __________________________________________________ ________________________________________________________________________ 4. What is 3637001 in word? __________________________________________________ ________________________________________________________________________ 5. What is four million , six hundred and eighty-six thousand, four hundred and twenty-nine in numerals? ____________________________________________________________ 6. What is seven million, two hundred and three thousand and fifty-one in numerals? ________________________________________________________________________ 7. What is eight million and eighty-eight in numerals? ________________________________________________________________________ 8. What is one million, forty-six thousand and seven in numerals? ________________________________________________________________________ 9. In 459812, what is the value of the digit 4? ________________________________________________________________________ 10. In 7981231, what is the value of the digit 8? ________________________________________________________________________ 11. In 3109276, what is the value of the digit 1? ________________________________________________________________________ 12. In 2473490, which digit is in the millions place? ________________________________________________________________________

79

Find the value of each of the following.

1. 48 + 19 – (16 ÷ 4 + 3)

6. 250 + 150 – (167 – 5 × 14)

2. 56 – (3 + 8 × 2) + 32 ÷ 4

7. 899 + 101 – (145 -350 ÷ 7) × 2

3. (640 ÷ 8 – 2) × 6 ÷ 3 – 95

8. 45 – 13 + 24 -120 ÷ 8

4. 169 ÷13 + 65 × 8 – 42

9. 225 ÷ 15 + 45 × (9 – 4) – 33

5. 340 – (123 + 66) ÷ 9 + 72

10.200 + 677 – (240 + 91 ÷ 13)

80

Problem solving with whole numbers 1. Alicia is 6 years older than her brother. Their total age is 24. How old is Alicia?

___________________ 2. Adam had 60 marbles less than Carl. Ben had 80 marbles more than Carl. If they had 800 marbles altogether, how many marbles did Ben have?

___________________ 3. Jerry went to a store to buy 20 bottles of apple juice. What was the smallest amount of money he could have spent on the 20 bottles of apple juice?

___________________

81

4. Tom was 67 years old in 2005. How old was he in 1987?

___________________ 5. Julia exchanges a $50 note for 20-cent coins. How many coins will she get?

___________________ 6. A whole number when rounded off to the nearest hundred becomes 5000.What is the largest possible number?

___________________ 7. Arrange these numbers in increasing order: 9911, 9119, 9191, 9199 38.

___________________

82

8. John wants to buy 12 toy dinosaurs. How much will he save if he buys them from Store B rather than from Store C?

___________________ 9. A group of 8 children shared a box of sweets. After they had taken 6 sweets each, there were 2 sweets left. How many sweets were there at first?

___________________ 10. Trees were planted at equal distances along a straight road. The distance between the first and the fifth tree is 40 m. Find the distance between the second and the ninth tree.

___________________

83

11. The total weight of Adam, Ben and Carl is 122 kg. Adam is 8 kg heavier than Ben and 20 kg heavier than Carl. What is Ben's weight?

___________________ 12. Peter is 6 times as old as Sally. Peter will be thrice as old as Sally in 6 years' time.

How old is Peter now?

___________________ 13. A beaker containing 7 identical marbles weighs 510 g. The same beaker containing 4 such marbles weigh 360 g. Find the weight of the empty beaker.

___________________

84

14. 10 carpenters took 10 days to make 10 tables. ____________carpenters took 1 day to make 1 table.

___________________ 15. Kimberly read from page 100 to page 200 of a storybook. How many pages did she read?

___________________ 16. Adam has twice as many marbles as Ben. Ben has 4 times as many marbles as Carl. If Adam has 28 more marbles than Carl, how many marbles does Ben have?

___________________

85

17. What day will it be 365 days from 1 June 2005?

___________________ 18. The number of sweets in a jar is between 40 and 90. If she sweets were to be packed in packets of 2 or 5, there will be no sweets left. If the sweets were to be packed in packed in packets of 3 or 4, there will be two sweets left. How many sweets are there in the jar?

___________________ 19. There are between 100 and 120 sweets in a jar. The sweets can be shared equally among 7 or 8 children. How many sweets are there in a jar?

___________________

86

20. Jean placed a bookmark between 2 pages of a storybook. There 2 page numbers add up to 545. What is the smaller page number?

___________________ 21.How many even-numbered pages are there between page 13 and page 537 of a book?

___________________

87

Test Question 1 to 5 carries 1 mark. Question 6 to 10 carry 2 marks each. For each question four options are given. One of them is the correct answer. Circle your choice (1, 2, 3 or 4). You are not allowed to use a calculator.

