PAPER 7A
QUESTION 1 [3 marks]
It takes 4 people 3 and a half hours to tidy a house.
How long would it take if 5 people volunteered to tidy the same house?
Give your answer in hours.
Answer type: Simple text answer
ANSWER: 2.8 hours
ANSWER: A
WORKING:
4 people \times \, 3.5 hours = \, 14 hours of work total
14 \div 5 = 2.8 hours for 5 people
QUESTION 2 [2 marks]
A group of students were asked how many brothers and sisters they had. Their answers are recorded in the table below.
If a student is chosen at random, find the probability that there are 3 children in that student’s family.
Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{4}{15}
WORKING:
Total number of students = 4+12+8+3+1+2 = 30
No. of siblings = 2, No. of students = 8
Probability = \dfrac{8}{30} = \dfrac{4}{15}
QUESTION 3 [1 mark]
Write the numbers in increasing order starting with the smallest.
1.045, \,\,\,\, 1.445, \,\,\,\, 4.115, \,\,\,\, 5.411, \,\,\,\, 0.1445
Answer type: Multiple choice type 2
A: 0.1445, \,\,\,\, 1.045, \,\,\,\, 1.445, \,\,\,\, 4.115, \,\,\,\, 5.411
B: 0.1445, \,\,\,\, 1.445, \,\,\,\, 1.045, \,\,\,\, 4.115, \,\,\,\, 5.411
C: 0.1445, \,\,\,\, 1.045, \,\,\,\, 1.445, \,\,\,\, 5.411, \,\,\,\, 4.115
D: 5.411, \,\,\,\, 4.115, \,\,\,\, 1.445, \,\,\,\, 1.045, \,\,\,\, 0.1445
ANSWER: A
QUESTION 4 [1 mark]
A headteacher surveys her staff to see when they take their main holiday. She knows that many people are likely to holiday in the UK and elsewhere in the world within the same year. The table below shows her findings.
Which was the modal combination of destinations?
Answer type: Multiple choice type 1
A: Italy and London
B: USA and Yorkshire
C: France and Dorset
D: Spain and Devon
ANSWER: A
QUESTION 5 [2 marks]
Work out \dfrac{5}{3}+\dfrac{1}{2}
Give your answer in simplest form.
Answer type: Fraction
ANSWER: \dfrac{13}{6}
WORKING:
\dfrac{5}{3}+\dfrac{1}{2}=\bigg(\dfrac{5}{3}\times\dfrac{2}{2}\bigg)+\bigg(\dfrac{1}{2}\times\dfrac{3}{3}\bigg)=\dfrac{10}{6}+\dfrac{3}{6}=\dfrac{13}{6}
QUESTION 6 [1 mark]
Calculate 10.762-8.9
Answer type: Simple text answer
ANSWER: 1.862
QUESTION 7 [3 marks]
Jane fills her empty car with 12 litres of petrol.
After driving for the day the car now has 7.5 litres of petrol in the tank.
Calculate the percentage decrease of petrol in the car.
Answer type: Simple text answer
ANSWER: 37.5 \%
WORKING:
12-7.5=4.5
\dfrac{4.5}{12}=0.375 using the bus stop method
0.375 = 37.5 \%
QUESTION 8 [2 marks]
Philippa aims to save £250 each month into a saving amount each month. On average she manages to save 20\% more than her target each month.
Work out have much she will have saved over the course of a year.
Answer type: Simple text answer
ANSWER: £3600
WORKING:
20\% + 100\% = 120\%120\% of £250 is £50 +£250 = £300
£300 \times 12 = £3600 saved over the course of a year
PAPER 7B
QUESTION 1 [2 marks]
Megan is a florist. She is arranging flowers for a display and has 16 roses, 8 daffodils and 13 tulips.
What is the probability of Megan randomly selecting a rose?
Give your answer to three decimal places.
Answer type: Simple text answer
ANSWER: 0.432
WORKING:
\dfrac{16}{16+8+13} = 0.432 (3 dp)
QUESTION 2 [1 mark]
What 3D shape can be created with the net shown above?
Answer type: Multiple choice type 1
A: Cube
B: Frustum
C: Square-based pyramid
D: Sphere
QUESTION 3 [2 marks]
Calculate the following:
(7+5)^2\div6^2-1
Answer type: Simple text answer
ANSWER: 3
(7+5)^2\div6^2-1=12^2\div6^2-1=144\div36-1=4-1=3
QUESTION 4 [3 marks]
Jeremy puts £2000 into a bank account that gains interest each year.
The bank account gains 1.5 \% interest for the first year, and decreases by 0.1 \% each year after that.
How much money will be in his bank account after 2 years, given that he does not take any money out?
Answer type: Simple text answer
ANSWER: £2058.42
WORKING:
Year 1: £2000 \times 1.015 = £2030
Year 2: £2030 \times 1.014 = £2058.42
QUESTION 5 [4 marks]
Shapes A (top left), B (top right), C (bottom left) and D (bottom right) are as follows:
Which two of the four shapes have the same area?
You are given that \pi = 3.14
\text{Area of trapezium} = \bigg( \dfrac{\text{base} + \text{top}}{2} \bigg) \text{height}
\text{Area of parallelogram} = \text{base} \times \text{height}
Answer type: Multiple choice type 1
A: B and C
B: A and B
C: C and D
D: B and D
ANSWER: A
WORKING:
Shape A = \pi r^2= 3.14 \times 3^2 =28.26 cm^2
Shape B = \text{base} \times \text{height}=27 cm^2
Shape C = \dfrac{(\text{top} + \text{bottom})}{2} \times \text{height}=27 cm^2
Shape D = 23 cm^2
B and C are have the same area
QUESTION 6 [4 marks]
Mrs Smith travels on Plane M, which flies at an average speed of 825 km/h for 7 hours and 24 minutes from Location A to Location B.
