Note:
For Q19-Q24, use Q1-Q6 from higher paper
Q1
Write 8931 correct to the nearest thousand.
Answer type: simple
Answer: 9000
Workings:
The number after the thousands column is 9, which is greater than 5 so the number rounds up to 9000
1 mark
Q2
2(a)
Write the following numbers in order of size.
Start with the largest number.
12 \quad -8 \quad 6 \quad 4 \quad -7
Answer type: multiple answers:
Answers:
Largest = 12
2nd Largest = 6
3rd largest = 4
4th largest = -7
Smallest = -8
1 mark
2(b)
Write the following numbers in order of size.
Start with the largest number.
1.23 \quad 1.203 \quad 1.023 \quad 1.32
Answer type: multiple answers:
Answers:
Largest = 1.32
2nd largest = 1.23
3rd largest = 1.203
Smallest = 1.023
1 mark
Q3
Write 75\% as a fraction in its simplest form.
Answer type: fraction
Answer: 3 / 4
Workings:
75\% = \dfrac{75}{100}=\dfrac{3}{4}1 mark
Q4
Here is a list of four fractions.
\dfrac{40}{100} \quad \dfrac{24}{54} \quad \dfrac{16}{40} \quad \dfrac{30}{75}
One of these fractions is not equivalent ot \dfrac{2}{5}
Give the value of this fraction.
Answer type: fraction
Answer: 24 / 54
Workings:
\dfrac{24}{54} = \dfrac{12}{27}=\dfrac{4}{9} which is not equal to \dfrac{2}{5}
1 mark
Q5
Write down the first even multiple of 15
Answer type: simple
Answer: 30
Workings:
1\times15=15
2\times15=30
30 is an even number as it is also a multiple of 2
1 mark
Q6
6(a)
Simplify 5\times7x
Answer type: multiple choice
Answer: 35 x
Wrong answers:
35 + x
5x\times7x
7(5+x)
Workings:
5\times7x=35x
1 mark
6(b)
Simplify 6m+13m-8m
Answer type: multiple choice
Answer: 11m
Wrong answers:
9m
10(m+1)
m(6+13-8)
Workings:
Collecting like terms,
6m+13m-8m = 19m-8m=11m
1 mark
Q7
Here is a probability scale.
It shows the probability of each of the events \text{A, B, C} and \text{D}
7(a)
Which letter represents an event which is impossible?
Answer type: multiple choice
Answer: \text{M}
Wrong answers:
\text{N}
\text{O}
\text{P}
Workings:
An impossible outcome has a probability of zero
1 mark
7(b)
Which letter represents an event which is likely?
Answer type: multiple choice
Answer: \text{O}
Wrong answers:
\text{M}
\text{N}
\text{P}
Workings:
An event which is likely to occur has a probability greater than \dfrac{1}{2} but less than 1
1 mark
7(c)
There are 16 sweets in a bag
5 of the sweets are lemon flavoured.
4 of the sweets are apple flavoured.
3 of the sweets are strawberry flavoured.
The rest of the sweets are banana flavoured.
Maria takes at random a sweet from the bag.
Calculate the probability that the sweet is either apple or banana flavoured.
Give your answer as a fraction in its simplest form.
Answer type: fraction
Answer: 1/2
Workings:
There are 16 sweets in the bag
The number of banana flavoured sweets is 16-5-4-3=4
The number of sweets which are either apple or banana flavoured is 4+4=8
The probability that the sweet is either apple or banana flavoured is therefore \dfrac{8}{16}=\dfrac{1}{2}
3 marks
Q8
600 g of herbs costs £7.20
Cecilia buys 150 g of herbs.
Work out how much Cecilia pays.
Answer type: simple
Answer: £1.80
Workings:
150\div 600 = 0.25 0.25\times £7.20=£1.802 marks
Q9
The centre of this circle is marked with a cross (\times).
9(a)
What is the mathematical name of the straight line shown in the circle?
Answer type: multiple choice
Answer: diameter
Wrong answers:
radius
tangent
segment
1 mark
9(b)
What is the mathematical name of the shaded area in the circle.
Answer type: multiple choice
Answer: sector
Wrong answers:
chord
segment
radius
1 mark
Q10
Terry and four of his colleagues are putting on a launch party for a new business.
The 5 colleagues will share the costs of the launch party equally.
Here are the costs for the launch party.
£1250 for the venue hire
£300 for catering
£105 for advertisements
Work out how much Terry has to pay for his share of the costs.
Answer type: simple
Answer: £ 331
Workings:
1250+300+105=1655
1655 \div 5 = 331
3 marks
Q11
Which of the following statements is not correct?
11(a)
Answer: All multiples of odd numbers are odd numbers
Wrong answers:
All multiples of even numbers are even numbers
All factors of odd numbers are odd numbers
Factors of even numbers can be odd or even
1 mark
11(b)
Answer: Any number with a 7 digit is odd
Wrong answers:
Any number ending in 1 is odd
Any number ending in 8 is even
Any number ending in 0 is even
1 mark
Q12
A dealership sells diesel, petrol and electric cars.
The composite bar chart shows information about sales over the last three years.
12(a)
How many diesel cars were sold in 2018?
Answer type: simple
Answer: 240
1 mark
12(b)
Work out the number of petrol cars sold over the three years.
Answer type: simple
Answer: 840
Workings:
In 2018, there were 200 petrol cars sold
In 2019, there were 300 petrol cars sold
In 2020 there were 340 petrol cars sold
The total over the three years is 200+300+340=840
3 marks
12(c)
Which type of car had the greatest increase in sales over the three years?