1. ¼ of a number is 54. What is 5/9 of the number?

1. 30 2. 60 3. 90 4. 120 2. The first two common multiples of 6 and 9 are ________ 1. 15 and 30 2. 18 and 36 3. 27 and 54 4. 54 and 108 3. How many hundreds are there in 84 500?

1. 5 2. 500 3. 840 4. 845 4. How many eights are there in 13 ¼?

1. 17 2. 2 3. 52 4. 106 5. Adrian’s mass is 5/7 of Bryan’s mass. What is the ratio of Bryan’s mass of their total mass?

1. 5 : 7 2. 5 : 12 3. 7 : 12 4. 12 : 7

88

6. Sherry bought 4 brownies and 3 muffins for $15. Each brownie cost 60c more than a muffin. How much did 1 brownie and 2 muffins cost?

1. $6 2. $ 6.80 3. $7.20 4. $8.40 7. The ratio of Glenda’s hair clips to Helen’s hair clips is 8 : 5. If Glenda has 18 more hair clips than Helen, find their total numbers of hair clips.

1. 78 2. 72 3. 48 4. 40 8. In the figure below, BCD is a straight line. AB=BC and ABC is a rightangled triangle. What is the value of <CAD? 1. 23o 2. 45o 3. 67o 4. 68o

A

22o B

C

D

9. Out of 80 students surveyed, 55% of them liked onion rings and the rest liked French fries. How many pupils liked French fries?

1. 36 2. 44 3. 45 4. 48 10. $ 31 500 was shared among Adam, Ben and Charles in the ratio 2 : 3 : 4.

How much more money than Adam did Charles get?

1. $ 3500 2. $ 7000 3. $ 10 500 4. $ 14 000 My Score:_______/ 15

89

90

Average Finding the average is a very straightforward concept. If you have a set of numbers, the average is found by adding all numbers in the set and dividing their sum by the total number of numbers added in the set.

1. Find the average of each of the following sets of numbers. a. 12, 27, 30, 67, 100

b. $6, $8, $20 ,

Average : __________________

$9

Average : __________________

c. 10cm, 25cm, 40cm, 85cm

Average : __________________

d. 0.3 L, 4.1 L, 7.6 L, 7.7 L , 9 L

Average : __________________

2. Cindy has $8. Her sister has $13. Her brother has $9. If all the money is shared equal among the three of them, how much money does each of them get?

Answer: __________________

91

3. Mr Smith has four children. Andrew is 12 years old. Ann is 10 years old. Andrea and Ashley are 3 years old and 7 years old respectively. a. What is the total age of the four children?

______________________

b. What is the average age of the four children?

______________________

4. Adrian scored a total of 243 marks for three subjects, English, Mathmatics and Science. What was his average score for these three subjects?

______________________ 5. Pete has a younger brother. Their total mass is 73 kg. What is their average mass?

______________________ 6. The school’s football team scored a total of 16 goals for 5 matches. What is the average number of goals scored for the 5 matches?

______________________

92

7. The average of three numbers is 27.8. Find the sum of these three numbers.

______________________ 8. The average length of 4 pieces of string is 9.5 cm. What is the total length of these 4 pieces of string?

______________________ 9. There are 8 cups. The average amount of water in each cup is 255ml . Find the total amount of water in the 8 cups. Give your answer in litres and millilitres.

______________________ 10. From Monday to Sunday, a pet shop owner sold an average of 6 hamsters per day.

How many hamsters did he sell from Monday and Sunday?

______________________

93

11. The total mass of 4 packets of rice is 5 kg 60 g. Find the average mass of each packet of rice. Give your answer in grams?

______________________ 12. The table shows the amount of money saved by 5 girls. Find their average savings.

May

Lynn

Mia

Emily

Hannah

$41

$26

$38

$31

$29

______________________ 13. The total mass of 6 mangoes is 2 kg 70g. Find the average mass of the 6 mangoes.

Give your answer in grams.

______________________ 14. The total mass of 3 packets of sugar is 3/8 kg. What is the average mass of these 3 packets of sugar?

______________________

94

15. The average of 9 numbers is 2.76. Find the sum of the 9 numbers.

______________________ 16. The average mass of 2 boys is 51kg. If one of the boy’s mass is 53.5 kg, what is the mass of the other boy?

