PAPER 5A
QUESTION 1 [2 marks]
Work out (16-3\times4)^2
Answer type: Simple text answer
ANSWER: 16
WORKING:
(16-12)^2=4^2=16
QUESTION 2 [2 marks]
What is \dfrac{11}{4} - \dfrac{3}{2}
Give your answer as an improper fraction.
Answer type: Fraction
ANSWER: \dfrac{5}{4}
WORKING:
\dfrac{11}{4} - \dfrac{3}{2}=\dfrac{11}{4}-\dfrac{6}{4}=\dfrac{5}{4}
QUESTION 3 [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 4 [2 marks]
Here are the ages of 10 children at a birthday party:
9, 10, 12, 13, 10, 11, 14, 10, 12, 12
Find the median.
Answer type: Simple text answer
ANSWER: 11.5
WORKING:
Order the numbers from smallest to largest.
9, 10, 10, 10, 11, 12, 12, 12, 13, 14
The median is the \dfrac{n+1}{2} = 5.5th value, so lies half way between the 5th and 6th value.
Median = \dfrac{11+12}{2} = 11.5
QUESTION 5 [2 marks]
Ruth is on holiday in Spain.
She spends €85.50 in a restaurant.
The exchange rate is £1 = €1.20
Calculate how much she spends in pounds (£).
Answer type: Simple text answer
ANSWER: £71.25
WORKING:
85.50 \div 1.20 = £71.25
QUESTION 6 [3 marks]
If 5 housemates get through 1.5 litres of milk per day, how much milk will they need for 2 days when 3 friends stay for the weekend?
Assume that each person consumes milk at the same rate.
Answer type: Simple text answer
ANSWER: 4.8 litres
WORKING:
2 \times \dfrac{1.5}{5} \times 8 = \dfrac{3}{5} \times 8 = 4.8 litres
QUESTION 7 [1 mark]
Calculate the following: 56.21-9.731
Answer type: Simple text answer
ANSWER: 46.479
QUESTION 8 [2 marks]
AB = AC
Find the missing angle labelled x.
Answer type: Simple text answer
ANSWER: 45 \degree
WORKING:
Triangles with 2 sides the same length are isosceles triangles, therefore triangle ABC has 2 equal angles.
All angles in a triangle add up to 180\degree,\,\, 180\degree-90\degree=90\degree
x = \dfrac{90\degree}{2}=45\degree
PAPER 5B
QUESTION 1 [1 mark]
Choose the correct coordinates of the point on the graph below.
Answer type: Multiple choice type 1
A: (8,2)
B: (2,8)
C: (0,10)
D: (10,0)
ANSWER: A
QUESTION 2 [2 marks]
Wayde van Niekerk set the world record for the 400 m with a time of 43 seconds.
Determine his average speed over the course of the race.
Give your answer to 1 decimal place.
Answer type: Simple text answer
ANSWER: 9.3 m/s
WORKING:
\text{speed}=\dfrac{\text{distance}}{\text{time}}=\dfrac{400}{43}=9.3 m/s (1 dp)
QUESTION 3 [4 marks]
Sugar can be purchased from four different shops.
Which shop provides the best value per gram of sugar?
Answer type: Multiple choice type 1
A: Shop A
B: Shop B
C: Shop C
D: Shop D
ANSWER: C
WORKING:
Shop A = \dfrac{79}{500} = 0.158p per gram
Shop B = 0.158p per gram
Shop C = 0.099p per gram
Shop D = \dfrac{129}{1250} = 0.1032p per gram
Shop C is the cheapest.
QUESTION 4 [4 marks]
In 2016, there were 10000 electric cars in the United Kingdom.
In 2017, there were 25000 electric cars.
Assuming the percentage increase of electric cars remains the same year on year, how many electric cars would you expect there to be in 2019?
Answer type: Simple text answer
ANSWER: 156250
WORKING:
10000 \times r =25000
r= \dfrac{25000}{10000} = 2.5
2018: \,\,\, 25000\times 2.5 = 62500
2019: \,\,\, 62500 \times 2.5 = 156250
QUESTION 5 [5 marks]
Laura used to earn £200 per week. She was given a pay rise equal to \dfrac{2}{5} of her weekly income at the start of the year.
Laura earns £3000 in bonuses over the next year, which is added to her annual income.
The first £12500 of her annual income is tax-free.
20\% tax is deducted on any annual earnings over £12500
Given that there are 52 weeks in a year, calculate Laura’s income this year after tax.
Answer type: Simple text answer
ANSWER: £16548
WORKING:
\dfrac{2}{5} of £200 = £80
Weekly income = £200 + £80 = £280
Yearly income before bonuses = £280 \times 52 = £14560
Yearly income including bonuses = £14560 + £3000 = £17560
£17560 - 12500 = £5060 over £12500 that gets taxed
£5060 \times 0.8 = £4048 earned over £12500
Final yearly income = £12500 + £4048 = £16548
QUESTION 6 [3 marks]
A football coach records the number of goals scored by his squad in the first few games of the season.