She then waits at Location B for 2 hours and 11 minutes, before flying to Location C on Plane N, which flies at an average speed of 722 km/h for 4 hours and 48 minutes.
Both planes fly in a straight line to their respective destinations.
What is the total distance of her journey in km to 1 decimal place?
Answer type: Simple text answer
ANSWER: 9570.6 km
WORKING:
7 hours and 24 minutes =7.4 hours
4 hours and 48 minutes = 4.8 hours
A to B: \text{Distance} = \text{S} \times \text{T} = 825 \times 7.4 = 6105 km
B to C: \text{Distance} = 722 \times 4.8 = 3465.6 km
\text{Total distance}= 6105 + 3465.6 = 9570.6 km
QUESTION 7 [2 marks]
96 identical books have a mass of 40 kg
Find the mass of 150 books.
Answer type: Simple text answer
ANSWER: 75 kg
WORKING:
\dfrac{40}{96} \times 150 = 62.5 kg
QUESTION 8 [4 marks]
Grayson Academy can choose from two suppliers when buying scissors.
The academy intends to purchase 250 scissors.
How much money would the school save if they bought the scissors from Delaware resources?
Answer type: Simple text answer
ANSWER: £5.06
WORKING:
Desk =\dfrac{250}{4} = 62.5 packs = \, 63 packs
63 \times £9.95 + £4.95 = £626.85 + £4.95 = £631.80
Delaware =\dfrac{250}{2} = 125 packs
125 \times £4.99 + £2.99 = £623.75 + £2.99 = £626.74
Savings = £631.80 - £626.74 = £5.06
QUESTION 9 [4 marks]
100 students in grade 11 either study French or German or Italian.
47 of the students are girls while the rest are boys.
12 girls study French. 15 girls and 17 boys study German.
A total of 30 students study Italian.
Work out how many boys study Italian.
Answer type: Simple text answer
ANSWER: 10
WORKING:
QUESTION 10 [5 marks]
Lucy is tiling her bathroom. She buys white and blue tiles in the ratio of 13:2
Blue tiles cost £2.80 whilst white tiles cost £2.35
There is a 10\% discount on orders over 100 tiles.
If she buys 16 blue tiles, how much does Lucy spend in total?
Answer type: Simple text answer
ANSWER: £260.28
WORKING:
The ratio is 2 parts blue to 13 parts white (2:13). Lucy buys 16 blue tiles, which is 2 parts.
So, 1 part =16 \div 2=8
No. of white tiles =13\times8=104 tiles
Cost of blue tiles =£2.80 \times 16 = £44.80
Cost of white tiles =104\times £2.35=£244.40
Hence, the total cost before the discount is £44.80+£244.40=£289.20
A 10\% discount means that she pays 90\% of the total cost.
Money spent after discount = £289.20 \times 0.9 = £260.28
QUESTION 11 [3 marks]
The semi-circle shown has centre O and a radius of 5 cm.
You are given that \pi = 3.14
Calculate the perimeter of the semi-circle.
Answer type: Simple text answer
ANSWER: 25.7 cm
WORKING:
Length of curved section = \dfrac{1}{2}\times 3.14 \times10=15.7 cm
Length of base = 10 cm
Total Perimeter = 10 +15.7 = 25.7 cm
QUESTION 12 [2 marks]
Thomas is 54 years old. His eldest son is \dfrac{1}{2} is age. His youngest son is \dfrac{1}{3} of his age.
Work out the age difference between his oldest and youngest son.
Answer type: Simple text answer
ANSWER: 9 years
WORKING:
Eldest son’s age =54\div2=27
Youngest son’s age 54\div3=18
27-18=9 years difference
QUESTION 13 [5 marks]
Mary has just given birth to a baby in hospital, that weighs 5.2 kg. The weights of other babies in the hospital can be seen in the table below.
By estimating the mean of the other babies in the hospital, calculate the difference between the weight of Mary’s baby and the estimated average weight of the other babies in the hospital.
Give your answer to 3 decimal places.
Answer type: Simple text answer
ANSWER: 0.574 kg
WORKING:
Find the midpoint of each weight group, and write them in a new column.
Then calculate \text{frequency} \times \text{midpoint} for each weight group, and write them in a new column.
See the table below.
Total frequency = 101+93+82+55+77=408
Total ‘f \times m‘ = 328.25 + 348.75 + 369 + 302.5 + 539 = 1887.5
Estimated mean = \dfrac{1887.5}{408} = 4.6262...
Difference = 5.2 - 4.6262... = 0.574 kg (3 dp)
QUESTION 14 [2 marks]
A car hire firm charges a fixed £50 fee then charges per mile driven.
Juan hires a car for a week from this firm, in which he drives 125 miles.
Juan has to pay an additional £50 car insurance on top.
Juan also spends £20 in petrol over the course of the week.
Using the conversion graph and the information provided, work out how much Juan spends in total to drive the car for a week.
Answer type: Simple text answer
ANSWER: £170
WORKING:
125 miles = £100
Total = £100 + £50 + £20 = £170
QUESTION 15 [2 marks]
The volume of a square-based pyramid is given by V = \dfrac{1}{3} a^2h
where V is the volume, a is the length of the base and h is the height of the pyramid.
Below is a diagram of a square-based pyramid.
The length of the base, a = 3 cm
The height of the pyramid, h = 7 cm
Calculate the volume of the square-based pyramid.
Answer type: Simple text answer
ANSWER: 21 cm^3
WORKING:
V = \dfrac{1}{3} \times 3^2 \times 7 = 21 cm^3