______________________ 17. The average of two number is 15. One of the numbers is greater than the other number by 4. What are these two numbers?

______________________ 18. The average mass of Adam and Tim is 37.5kg. Adam’s mass is twice as much as Tim’s mass. What is Adam’s mass?

______________________

95

19. Amelia is 6 years older than her younger sister. The average age of the two girls is 12 years old. Find the age of each girl.

______________________ 20. The average number of pupils absent in a class from Monday to Friday is 3.4. Two pupils were absent on each of the three days, Tuesday, Wednesday and Thursday.3 more pupils were absent on Monday than on Friday. How many pupils were absent on Monday?

______________________ 21. The average volume of water in two water bottles is 625 ml. The volume of water in one of the water bottle is 4 times the volume of water in the other water bottle. Find the volume of water in each water bottle.

______________________

96

22. The table below shows the marks of 5 students in a science test.

Name

Marks

Nick

71

Jessica

64

Sienna

70

Natasha

80

Adam

75

a. Find the average score. ______________________ b. Which student scored nearest to the average score? _____________________ 23. The table below shows the average marks of ICAS Tests of 6 students.

Name

Marks

Emily

236

Jessica

251

Sienna

224

Natasha

327

Adam

255

Scarlet

230

a. Find the average score.

____________________

b. Which student scored furthest the average score?

____________________

97

24. The average of 2 numbers is 9. One of the numbers is changed to 8. The average of the 2 numbers now becomes 10. a. Find the number that remains unchanged.

___________________

b. Find the original number that has been changed to 8.

___________________

25. The average of 2 numbers is 25. One of the numbers is changed to 21. The average of the 2 numbers now becomes 22.5. a. Find the number that remains unchanged.

_____________________

b. Find the original number that has been changed to 21.

_____________________

26. The average mass of two boys is 50kg. A third boy joins them and now the average mass of the group becomes 60 kg. What is the mass of the third boy?

_____________________

98

27. The average mass of the group of 3 girls is 34kg. A fourth girl joins the group and now the average mass of the group becomes 32 kg. What is the mass of the fourth girl?

_________________ 28. The average of 3 consecutive numbers is 39. What is the largest number?

_________________ 29. The average of 4 consecutive even numbers is 105. What is the smallest number?

_________________ 30. The average of 7 numbers is 100. If one of the numbers is removed, the average of the remaining 6 numbers becomes 101. What is the number that is removed? _________________ 31. The average test marks of Tim, Micheal, Jim and Omar was 67.5. Jim and Michael scored the same marks. Omar scored 70 marks and Tim scored 80 marks. Find Micheal’s test marks.

__________________

99

Test Question 1 to 5 carries 1 mark. Question 6 to 10 carry 2 marks each. For each question four options are given. One of them is the correct answer.

Circle your choice (a, b, c or d). You are not allowed to use a calculator.

1. There are 40 students in a classroom. There are 16 boys. What fraction of the students are girls? a. 2/6 b. 2/5 c. 2/4 d. 3/5 2. There are two numbers. One number is 5/8 of the other number. The difference between the two numbers is 57. What is the sum of the numbers? a. 19 b. 95 c. 152 d. 247 3. Leon gave Tim 1/10 of his stickers and 2/3 of the remainder to Max. What fraction of Leon’s stickers was left? a. 3/10 b. 2/5 c. 3/5 d. 7/10 4. Which of the following is equal to 7/11? a. 1-5/11 b. 14/22 c. 21/22 d. 3/11*4 5. 0.75 is equal to _______ a. 0.75% b. 7.5% c. 70% d. 75%

100

6. The ratio of the sides of a triangle is 2 : 3 : 4. The perimeter of the triangle is 63 cm. What is the length of the longest side? a. 14 cm b. 21 cm c. 28 cm d. 49 cm 7. Find the sum of 31+32+33+34+35+36+37+38+39+40. a. 345 b. 355 c. 365 d. 375 8. 1/3 of Aden’s money is equal to 2/3 of Bryan’s money. They have $108 altogether. How much does Aden have? a. $ 24 b. $ 36 c. $ 72 d. $ 90 9. I am thinking of a 7-digit number. The digit 5 stands for 50 000. The digit 7 has greater value than the digit 5. The digit 8 in the hundreds place. The digit 6 is in the million places. There are three zeros in the number. What is the number? a. 7 758 000 b. 6 750 800 c. 6 750 080 d. 6 758 000 10. In the figure below, ABC and DBE are straight lines. Find <x if <FBE = 124o. a. 56o b. 66o c. 124o d. 146o

My Score:_______/ 15

101

102

1. The table shows the scores obtained by Jimmy in 4 subjects.

(a) How many marks did he obtain for Mathematics?