Calculate the mean number of goals scored per person. Give your answer to two decimal places.
Answer type: Simple text answer
ANSWER: 0.63
WORKING:
Total number of goals = (19\times0)+(1\times5)+(2\times4)+(3\times2) = 19
Total frequency = 30
Mean = \dfrac{19}{30}=0.63 (2 dp)
QUESTION 7 [4 marks]
300 students are asked to choose between strawberry and chocolate ice-cream.
54\% of the students picked chocolate.
48\% of the students are girls.
26\% of the students are girls who chose chocolate.
Work out the number of boys who selected strawberry.
Answer type: Simple text answer
ANSWER: 72
WORKING:
300\times0.54=162 (Total number of students who picked chocolate)
300\times0.48=144 (Total number of girl students)
300\times0.26=78 (Total number of girls who picked chocolate)
72 boys selected strawberry.
QUESTION 8 [1 mark]
A multivitamin contains 16.2 mg of vitamin C. This is 24\% of the recommended daily intake.
What daily intake of vitamin C is recommended?
Give your answer in milligrams.
Answer type: Simple text answer
ANSWER: 67.5 mg
WORKING:
16.2 \div 0.24 = 67.5 mg
QUESTION 9 [5 marks]
A shape is made from a cylinder of radius 5 cm and height 4 cm.
A cuboid measuring 6 cm wide, 1 cm long and 4 cm deep is cut out of the centre as shown.
Calculate the surface area of the new shaped formed by removing the cuboid.
You are given that \pi = 3.14
Give your answer as a decimal to 1 decimal place.
Answer type: Simple text answer
ANSWER: 326.6 cm^2
WORKING:
Surface area of cylinder = 2 \pi r^2 + 2 \pi rh
(2 \times 3.14 \times 5^2) + (2 \times 3.14 \times 5 \times 4) = 282.6
Surface area of cylinder – 2 cuboid faces:
282.6 -(2\times6\times1)=270.6
Inside faces: (6\times4)\times2 =48, \,\,\, \,\,\, (4\times1)\times2=8
Total: 270.6+48+8=326.6 cm^2
QUESTION 10 [3 marks]
A person wishes to post a package that weighs 6.5 lb.
When they get to the post office, they’re told that the first 2 kg cost £10 to post, and every interval of 500 g over will cost an additional £2
If 1 lb = 453 g, how much will it cost to post the package?
Answer type: Simple text answer
ANSWER: £14
WORKING:
6.5 \times 453 = 2944.5 g
The first 2 kg costs £10
Then there are 2 intervals of 500 g over, which costs £4
Total = £14
QUESTION 11 [2 marks]
Four friends order pizza from a take away. The amount of pizza each person eats is shown below.
Matthew eats 0.8 of a pizza
Lily eats \dfrac{3}{4} of a pizza
George eats 77\% of a pizza
Sam eats 82\% of a pizza
Which person eats the most pizza?
Answer type: Multiple choice type 1
A: Sam
B: Lily
C: Matthew
D: George
ANSWER: A
WORKING:
0.8 = 80\% and \dfrac{3}{4} = 75\%
Sam eats the most, since 82\% is the biggest.
QUESTION 12 [2 marks]
Choose the correct drawing of the shape on the 1 cm by 1 cm grid at a scale of 1 : 30 cm
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
QUESTION 13 [4 marks]
The diagram shows the outline of a cuboid, ABCDEFGH.
The cuboid has a mass of 300 g
Given that: AB=3 cm, BC=12 cm, and CF=16 cm.
Find the density of the cuboid.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 0.52 g/cm^3
WORKING:
\text{Volume} = 3\times12 \times16=576 cm^3
\text{Density} = \text{Mass} \div \text{Volume} = 300 \div 576 = 0.52 g/cm^3 (2 dp)
QUESTION 14 [2 marks]
The table below displays the time taken by students to complete an event on a school sports day.
What proportion of students completed the event in 2 minutes or under?
Give your answer as a decimal correct to two decimal places.
Answer type: Simple text answer
ANSWER: 0.47
WORKING:
\dfrac{0+2+11+32}{0+2+11+32+33+18}=0.46875=0.47 to two decimal places
QUESTION 15 [3 marks]
This is a conversion graph between cm and inches.
The ratio between the size of a cricket ball and the size of a table tennis ball is 7:4
The diameter of a cricket ball is 2.8 inches.
Using the conversion graph, calculate the diameter of a table tennis ball, in cm.
Your answer should be a whole number.
Answer type: Simple text answer
ANSWER: 4 cm
WORKING:
Using the conversion graph, 4 inches =10 cm
1 part of ratio: 2.8 \div 7 = 0.4 inches
Diameter of table tennis ball in inches = 4 \times 0.4 = 1.6 inches
Diameter of table tennis ball in cm = \dfrac{1.6}{4} \times 10 = 4 cm