Year 7 Summer Workbook - Maths

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MATHEMATICS YOU R S UM MER BO O KL ET Dear Year Seven We know you will have missed being with your friends and teachers over the last few weeks and that you have worked really hard with home learning tasks. We want you to enjoy this summer holiday but we also want to make sure you do not forget all the amazing maths you have learnt. This booklet is just something to keep your brain active over the summer and we hope you enjoy trying some of the questions.

There is a page for each week of the holiday and we know your new teachers would love to see your answers in September.

Enjoy Maths Team at Delta

Mathematics

Mathematics

WEEK 1

WEEK 1 SKILLS QUESTIONS 1. Work out the total of 300 + 15 + 5

INFORMATION FOR TOPIC: ADDING AND SUBTRACTING FRACTIONS 2. 6 × 10 =

3. What are the next three terms in the following sequence?

3, 7, 11, 15…

4. What is the third square number?

You can only add/subtract fractions if they have the SAME DENOMINATOR.

Example 1 Work out

To add or subtract fractions without a calculator, there are two steps: 1. Use EQUIVALENT fractions to make the DENOMINATOR of all the fractions the same.

2. Add or subtract (depending on which the question requires) the NUMERATORS

5. Simplify

12

6. 4 km = ____ m

15

7. What are the first five multiples of 3?

1

be as 8. What would 5 a decimal?

2 5

+

3

1. The lowest common denominator is 10

x2 2

2. Add the numerators together.

4

x2 5

10

Example 2 Work out

10

+

+ 3 10

3 10 7

=

10

2 3

1

-

7

1. The lowest common denominator is 21

x7 2

2. Now subtract the numerators.

14

-

x7 3

21

-

3 21

1 x3 7 x3 =

11 21

QUESTIONS FOR TOPIC: ADDING AND SUBTRACTING FRACTIONS 1. Work out the following:

a)

3 6

+

2

2

4

5

3

9

9

7

14

b) + c) +

6

4

1

1

2

3

1

8

32

2

3

5

6

d) + e) + f) +

9. What is

1 3

of 21?

10. What is the sum of the angles on a straight line?

11. Express 2

1 5

as an

12.

2 5

+

1 5

=

improper fraction

2. Work out the following:

a)

3 8

-

2

7

3

4

3

10

10

5

25

b) c)

8

25

8

1

1

3

1

30

15

2

9

11

8

d) e) f)

13.

2 7

×

1 4

=

14. Solve x + 7 = 15

15. Find the nth term of 12, 14, 16, 18…

16. What is the formula for the area of a rectangle?

2

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19. Find the mode of 5, 3, 5, 4, 3, 4, 5, 5, 2

MATHS CHALLENGE

Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9)

The folding challenge:

An example that doesn’t work: 18. Fill in the blank using < = or > 0.789 __ 0.8

MATHS PUZZLE

into a single fraction that equals exactly

17. Work out 25 × 7

7192 38456

1 3

(one third)?

= 0.187

See if you can complete the folding challenge with Matt Parker – you just need a piece of paper.

20. 2 days = ______ hours

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Mathematics

Mathematics

WEEK 2

WEEK 2 SKILLS QUESTIONS

INFORMATION FOR TOPIC: AREA Finding the area of a rectangle, triangle, parallelogram and trapezium.

3. What are the next three terms in the following sequence?

17, 14, 11, 8…

4. What is the second cube number?

Example 1 Calculate the area of

6cm

Area =6×5 = 30 cm²

Example 2 Calculate the area of

Area of a triangle =

Area of a rectangle = base × height

Area =

8mm Example 3 Calculate the area of

6. 5m = ____ cm

25

7. What are the factors of 24?

3

8. What would be as 5 a decimal?

× base × height

1

× 8 × 6 = 24 mm²

2

Area of a trapezium = a

5cm

800cm Area of a parallelogram Area = 8 × 4 = base × height (perpendicular height) = 32 m²

10cm

Area =

1 2

× (5 + 10) × 3

1 2

or

h

Remember the order of operation

3cm

15

2

Example 4 Calculate the area of

Note: There are two different units used here so one will need converting 800cm = 8m

4m

5. Simplify

1

(perpendicular height)

6mm

2. 5.4 × 10 =

5cm

1. Work out the sum of 330 + 17 + 6

a

× (a + b) × h h

b

b

(a and b are the parallel lines) = 22.5 cm²

QUESTIONS FOR TOPIC: AREA 1. Work out the area of the following:

10. What is the sum of angles around a point?

11. Express 3

3 4

as an

12.

1 5

+

2 3

=

improper fraction

7cm

9mm

6m

13.

