Name:________________
Form class:___________
Set:1
Multiplication and Division: Level 5
1
34 x 78
6
6532 x 24
2
29 x 75
7
276 ÷ 12
3
76 x 76
8
420 ÷ 12
4
405 x 17
9
416 ÷ 13
5
324 x 14
10 456 ÷ 19
Overall, for this homework I think my success level is: I need to practice………
Low
O
High
O
O
O
BODMAS: Level 5
1
7 + 24 ÷ 6
8
36 ÷ (6 ÷ 2)2
15
3 + 2 x 4 + 1 = 21
2
(24 – 9) ÷ 3
9
2 + (4 + 3)2
16
3 + 2 x 4 + 1 = 25
3
4 + 32
10
7 + 5 x (2 + 5)2
17
3 + 2 2 x 3 – 1 = 50
4
(3 + 2)2
11
92 + 42 + (4 ÷ 2)2
18
40 ÷ 3 + 2 x 4 = 2
5
2
( [3 + 1] x 2) - 5
2
Complete the boxes: 19 x( ) = 12 Using 2, 3, 4, 6, 10
6 + 12 ÷ 4 – 2
12
6
5 x ( 2 + 3) – 4
Insert brackets if needed: 13 6 + 20 ÷ 5 = 10 20
7
(3 + 9) ÷ ( 2 + 1)
14
7+2x3+1
Overall, for this homework I think my success level is: I need to practice………
21
x( + ) = 100 Using 2, 3, 4, 6, 10
÷( )=5 Using 2, 3, 4, 6, 10
Low
O
O
O
High
O
Substitution: Level 6
1)
2)
3)
If a)
a = 5 b = 2 c = 3 d = 7. Find: 7a + 3b b)
ab – 3c
c)
5a ( bc + 2d )
2a2
If a)
a = 3 b = 4 c = 7 d = 6. Find: 3b – 2a b)
bc + 3ad
c)
7a (2b + 3c - 2d)
5a2b
If
s = ut + ½ at2
a)
u = 2 , a = 10 , t = 2
b)
u = 7 , a = 10 , t = 5
c)
a=3,u=6,t=2
d)
t=5,u=5,a=1
d)
d)
find s when:
Overall, for this homework I think my success level is: I need to practice………
Low
O
O
O
High
O
Brackets: Level 6
1)
2)
Expand a) 3(x + 2)
b) 2(x + 5)
c) 5(x + 3)
d) 7(x + 4)
e) 2(x – 2)
f) 5(x – 3)
g) 3(x – 4)
h) 4(x – 1)
i)
2(3x + 2)
j) 5(2x + 3)
k) 4(5x + 1)
l) 2(7x + 5)
m) 3(2x – 3)
n) 7(2x – 5)
o) 2(5x – 4)
p) 8(3x – 5)
q) 3(1 + 3x)
r) 2(5 – 3x)
Expand and Simplify a) 3(x + 2) + 2(x + 5)
b) 5(x + 3) + 7(x + 4)
c) 2(x – 2) + 5(x – 3)
d) 3(x – 4) + 4(x – 1)
e) 2(3x + 2) + 5(2x + 3)
f) 4(5x + 1) + 2(7x + 5)
g) 3(2x – 3) + 7(2x – 5)
h) 3(1 + 3x) + 2(5 – 3x)
Overall, for this homework I think my success level is: I need to practice………
Low
O
O
O
High
O
Number Patterns: Level 6
1. Put the next 3 numbers in each of these patterns, state the nth and find the 50 th term: a) 2, 6, 10, 14, …
g) 0, 3, 6, 9, 12, …
b) 30, 20, 10, 0, …
h) 1, -1, -3, -5, …
c) 1, 21, 41, 61, …
i) 100, 91, 82, 73,...
d) 5, 8, 11, 14, …
j) 10, 7, 4, 1, -2, …
e) 9, 14, 19, 24, …
k) 9, 7, 5, 3, …
f) 3, 10, 17, 24, …
l) 18, 14, 10, 6, …
2. Put the next 3 numbers in each of these patterns, state the nth term: a) 1, 4, 9, 16 b) 2, 8,18, 32 c) 3, 6, 11, 18
Overall, for this homework I think my success level is: I need to practice………
Low
O
O
O
High
O
Angles: Level 6
1.