Answer type: multiple choice
Answer: Electric
Wrong Answers:
Diesel
Petrol
2 marks
12(d)
Arjun says,
“In 2020, the petrol cars had the most sales. This means the dealership makes the most profit from petrol cars.”
Is Arjun correct?
Answer type: multiple choice
Answer: It is not possible to say
Wrong Answers:
Yes
No
Workings:
The petrol cars had the most sales, but this does not necessarily mean they were the most profitable as the costs, prices or profits from each car are unknown.
1 mark
Q13
A wooden log is 450 cm long.
Tyrell cuts 70 cm off the end of the log.
He then cuts the rest of the log into as many 30 cm lengths as possible.
Work out how many 30 cm lengths of the log Tyrell can cut.
Answer type: simple
Answer: 12
Workings:
450-70=380
380\div30 = 12 \text{r }20
So Tyrell can cut 12 30 cm lengths from the log, with a 20 cm section remaining.
3 marks
Q14
Sophie, Rashid and Stuart each earn the same monthly salary.
Each month,
Sophie saves 35\% of her salary and spends the rest of her salary
Rashid spends \dfrac{4}{5} of his salary and saves the rest of his salary
The amount of salary Stuart Saves : The amount of salary he spends = 1 : 3
Work out who saves the most of their salary each month.
Answer type: multiple choice
Answer: Sophie
Wrong Answers:
Rashid
Stuart
They each save the same amount
Workings:
Sophie saves 35\% of her salary.
Rashid spends \dfrac{4}{5} of his salary, which is equivalent to 80\%, so he saves 20\%
Stuart saves 1 part of his salary for every 3 parts he spends.
The total parts is 4, so Stuart saves \dfrac{1}{4} of his salary, which is equivalent to 25\%
Thus, Sophie saves the most of her salary each month.
1 mark
Q15
Work out 11\% of 200 millilitres.
Answer type: simple
Answer: 22 millilitres
Workings:
10\% of 200 ml is 20 ml
1\% of 200 ml is 2 ml
11\% = 10\% + 1\% = 20+2 = 22 ml
2 marks
Q16
A=7b-2c
b=4
c=-6
16(a)
Work out the value of A
Answer type: simple
Answer: 40
Workings:
Substituting in the values of b and c:
A=7\times 4-2\times(-6) = 28+12=402 marks
16(b)
Expand 12i(2i-3)
Answer type: multiple choice
Answer: 24i^2-36i
Wrong answers:
24i-36i^2
24(i^2-4)
12(2i^2)-36
Workings:
12i(2i-3)=12i\times2i-12i\times3=24i^2-36i
2 marks
16(c)
Solve 5(k+12)=90
Answer type: simple
Answer: k = 6
Workings:
\begin{aligned}5(k+12) &= 90 \\ 5k+60 &= 90 \\ 5k &= 30 \\ k &= 6 \end{aligned}2 marks
Q17
There are some books on a shelf.
\dfrac{1}{5} of the books are fiction.
The rest of the books are non-fiction.
What is the ratio of the number of fiction books to the number of non-fiction books in the form 1:n
Answer type: multiple choice
Answer: 1:4
Wrong answers:
1:5 1:6 2:10Workings:
\dfrac{1}{5} of the books are fiction, so \dfrac{4}{5} of the books are non-fiction.
Hence the ratio of he number of fiction books to the number of non-fiction books is 1:4
2 marks
Q18
X = {multiples of 3 between 23 and 35}
Y = {even numbers between 23 and 35}
18(a)
Which of the following lists contains all the members of X \cup Y?
Answer type: multiple choice
Answer: 24, 26, 27, 28, 30, 32, 33, 34
Wrong answers:
27,33
23,24,26,27,28,29,30,32,33,34
24, 30
Workings:
X \cup Y is the numbers in X or Y
X=\{24,27,30,33\}
Y= \{24,26,28,30,32,34 \}
X \cup Y contains the numbers from both sets (numbers in both sets are only listed once)
2 marks
18(b)
Which of the following lists contains all the members of X \cap Y?
Answer: 24, 30
Wrong answers:
27,33
23,24,26,27,28,29,30,32,33,34
24, 26, 27, 28, 30, 32, 33, 34Workings:
X \cap Y contains the numbers in X and Y
X=\{24,27,30,33\}
Y= \{24,26,28,30,32,34 \}
The numbers which appear in both are 24 and 30
1 mark
Q25
On the grid below, which of the lines corresponds to the graph of y=2+2x?
Answer: B
Wrong answers:
A
C
D
Workings:
The graph of y=2+2x has a gradient of 2 and a y-intercept of +2
This corresponds to the line B on the grid.
3 marks
26
\textbf{a} = \begin{pmatrix} 3 \\ 7 \end{pmatrix}
\textbf{b} = \begin{pmatrix} 6 \\ -5 \end{pmatrix}
Work out \textbf{a}+4\textbf{b} as a colomn vector.
Select the correct answer from the options below.
Answer: \begin{pmatrix} 27 \\ -13 \end{pmatrix}
Wrong answers:
\begin{pmatrix} 18 \\ 23 \end{pmatrix}
\begin{pmatrix} 27 \\ 27 \end{pmatrix}
\begin{pmatrix} 27 \\ 13 \end{pmatrix}
Workings:
\textbf{a}+4\textbf{b} = \begin{pmatrix} 3+4\times6 \\ 7+4\times(-5) \end{pmatrix} = \begin{pmatrix} 27 \\ -13 \end{pmatrix}
2 marks