6

×

3 7

=

17. Work out 30 × 42

4

14. Solve x - 8 = 15

18. Fill in the blank using < = or > 0.868 __ 0.9

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15. Find the n term of 7, 10, 13, 16… th

19. Find the median of 5, 3, 5, 4, 3, 4, 5, 5, 2

16. What is the formula for the area of a parallelogram?

h) 7cm

11cm 8cm

5cm

5

12cm

g) 6cm

2.5cm

f) 7cm

e)

8cm 5cm

of 60?

d)

0.95m

5

c) 5m

2

3cm

9. What is

b) 4mm

a)

15cm

40mm

MATHS PUZZLE

MATHS FACTS

Can you draw this shape without taking your pencil off the paper and without going over any line more than once?

This puzzle comes from a very famous maths problem – The seven bridges of Königsberg.

20. 72 hours = _____ days

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Mathematics

Mathematics

WEEK 3

WEEK 3 SKILLS QUESTIONS 1. Calculate 100 + 7 + 0.6

5. Simplify

21

INFORMATION FOR TOPIC: PROPERTIES OF ANGLES 2. 18.02 × 10 =

6. 102mm = ____ cm

28

3. What are the next three terms in the following sequence?

10, 12.5, 15, 17.5…

7. What is the lowest common multiple of 12 and 18?

4. What is the fifth prime number?

Example 1

Example 2

Example 3

Angles on a straight line add to make 180°

Angles around the point add to make 360°

Vertically opposite angles are equal

-150°

150°

8. Express 0.8 as a fraction

3 7

of 42?

10. What is the sum of the interior angles of a triangle?

11. Express 4

1 5

as an

x = 30°

x°

2 5

+

3 8

150°

177°

-327°

b)

c)

53°

x°

32°

e)

d)

84°

x°

x°

144°

÷

1 10

=

17. Work out 157 × 60

14. Solve 20 - x = 4

18. Fill in the blank using < = or > 0.77 __ 0.709

15. Find the nth term of 6, 10, 14, 18…

19. Find the median of 7, 8, 12, 13, 15, 4, 4, 12

16. What is the formula for the area of a triangle?

70°

x°

20. 2 hours = ____ minutes

6 9

7

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9

5

8

4

1

6 3

x°

30°

3

How to measure very tall things you can’t reach to the top of!

3

5

1

2

4

4 7

4

8

5

2

YOU R S U MMER BO O KL ET

x°

116°

MATHS CHALLENGE

5

1 4

6

x°

MATHS PUZZLE This is a Sudoku puzzle. Each 3 × 3 square, row and column has to contain the numbers 1-9. Can you fill in the missing numbers?

240°

x° h)

5

x°

g)

139°

4

x = 95°

because they are vertically opposite angles and equal

f)

improper fraction

59°

13.

-327°

x°

x = 33°

=

95°

Work out the missing angles: a)

12.

150° + 177° + x = 360° 327° + x = 360°

-150°

QUESTIONS FOR TOPIC: PROPERTIES OF ANGLES

x° 9. What is

x°

150° + x = 180°

1 4 6

6 8 9

7 4

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Mathematics

WEEK 4

WEEK 4 SKILLS QUESTIONS 1. Work out the sum of 650 + 30 + 9 + 0.8 + 0.02

INFORMATION FOR TOPIC: AVERAGES 2. 80 ÷ 10 =

3. Find the missing numbers in this sequence.

6, 9, __, 15, __

4. What is the seventh square number?

MODE

MEAN

MEDIAN

4, 5, 4, 7, 2, 5, 4

5, 7, 4, 10, 9

Example 2 (even pieces of data)

There are more 4’s in this data list than any other number.

5 + 7 + 4 + 10 + 9 = 35

Example 1 (odd piece of data) 3, 6, 5, 3, 1

5, 6, 6, 9, 9, 10

35 ÷ 5 = 7 To work out the mean we: 1. Add up all the pieces of data.

2. Divide by how many pieces of data. In this case there are 5 pieces of data

The MODE is the value that occurs the most often

MODE = 4 5. Simplify

9. What is

13.

4 9

÷

2 3

45

6. 670 cm = ____ m

50

4 15

of 90?

=

10. What is the sum of the interior angles of a quadrilateral?

14. Solve 8x = 56

7. What is the lowest common multiple of 20 and 35?

11. Express

11 5

as a

8. What would 0.3 be as a fraction?

When there are an even number of pieces of data in the list we have to find the average (mean) of the middle two numbers. In this case between 6 and 9

MEDIAN = 3 The MEDIAN is the value in the middle when the data list is in order

MEAN = 7

MEDIAN

6+9 2

=

15 2

= 7.5

QUESTIONS FOR TOPIC: AVERAGES

12.

2 3

+

7 10

=

mixed number

15. Find the nth term of -3, 1, 5, 9…

Write the numbers in order of size number.