Work out the size of each missing angle in the diagrams below. (a)
Not drawn accurately
50°
p
30°
Answer p = ………………………………………degrees (b)
Not drawn accurately
120° 100° q
Answer q = ………………………………………degrees (c)
Not drawn accurately r
36° ..................................................................................................................................... ..................................................................................................................................... Answer r = ………………………………………degrees (d)
Not drawn accurately s 72°
Answer s = ………………………………………degrees 2.
(a)
Triangle PQR is isosceles.
PQ = PR
Angle R = 44°
P N o t d ra w n a c c u ra te ly
Q
44°
R
Calculate the size of angle P. ..................................................................................................................................... Answer ............................................................. degrees .
(b)
The words in this list are used to describe angles. alternate corresponding exterior
interior opposite
c e N o t d ra w n a c c u ra te ly d
Choose a word from the list to describe each of these pairs of angles.
3.
(i)
c and d are ............................................................................. angles
(ii)
d and e are ............................................................................. angles
In the diagram, AB is parallel to CD. C
A x
112º
N o t d ra w n a c c u ra te ly
130º y
B
(a)
D
State the value of x. Give a reason for your answer. Answer ..................................................................... degrees Reason ..........................................................................................................................
(b)
Find the value of y. Give a reason for your answer ................................................................................................................................................ Answer .......................................................... degrees Reason………………………………………………………………………………………
Overall, for this homework I think my success level is: I need to practice………
Low
O
O
O
High
O
Probability: Level 6 1)
5 red, 3 blue and 2 yellow discs were placed in a bag. Find the probability of picking a) a red disc
________________________________
b) a blue disc
________________________________
c) a black disc
________________________________
d) not a yellow disc
________________________________
2)
The probability of a train being on time is 0.4 what is the probability of the train being late. _________________________________________________________
3)
The probability that England win a cricket match against Australia is 0.1 and of a draw is 0.2. What is the probability of Australia winning the match? _________________________________________________________
4)
A box of biscuits contains ginger, chocolate and plain biscuits. Is the probability of picking a ginger biscuit at random 1/3? Explain your answer. ___________________________________________________________ _________________________________________________________
5)
A pack of 9 cards numbered from 1 to 9 inclusive are laid face down on the table. If you choose a card at random find the probability of choosing a) an even number
___________________________________
b) an odd number
___________________________________
c) a prime number
___________________________________
d) a square number
___________________________________
e) a triangular number
___________________________________
f)
(i)
the same number on each dice
_____________
(ii)
an even score
_____________
(iii)
a score which is a multiple of 3
_____________
(iv)
a score above 12
_____________
Which is the most likely score to throw? _____________
6)
The table below gives the membership of a golf club Male 70 240
Child Adult
Female 30 160
a) There was Christmas draw for child members where each child’s name was placed in a hat and one was drawn out. What was the probability the first drawn was female? _____________________________________________________ b) A similar draw was done with the adults. What was the probability the first adult drawn was female? _____________________________________________________ c) When everyone was in the hat for the summer draw. What was the probability the first drawn was female? _____________________________________________________ 7)
A red and blue dice are thrown. a) Complete the sample space diagram below to illustrate all the possible total scores. 1 2 3 4 5 6
1 2
2 3
3
4
5
6
b) What is the probability of throwing (i)
the same number on each dice
_____________
(ii)
an even score
_____________
(iii)
a score which is a multiple of 3
_____________
(iv)
a score above 12
_____________
c) Which is the most likely score to throw?
_____________
Overall, for this homework I think my success level is: I need to practice………
Low
O
O
O
High
O
Exam style questions Multiplication and Division Q1.