______________

(b) How many more marks did he obtain for English than for Chinese? ______________ (c) What is the average score for the 4 subjects?

______________

(d) The teacher gave him a star for a score above 80 marks. How many stars did he obtain? ______________

2. The bar graph shows the games selected by the Primary 6 students of a school as part of their co-curricular activities.

(a) How many Primary 6 students are there in the school?

______________

(b) If there are 6 Primary classes in the school, what is the average number of students per class? ______________ (c) Which is their favourite game?

______________

(d) How many more pupils selected table tennis than tennis?

______________

103

3.The table shows the number of T-shirts Elizabeth sold in a day.

(a) How many small T-shirts did she sell?

______________

(b) How many more large than small T-shirts did she sell?

______________

(c) How many T-shirts did she sell altogether?

______________

(d) What percentage of the T-shirts sold were small?

______________

4. The bar graph shows the number of ribbons made by 5 girls.

(a) Who made the least number of ribbons?

______________

(b) How many girls made more ribbons than Alicia?

______________

(c) Express the number of ribbons made by Elizabeth as a fraction of the number of ribbons made by Alicia. (d) What was the average number of ribbons made by the 5 girls?

______________ ______________

104

5. The table shows the weights of some marbles.

(a) What is the weight of marble B?

______________

(b) How much heavier is marble C than marble B?

______________

(c) What is the weight of marble D?

______________

(d) What is the average weight of marbles A, B, C and D?

______________

6. The bar graph shows the number of absentees in a school last week.

(a) How many absentees were there on Monday?

______________

(b) How many more absentees were there on Thursday than on Wednesday? __________ (c) If the total number of absentees last week was 120, draw and shade the appropriate bar in the graph to represent the number of absentees on Friday.

______________

105

7. The table shows the number of beads Alicia has.

(a) How many green beads does she have?

______________

(b) How many more blue than red beads does she have?

______________

(c) How many beads does she have altogether?

______________

(d) What percentage of her beads are yellow?

______________

8. The bar graph shows the number of children in 4 classes.

(a) Which class has the least number of boys?

______________

(b) Which class has more boys than girls?

______________

(c) How many children are there in Class 6B?

______________

(d) How many boys are there in the 4 classes altogether?

______________

106

9. The table shows the number of magazines Fred sold in a week.

(a) How many magazines did he sell on Monday?

______________

(b) On which day did he sell the greatest number of magazines? ______________

(c) On which day did he sell the least number of magazines?

______________

(d) If he earned 40 cents for each magazine sold, how much more money did he earn on Saturday than on Wednesday? ______________

107

10. The table shows the end-of-year examination scores of 5 girls.

(a) What is Fiona's English score?

______________

(b) What is Amy's Science score?

______________

(c) How many of the girls obtained a higher score in English than in Science? ______________ (d) Who scored the highest in the 2 subjects?

______________

11. Some students made a pie graph based on the population of some of the biggest

cities in the world. Measure the angles of the parts and answer the questions.

All angles are multiples of 10.

a) What fraction of the pie graph represents Tokyo?

_______

b) What is the ratio of the population of New York to that of Bangkok? _______ c) If 15 million people live in Paris, how many people live in Tokyo?

_______

108

12. The bar graph shows the number of rotten apples in 7 boxes. There are 100 apples in each box.

(a) How many rotten apples were there altogether?

______________

(b) How many boxes did not have rotten apples?

______________

(c) In which box was the greatest number of rotten apples found?

______________

(d) What fraction of the total number of apples were rotten?

______________

13. The table shows the weights of some marbles.

(a) What is the average weight of marbles A and B?

______________

(b) What is the weight of marble C?

______________

(c) What is the average weight of marbles A, B and C?

______________

109

14. The bar graph shows the weights of a beaker when empty and when different balls are placed in it.

(a) What is the weight of ball A?

______________

(b) How much heavier is ball C than ball B?

______________

(c) Which is the heaviest ball?

______________

(d) What is the average weight of balls A, B and C?

______________

110

15. The bar graph shows the weights of a beaker when empty and when different balls are placed in it.

(a) What is the weight of the empty beaker?

______________

(b) What is the weight of ball A?