1, 3, 3, 5, 6

16. What is the formula for the area of a trapezium?

1. Find the mode of the following

a) 13, 17, 15, 11, 13

b) -4, -6, 6, -4, 3

c) 0.6, 0.5, 0.4, 0.3, 0.5

2. Find the median of the following

a) 7, 17, 21, 25, 15

b) 7, -9, 0, -6, 10

c) 0.7, 0.1, 0.8, 1.1, 0.5, 0.2

3. Find the mean of the following

a) 4, 9, 2, 9, 6

b) 6, 13, 18, 3, 35

c) 0.1, 0.4, 1.3, 1.3, 1.5, 0.9

MATHS PUZZLE

MATHS CHALLENGE

Four English football teams compete against each other to see who is the best – Manchester City, Liverpool, Derby County and Chelsea. After every team has played every other team in a mini league competition, they finish as follows.

Can you solve the prisoner hats riddle?

• Chelsea finished above Manchester City.

17. Work out 162 × 127

8

18. Fill in the blank using < = or > 0.139 __ 0.2

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19. Find the mean of 10, 8, 9, 8, 5

20. A fair ten sided dice is rolled. What is the probability of getting a number greater than 4?

• Liverpool were not third.

• There were two teams between Manchester City and Derby County List the order the teams finished in.

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Mathematics

Mathematics

WEEK 5

WEEK 5 SKILLS QUESTIONS 1. Work out the value of 48 + 8 + 7.2

INFORMATION FOR TOPIC: SEQUENCES 2. 8 ÷ 10 =

3. What are the missing terms in the following sequence?

4, 11, __, 25, __

4. What is the fourth cube number?

Sequences are arithmetic when they increase or decrease by the same amount each time.

Example : Find the nth term of an arithmetic sequence 3 , 8 , 13 , 18 , 23 Step 1: Find the common difference between the values 3 , 8 , 13 , 18 , 23

5. Simplify

18

6. 4 kg = ____ g

30

7. What is the highest common factor of 24 and 32?

8. What would 0.4 be as a fraction in its simplest form?

+5

+5

+5

+5

As the common difference is +5 this means the nth term begins with 5n Step 2: Write out your 5 times table and find out how far has the sequence been ‘shifted’ from it.

5 times table: 5 10 15 20 25

3 , 8 , 13 , 18 , 23

-2

We have subtracted 2 to ‘shift’ from the 5 times table to our sequence Our nth term is therefore

5n - 2

QUESTIONS FOR TOPIC: SEQUENCES Find the nth term of the following sequences.

9. What is

13.

8 11

×

3 7

7 12

of 490?

=

10. What is the sum of the exterior angles of any polygon?

14. Solve

x 3

=9

11. Express

20 3

as a

12.

7 11

+

8 9

b) 5, 8, 11, 14,

c) 32, 35, 38, 41,

d) -1, 1, 3, 5,

e) 6, 2, -2, -6,

f) -1, -6, -11, 16,

g) 2.5, 5, 7.5, 10,

h) 1.5, 2, 2.5, 3,

i) 6, 3.5, 1, -1.5,

=

mixed number

15. Find the nth term of -5, -2, 1, 4…

a) 1, 6, 11, 16,

16. What is the formula for the area of a circle?

MATHS PUZZLE

MATHS FACTS

A rat was crawling up a ship’s rope which was 30 feet long. It climbed up 3 feet a minute but then slipped back 2 feet with exhaustion!

Watch a maths version of Alice in Wonderland – Alice in Fractalland

How long did it take to reach the ship?

17. Work out 15 × 1.2

10

18. Fill in the blank using < = or > 0.6 __ 0.52

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19. Find the mean of 7, 10, 8, 8, 14, 13

20. 180 minutes = ________ hours

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Mathematics

Mathematics

WEEK 6

WEEK 6 SKILLS QUESTIONS 1. Work out the total of 352 + 56 + 9.6 + 3.08

INFORMATION FOR TOPIC: FRACTIONS OF AMOUNTS 2. 8.72 ÷ 10 =

3. What are the missing terms in the following sequence?

40, 36, __ , 28, __

4. What is the tenth prime number?

Example 1 Work out

1 3

Example 2 Work out

of 18

This bar represent 24.

We want to split it into eighths.

36

6. 5640 g = _____ kg

50

7. What is the highest common factor of 27 and 63?

8. Express 0.125 as a fraction.

1 3

So

9

of £810?

10. Vertically opposite angles are _________

11. Express

8

as a

12.

7 12

-

3 8

=

6 7

=

14. Solve 2x + 3 = 15

15. Find the nth term of 21, 14, 7, 0…

16. What is the formula for the circumference of a circle?

1 2

of 280 or

5

3 8

7

1 4

8

of this money on rent. Sarah spends

20. 1.5 hours = ________ minutes

2 5

of the money on food and bills.

of 400?

