PAPER 4A
QUESTION 1 [1 mark]
Sammy runs half a mile and records his time at 6.22 minutes.
Estimate how long it would take for Sammy to run 10 miles.
Answer type: Multiple choice type 1
A: 120 minutes
B: 100 minutes
C: 60 minutes
D: 50 minutes
ANSWER: A
WORKING:
6 \times 20 = 120 minutes
QUESTION 2 [2 marks]
Work out 2(18\div3)^2
Answer type: Simple text answer
ANSWER: 72
WORKING:
2(18\div3)^2=2(6)^2=2\times36=72
QUESTION 3 [2 marks]
Find the missing angle labelled A.
Answer type: Simple text answer
ANSWER: 114 \degree
WORKING:
Angles in a triangle add up to 180\degree
180\degree-33\degree-33\degree= 114\degree
QUESTION 4 [2 marks]
The cost of hiring a boat on holiday in Florida is calculated using the formula,
Hire Cost in dollars (\$) = ( 15 \, \times Number of hours) + \, 45
£1 = \$ 1.25
Calculate the cost of hiring a boat for 3 hours, in pounds (£).
Answer type: Simple text answer
ANSWER: £72
WORKING:
Hire cost in dollars = ( 15 \, \times3) + \, 45=\$90
Hire cost in pounds = 90 \div 1.25 = £72
QUESTION 5
A Data set is comprised of 7 data points:
12, 17, 29, 16, 3.3, 8, 22
Question 5 [1 mark]
Calculate the median of the set.
Answer type: Simple text answer
ANSWER: 16
WORKING:
Order the numbers from smallest to largest:
3.3, 8, 12,16,17,22,29
The median is the middle value, which is 16
QUESTION 6 [2 marks] – h
Esther has baked 40 cookies. 20\% of the cookies are chocolate. \dfrac{1}{4} of the cookies are blueberry.
0.3 of the cookies are lemon. The rest are plain.
How many cookies are plain?
Answer type: Simple text answer
ANSWER: 10
WORKING:
Convert all to decimals:
0.2 chocolate, 0.25 blueberry and 0.3 lemon
1 - 0.2 - 0.25 - 0.3 = 0.25 plain
So, there are 40 \times 0.25 = 10 plain cookies
QUESTION 7 [1 mark]
Calculate 8.462-2.285
Answer type: Simple text answer
ANSWER: 6.177
Question 8 [3 marks]
Brett works for a company that make chairs. It takes Brett and his 2 colleagues 15 days to complete an order for 200 chairs.
How many extra workers are needed to complete an order for 200 chairs in 9 days, assuming everyone works at the same rate?
Answer type: Simple text answer
ANSWER: 2
WORKING:
3 workers \times \, 15 days = 45 days work in total
\dfrac{45}{9} = 5 workers needed to complete the order in 9 days
So, there are 5-3=2 extra workers needed.
PAPER 4B
QUESTION 1 [1 mark]
Choose the plan view that accurately represents the 3D shape shown.
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A
QUESTION 2 [2 marks]
Rory has a box of pens. 8 of the pens are black, 12 are blue and 10 are green.
What is the probability of Rory randomly selecting a blue pen from the box?
Give your answer as a decimal.
Answer type: Simple text answer
ANSWER: 0.4
WORKING:
8+12+10=30
Probability = \dfrac{12}{30}=0.4
QUESTION 3 [6 marks]
A gardener is planning a new garden that is in the shape of a parallelogram.
It features two ponds and a flower bed.
The rest of the space will be filled with grass.
The plan of the garden has been drawn to scale on a 1 cm grid labelled below.
Scale: 1 cm = 5 m
You are given that \pi = 3.14
Area of Flower bed = \bigg(\dfrac{a+b}{2} \bigg) L
a is the short width and b is the long width of the flower bed and L is the length of the flower bed.
Area of garden = w \times L
w is the width of the garden and L is the length of the garden, which is the same as the length of the flower bed.
Calculate the area that will be covered with grass.
Answer type: Simple text answer
ANSWER: 886 m^2
WORKING:
Total area = base \times height =50\times 30=1500 m^2
Flower bed area = \bigg(\dfrac{15+5}{2} \bigg) \times 30=300 m^2
Pond area = \frac{1}{2}\times 3.14 \times 10^2=157 m^2
Pond area = \frac{1}{2}\times 3.14 \times 10^2=157 m^2
Grass area = 1500-300-157-157=886 m^2
QUESTION 4 [3 marks]
A car has a range of 440 miles on a full tank. The tank holds 13.2 gallons.
The fuel gauge on the car shows that there is 24 litres remaining in the tank.
1 litre = 0.22 gallon
How many more miles can the car drive before completely running out of fuel?
Answer type: Simple text answer
ANSWER: 176 miles
WORKING:
13.2 gallons =13.2 \div 0.22 = 60 litres
\dfrac{24}{60} \times 440 = 176 miles
QUESTION 5 [5 marks]
Margherita pizza comes in three different sizes and at three different prices.
You are given that \pi = 3.14
Which pizza is the best value for money?