______________

(c) What is the weight of ball B?

______________

111

16. The bar graph shows the weights of a beaker when empty and when different balls are placed in it.

(a) What is the weight of the empty beaker?

______________ (b) What is the weight of ball A?

______________

112

17. Four balls A, B, C and D are placed inside a container, one after another. The bar graph shows the weight of the container when empty and when different balls are placed in it. Which ball is the heaviest?

______________

113

Test Question 1 to 5 carries 1 mark. Question 6 to 10 carry 2 marks each. For each question four options are given. One of them is the correct answer.

Circle your choice (1, 2, 3 or 4). You are not allowed to use a calculator.

1. The value of the digit 4 in the number 640 738 is _______ 1. 4 * 100 2. 4 * 1000 3. 4 * 10 000 4. 4 * 100 000 2. 0.345 * 100 = _____ / 10.

1. 3.45 2. 34.5 3. 345 4. 3450 3. The mass, to the nearest kilogram, of an item is 8 kg. Which of the following is a possible mass of 10 such items?

1. 7.95 kg 2. 8.5 kg 3. 74.5 kg 4. 79.5 kg 4. The ratio of the angel fish to turtles to goldfish is 3 : 5 : 4. If there are 203 fishes, how many turtles are there?

1. 174 2. 154 3. 168 4. 145 5. Sophia had $ 85. She spent $ 51. What percentage of her money had she left?

1. 35 % 2. 40 % 3. 45 % 4. 60%

114

6. The average age of Ian, Jay and Keith is 13 years. The average of Ian and Keith is 12 years. How old is Jay? 1. 12 2. 13 3. 15 4. 18 7. The figure below shows a rectangle. Find the perimeter of the rectangle.

1. 20 cm 2. 50 cm 3. 60 cm Area = 250 cm2 4. 70 cm

25 cm 8. A dress was sold for $ 170 after a discount of 15 %. The original price was _____ discount.

1. $ 30 2. $ 144.50 3. $ 180 4. $ 200 9. The usual price of a belt was $ 96. A discount of 25 % was given at a sale.

Andrew bought the belt and paid the cashier $ 100. How much change did he receive?

1. $ 28 2. $ 25 2. $24 4. $ 4 10. 40 % of a number is 56. What is 255 of the number?

1. 28 2. 35 3. 100 4. 140 My Score:_______/ 15

115

116

The Circle’s Components Label the circle, radius, and diameter and draw a line on each circle using the clues to the right.

Review: The name of the point in the center of the circle is also the name of that circle.

A line from the point in the center of the circle to the point on the edge of the circle is called the radius.

A line from the point on the edge of the circle through the point in the center of the circle to another point on the edge of the circle is called the diameter.

117

Formulas For The Circle

118

119

1. Find the circumference of a circle of diameter 28 cm. (Take π= 22/7 )

________________ 2. Find the circumference of a circle of diameter 9 cm. (Take π = 3.14)

________________ 3. The figure shows a circle within a square. Find the circumference of the circle.

(Take π = 3.14)

________________

120

4. The figure shows a circle within a rectangle. Find the circumference of the circle.

(Take π = 22/7)

_______________ 5. A wire is bent into a figure consisting of 3 semicircles. Find the length of the wire.

(Take π = 3.14)

________________ 6. Find the circumference of the circle. (Take π= 22/7 )

________________

121

7. Find the perimeter of the semicircle. (Take π = 22/7)

________________

8. Find the perimeter of the quarter circle. (Take π= 3.14)

________________

9. The figure shows a rectangle and a semicircle. Find the perimeter of the shaded part.

(Take π =22/7 )

________________

122

10. Find the area of a circle of radius 3 cm. (Take π = 3.14)

________________ 11. Find the area of a circle of diameter 14 cm. (Take π =22/7)

________________ 12. Find the area of the semicircle. (Take π = 3.14)

________________

123

13. Find the area of the quarter circle.

________________ 14. Find the area of the circle. (Take π = 3.14)

________________

15. Find the area of the circle. (Take π=22/7 )

________________

124

16. The figure shows a square and 2 semicircles. Find the area of the shaded part.

(Take π=22/7)

________________

17. Find the area of the circle. (Take π = 3.14)

________________

125

18. The figure shows two circles. Find the area of the shaded part. (Take π = 3.14)

________________ 19. The figure shows a quarter circle in a square. Find the area of the shaded part. (Take π=22/7)

________________

126

20. The figure is made up of 2 quarter circles in a square. Find the area of the shaded part.

(Take π=22/7)

________________ 21. The figure is made up of 4 quarter circles in a square. Find the area of the shaded part.

(Take π=22/7)

________________

127

Test Question 1 to 5 carries 1 mark. Question 6 to 10 carry 2 marks each. For each question four options are given. One of them is the correct answer.