Two whole numbers multiply together to give an answer of 1000. Neither of the numbers contains the digit zero. What are the two numbers? .................................................................................................................................. ..................................................................................................................................
Q2.
Susan is choosing pairs of numbers from this list. 6 (a)
23
24
51
108
She multiplies two numbers together. Which two numbers should she choose to get an answer between 200 and 300? .........................................................................................................................
(b)
She divides one number by another number. What is the largest possible answer? .........................................................................................................................
Substitution Q1.
(a)
Find the value of 3x + 4y when x = 6 and y = –3 ..........................................................................................................................
(b)
Sam buys x packets of sweets. Each packet of sweets costs 22 pence. Sam pays with a £5 note. Write down an expression for the change, in pence, Sam should receive. ..........................................................................................................................
Q2.
(a)
Find the value of 3x + 5y when x = –2 and y = 4 .........................................................................................................................
(b)
Find the value of 3a2 + 5 when a = 4 .........................................................................................................................
(c)
k is an even number. Jo says that 1/2k + 1 is always even. Give an example to show that Jo is wrong. .........................................................................................................................
(d)
The letters a and b represent prime numbers. Give an example to show that a + b is not always an even number. .........................................................................................................................
Brackets Q1.
(a)
Expand and simplify
4(2x – 1) + 3(x + 6)
......................................................................................................................... ......................................................................................................................... (b)
Expand
x2(4 – 2x)
......................................................................................................................... ......................................................................................................................... Q2.
(a)
Simplify 2x + 8 + 4x – 3 .........................................................................................................................
(b)
Solve the equation.
......................................................................................................................... (c)
Tom is investigating the two expressions ab + c and a(b + c) (i)
He finds that both expressions have the same value when a = 1, b = 3 and c = 4. Show that this is true. ................................................................................................................ ................................................................................................................
(ii)
Tom says that this means that a(b + c) = ab + c. Explain why Tom is wrong. ................................................................................................................ ................................................................................................................
Number Patterns Q1.
The nth term of a sequence is given by the expression n2– 3 Write down the first three terms of the sequence. ..................................................................................................................................
Q2.
(a)
A sequence starts 2,
7,
17,
......
The rule for finding the next term in this sequence is to multiply the previous term by 2 and then add on 3 Work out the next term. ......................................................................................................................... (b)
The rule for finding the next term in a different sequence is to multiply the previous term by 2 and then add on a, where a is an integer. The first term is 8 and the fourth term is 127 8
......
......
127
Work out the value of a. ......................................................................................................................... .........................................................................................................................
Angles Q1.
AC and DG are parallel lines. Angle ABE = 40째 Angle BFG = 110째
Not drawn accurately (a)
Explain why angle BEF is 40째 ........................................................................................................................
(b)
Show, giving reasons, that triangle BEF is isosceles. ........................................................................................................................ ........................................................................................................................
Q2.
Write down the values of a and b.
Answer a = ...................... degrees, b = ..................... degrees (Total 2 marks) Q3.
ABCD is a rhombus and ABCE is a kite.
Work out the value of x. ..................................................................................................................................
Probability Q1. Forty people take a driving test at Centre A on one day. The table shows the results. Pass
Fail
Male
10
13
Female
6
11
(a )A person is chosen at random from the group. What is the probability that the person is male? .........................................................................................................................
(b) A person is chosen at random from the group. What is the probability that the person passed the test? ......................................................................................................................... (c) It is known that throughout Britain the probability of a person passing their test is 0.7. John says it is easier to pass the test at Centre A. Explain why John could be wrong. ......................................................................................................................... ......................................................................................................................... Q2. Twenty pupils each shuffle a pack of coloured cards and choose a card at random. The colour of the card is recorded for each pupil. B G Y B
Y R R B
Y Y B G
G B B R
R B Y Y
(a) Use these results to calculate the relative frequency of each colour.
Colour
Red
Blue
Green
Yellow
Relative frequency
(b) Use the results to calculate how many times you would expect a blue card if 100 pupils each choose a card at random. ..........................................................................................................................