Answer type: Multiple choice type 1
A: Small
B: Medium
C: Large
ANSWER: C
WORKING:
Small area =16\pi inches^2
Medium area =25\pi inches^2
Large area =36\pi inches^2
Small = \dfrac{799}{16} = 49.94p
Medium = \dfrac{999}{25} = 39.96p
Large = \dfrac{1299}{36} = 36.08p
Therefore large is the best value.
(Note that we do not need to use the fact that \pi = 3.14 in this question)
QUESTION 6 [3 marks]
The value of a vintage car increases at a rate of 2\% per year.
Jermaine bought the car in 2015 for £12500
2 years later, in 2017, he sells the car for £14000
How much profit has Jermaine made?
Answer type: Simple text answer
ANSWER: £995
Year 1: £12500 \times 1.02 = £12750
Year 2: £12750 \times 1.02 = £13005
Profit = £14000 - £13005 = £995
QUESTION 7 [4 marks]
A school is investigating how much their students use social media.
They give their results, measured in minutes, in the table.
By calculating means, work out the difference in the average times spent on Facebook and Twitter.
Answer type: Multiple choice type 1
A: 3 minutes 24 seconds
B: 3 minutes 54 seconds
C: 3 minutes 4 seconds
D: 3 minutes 40 seconds
ANSWER: A
WORKING:
Facebook Mean = 463 \div 5 = 92 minutes 36 seconds
Twitter Mean = 480 \div 5 = 96 minutes
Difference = 3 minutes 24 seconds
QUESTION 8 [3 marks]
Find the perimeter of the compound shape, in m.
Answer type: Simple text answer
ANSWER: 6.7 m
WORKING:
Perimeter =45+200+135+65+(135-45)+(200-65) =670 cm =6.7 m
QUESTION 9 [1 mark]
Three friends flip the same biased coin several times.
Their results are shown in the table below.
Each of the friends calculates their own probability of heads.
State which friend is likely to have the probability closest to the true probability.
Answer type: Multiple choice type 2
A: Sonya
B: Clive
C: Lucy
ANSWER: A
WORKING:
Sonya is most likely to be the closest to the true probability because she did the most trials (120)
QUESTION 10 [5 marks]
The current exchange rate between the British Pound and the Chinese Yuan is £1 = ¥8.80
The cost of a large stuffed panda toy is ¥154
The total cost for international shipping is ¥132 when you buy less than 10 pandas, every panda more costs ¥20 extra.
Given that the customs charge a 10\% import fee based on the value of a shipment’s contents, what is the total cost to buy 5 large stuffed panda toys, in pounds?
Answer type: Simple text answer
ANSWER: £111.25
WORKING:
5 \times 154 = ¥770
770 \times 1.10 = ¥847
847 + 132 = ¥979
Total cost = 979 \div 8.80 = £111.25
QUESTION 11 [2 marks]
A student wishes to calculate his final percentage mark for his two geography tests that he sat in class. Each test was out of a maximum of 100 marks. Test 1 carries a 40\% weighting and test 2 carries a 60\% weighting.
Using the formula above, what was the final \% mark that the student achieved?
Answer type: Simple text answer
ANSWER: 55.2 \%
WORKING:
Final % mark = (0.4\times48)+(0.6\times60)=55.2\%
QUESTION 12 [3 marks]
A steel block is in the shape of a rectangle, shown below.
The steel block has a density of 8.05 g/cm^3.
Calculate the mass of the steel block, in kg.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 1.61 kg
WORKING:
Volume = 10\times5\times4=200 cm^3
\text{Mass} = \text{density} \times \text{volume} = 8.05 \times 200 = 1610 g = 1.61 kg
QUESTION 13
Question 13(a) [1 mark]
Choose the correct line of best fit for the scatter graph.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
Question 13(b) [1 mark]
Hence, predict the English score for another student who scored 80\% on their maths paper.
Answer type: Multiple choice type 1
A: 73 \%
B: 88 \%
C: 66 \%
D: 80 \%
ANSWER: A
QUESTION 14 [2 marks]
Calculate 3 \dfrac{1}{4} - 2 \dfrac{2}{3}
Give your answer in simplest form.
Answer type: Fraction
ANSWER: \dfrac{7}{12}
WORKING:
3 \dfrac{1}{4} = \dfrac{13}{4}
2 \dfrac{2}{3} = \dfrac{8}{3}
\dfrac{13}{4} - \dfrac{8}{3} = \dfrac{13\times3}{4 \times 3} - \dfrac{8 \times 4}{3 \times 4} = \dfrac{39}{12} - \dfrac{32}{12} = \dfrac{7}{12}
QUESTION 15 [3 marks]
Helena receives £15 pocket money each week from her parents. 30\% of this amount is spent on a magazine subscription, and the rest she spends on stickers, chocolate and fizzy drinks in the ratio of 4:2:1.
Assuming Helena is consistent with her spending, how much does she spend on stickers in 6 weeks?
Answer type: Simple text answer
ANSWER: £36
WORKING:
0.3 \times £15 = £4.50 on magazines per week.
£15 - £4.50 = £10.50 spent on stickers, chocolate and fizzy drinks.
In the ratio 4:2:1 there are 4+2+1= 7 parts
1 part = £10.50 \div 7 = £1.50
4 \times £1.50 = £6 on stickers per week.
So, she spends £6 \times 6 = £36 on stickers in 6 weeks.