Circle your choice (1, 2, 3 or 4). You are not allowed to use a calculator.

1. Five million, seven hundred and forty thousand and nineteen in numerals is ___.

1. 5 470 019 2. 5 470 090 3. 5 740 019 4. 5 740 090 2. 13 * ------ = 91 0000 1. 7 3. 700 3. Find the value of 90 + 1. 12 3. 120

2. 70 4. 70 000 x 4.

2. 93 4. 138

4. The figure below shows a parallelogram. Find the value of x.

1. 22o X 2. 68o 3. 112o 4. 132o

68o

5. Which number gives a quotient of 27 and a remainder of 4 when it is divided by 8?

1. 116 2. 140 3. 220 4. 248

128

6. In the figure below, BAC is a right-angled triangle and BCDE is a trapezium.

Find <ABE. 1. 44o 2. 54o 3. 102o

A

4. 112o

36o

B

C

122o

E

D

7. 2/7 of the students are boys. ¼ of the boys wear spectacles. If 14 boys wear spectacles, how many students are there altogether?

1. 28 2. 42 3. 140 4. 196 8. Mr. Azman has some goats and chickens on his farm. If the animals have a total of 13 heads and 40 legs, how many chickens are there on the farm?

1. 6 2. 7 3. 8 4. 13 9. In the morning, a fishmonger sold 50 fishes at the usual price. To clear his fishes in the afternoon, he sold the rest of his 50 fishes at half the usual price.

He collected a total of $ 525. What was the usual price of a fish?

1. $ 3.50 2. $ 7.00 3. $ 7.50 4. $ 10.00 2 10. Square A has an area of 144 cm and rectangle B has an area of 108 cm2. The ratio of the length to the breath of the rectangle is 4 : 3. Find the difference in the perimeter between the square and the rectangle.

1. 10 cm 2. 8 cm 3. 6 cm 4. 4 cm My Score:_______/ 15

129

130

Speed Speed = Distance = Time

=

Distance Time Speed x Time Distance Speed

1. Mark ran 1080 m in 9 minutes. Find his average speed in m/min.

________________ 2. A van travelled 260 km in 4 hours. Find its average speed in km/h.

________________ 3. A bullet train travels 165 m in 3 seconds. Find its speed in m/s.

________________

131

4. A metal ball rolled 875 cm in 25 seconds. Find its average speed in cm/s.

________________ 5. Jennifer took 15 minutes to travel from Town A to Town B. If the distance between Town A and Town B is 20 km, find Jennifer's average speed in km/h.

________________ 6. A truck is travelling at a speed of 55 km/h. How far can it travel in 3 hours?

________________

132

7. Sarah is running at a speed of 80 m/min. How far can she run in 12 minutes?

________________ 8. Jane left Town A at 2.30 p.m. and reached Town B at 6.30 p.m. She drove at an average speed of 75 km/h. Find the distance between Town A and Town B.

________________ 9. Susan is swimming at a speed of 45 m/min. How far can she swim in 8 minutes?

________________

133

10. The speed of a bullet is 260 m/s. How far can it travel in 2 seconds?

________________ 11. A bus travelled 280 km at an average speed of 70 km/h. What was the time taken?

________________ 12. Danny ran round a 400-m track 3 times. If his average speed was 100 m/min, how long did he take?

________________

134

13. The distance between Town A and Town B is 240 km. Ken drove from Town A to Town B at an average speed of 80 km/h. If he started from Town A at 8 a.m., at what time did he reach Town B?

________________ 14. Thomas is running at a speed of 5 m/s. How long will he take to run a distance of 200 m?

________________ 15. The distance between Town A and Town B is 260 km. If a car travels from Town A to Town B at an average speed of 65 km/h, how long will it take to reach Town B?

________________

135

16. Janet took 3 hours to drive from Town A to Town B at an average speed of 60 km/h.

David took 2 hours for the same journey. Find David's average speed.

________________ 17. Peter took 5 hours to drive from Town A to Town B at an average speed of 60 km/h.

Carl drove from Town A to Town B at an average speed of 75 km/h. How long did Carl take?