MATHS FACTS

MATHS PUZZLE

Do you want to be able to multiply any number by 11 in your head?

The Monty Hall Problem.

1. Write the first digit

19. Find the mean of 14, 20, 16, 15, 20

g) of 2 weeks h) of 14kg

To multiply a two digit number e.g.

18. Fill in the blank using < = or > 0.672 __ 0.7

9

You should be able to do any single digit number by learning your times tables

17. Work out 3.6 × 4.5

4

5

4

mixed number

3. Which is larger

×

2

8

How much money has she got left?

4

of 24 = 15

1 2 of 18 b) of 16 c) of 21 3 8 3

2. Sarah earns £800 a month. She spends

3

8

d) of 24 e) of 35 days f) of 72kg

13. 1

5

1

5

9. What is

5 lots of 3 = 15

QUESTIONS FOR TOPIC: FRACTIONS OF AMOUNTS

17

We want 5 of these eighths.

of 18 = 6

1. Find the fractions of amounts a)

5

So there are 3 in each part.

3 3 3 3 3 3 3 3

We want one of these thirds.

So

5. Simplify

24 ÷ 8 = 3

3 3 3 3 3 3 3 3

So there are 6 in each part.

6

of 24

We want to split it into thirds.

18 ÷ 3 = 6 6

8

Here is a bar that represents 18.

So we split 18 equally into 3.

6

5

18 × 11 1

To multiply a three digit number e.g.

124 × 11 1. Write the first digit

1

2. Add the two digits together and write it next 1+8=9

2. Add the next two digits together

1+2=3

3. Write the second digit

3. Move across and add the next two digits together

2+4=6

The answer would be If we did 1. Write the first digit

8 198 48 × 11 4

4. Write the last digit

4

The answer would be

1364

This is a really popular maths problem – all about a game show.

2. Add the two digits together and write it next 4 + 8 = 12 3. Write the second digit The answer would be 5 (4 + 1 from the 12) 28 =

12

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Mathematics

Mathematics

ANSWERS WEEK 1

ANSWERS

WEEK 2

WEEK 3

WEEK 4

WEEK 5

Week 1 5 1) a)

WEEK 6

1

320

353

107.6

689.82

63.2

420.68

2

60

54

180.2

8

0.8

0.872

f)

6 23

19, 23, 27

5, 2, -1

20, 22.5, 25

12 and18

18 and 32

32 and 24

4

9

8

11

49

64

29

4

3

3

9

3

18

5

5

4

10

5

25

6

4000

500

10.2

6.7

4000

5.64

7

3, 6, 9, 12, 15

1, 2, 3, 4, 6, 8, 12, 24

36

70

8

9

8

0.2

0.6

4

3

2

125

5

10

5

1000

9

7

24

18

24

210

£450

10

180°

360°

180°

360°

360°

Equal

11

15

21

1

2

1

5

4

5

3

13

31

41

151

5

5

15

40

30

99

24

5

11 12 13

28

=

1

15

14

42

10

5

= 14

=

2

12

8

18

6

5

=

2

56

3

132

=

14

42

33

28

=

= x=6

15

2n + 10

3n + 4

4n + 2

4n - 7

3n - 8

-7n + 28

16

Base × height

Base × perpendicular height

Base × height

1

2

2

17

175

1260

9420

20574

18

16.2

18

<

<

>

<

>

<

19

5

4

10

8

10

17

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6 10

3

32

e)

7 6

1

= 1 6

10

5

17

c) 25

d)

9 30

3

7

10

18

= e)

88

2 r or

90

b) 18mm²

c) 30m² d) 50cm² e) 17.5cm² f) 20cm²

8

a)127°

b) 58°

g) 70°

h) 86°

c) 48°

d) 120° e) 162° f) 108°

1) a) 13 b) -4

c) 0.5

2) a) 17 b) 0

c) 0.6

3) a) 6 b) 15

c) 0.95

2

x = 27

120

14

2

Week 3

3

x=7

3

3

=

1

8

x = 16

48

17

Week 4

x = 23

r2

4

13

g) 97.5cm² h) 380cm² or 0.038m² or 38000mm²

x=8

× (a + b) × h

8 13

1) a) 21cm²

2

3

f)

b)

9

2

= c) d)

Week 2

14

20

14

2

8

2) a)

6

30 1

3

b)

Week 5 a) 5n – 4

b) 3n + 2 c) 3n + 29 d) 2n – 3 e) -4n + 10

f) -5n + 4 g) 2.5n h) 0.5n + 1 i) -2.5n + 8.5 d

Week 6 1) a) 6 b) 2 f) 32kg

c) 14

d) 15

e) 14 days

g) 8 days h) 8.75kg

2) £280 3)

3 8

of 400

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