________________ 18. James drove for 3 hours at 90 km/h. He then drove for another 2 hours at 80 km/h.

Find his average speed for the whole journey.

________________

136

19. Sean and James left Happy Valley for George Town at noon. Sean’s speed was 60 km/h. After travelling for 4 hours, James was 24 km behind Sean. What was James’ speed?.

________________

20. The distance between Town A and Town B is 285 km. Jeremy travelled the first 120 km at an average speed of 60 km/h. He then travelled the remaining distance at an average speed of 55 km/h. Find his average speed for the whole journey.

________________

137

21. Sarah drove from Town A to Town B at a speed of 75 km/h. She took 2 hours to complete of the journey. Find the distance between Town A and Town B.

________________ 22. Fred and Larry both left Town A for Town B at the same time. When Fred reached Town B after 4 hours, Larry had only completed half of the journey. Fred's speed was 18 km/h faster than Larry's speed. Find Fred's speed.

________________

138

23. At 1 p.m., Tim left Town A and drove towards Town B at 80 km/h. At 3 p.m., Dave left Town B and drove towards Town A at 60 km/h. If they met each other at 5 p.m., find the distance between Town A and Town B.

________________ 24. David and John both drove a distance of 240 km from Town A to Town B. They started their journey at the same time. After John reached Town B, David took one more hour to reach Town B. If John's average speed was 80 km/h, find David's average speed.

________________

139

Test Question 1 to 5 carries 1 mark. Question 6 to 10 carry 2 marks each. For each question four options are given. One of them is the correct answer.

Circle your choice (A, B, C or D). You are not allowed to use a calculator.

1. Ronald has 30 stickers. Kevin has 5 times as many stickers as Ronald and Steve has 20 more stickers than Ronald. How many more stickers does Kevin have than Steve?

A. 100 B. 120 C. 130 D. 150 2. 3 + 4 ¾ +---------- = 10 .

A. 2 B. 2 C. 7 ½ D. 9 3. The ratio of the number of people at a carnival of Australians to Spanish to Chinese is 9 : 8 : 7. There are 360 Spanish. The total number of Australians and Chinese at the carnival is ________ A. 315 B. 405 C. 640 D. 720 4. Rosita bought 5.6 kg of flour. She used 3.26 kg of it to bake some cakes and another 1 kg 40 g to bake curry puffs. How many kilograms of flour had she left?

A. 0.94 kg B. 1.3 kg C. 1.336 kg D. 2.3 kg 5. What is the value of 48-8/2+6 X 3?

A. 38 B. 2 C. 45 D. 62

140

6. The average of five numbers is 50. When a 6th number is added, the new average becomes 51. What is the 6th number?

A. 10 B. 16 C. 56 D. 74 7. In a class of 36 students, 50 % of them were girls. 4 more girls joined the class after a few weeks. What percentage of the class were girls in the end?

A. 45 % B. 50% C. 55% D. 70% 8. A container is 1/3 filled. It holds 24 l of water. What is the capacity of the container when it is full?

A. 8 l B. 16 l C. 36 l D. 72 l 9. The volume of a cuboid is 1008cm3. Its height is 28 cm. Find the base area of the cuboid.

A. 72 cm2 B. 36 cm2 C. 34 cm2 D. 32 cm2 10. Doris bought a packet of 120 sweets. She gave 1/5 of it to her brother and shared the rest with her three friends. How many sweets did each friend get?

A. B. C. D.

24 32 72 96 My Score:_______/ 15

141

Week

1

2

3

4

5

Homework Complete

“I’m Late”

Mathematics Page number(s) ___________________ ___________________

Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Mathematics Page number(s) ___________________ ___________________

Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Mathematics Page number(s) ___________________ ___________________

Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Mathematics Page number(s) ___________________ ___________________

Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Mathematics Page number(s) ___________________ ___________________

Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Parent(s) / Guardian(s) Signature:

142

week

Homework Complete

“I’m Late”

Mathematics

Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________

Page number(s) 6

___________________ ___________________

Mathematics Page number(s) 7

___________________ ___________________

Mathematics Page number(s) 8

___________________ ___________________

Mathematics 9

Page number(s) ___________________ ___________________

Mathematics 10

Page number(s) ___________________ ___________________

Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ Time In:__ +________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ Time In:__________ Reason For Being Late ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Parent(s) / Guardian(s) Signature: