PAPER 5A

 

QUESTION 1 [2 marks]

Work out (16−3×4)2(16-3\times4)^2

 

Answer type: Simple text answer

ANSWER: 16

WORKING:

(16−12)2=42=16(16-12)^2=4^2=16

 

 

QUESTION 2 [2 marks]

What is 114−32 \dfrac{11}{4} - \dfrac{3}{2}

Give your answer as an improper fraction.

 

Answer type: Fraction

ANSWER: 54\dfrac{5}{4}

WORKING:

114−32=114−64=54 \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 1010 children at a birthday party:

99, 1010, 1212, 1313, 1010, 1111, 1414, 1010, 1212, 1212

Find the median.

 

Answer type: Simple text answer

ANSWER: 11.5

WORKING:

Order the numbers from smallest to largest.

9,10,10,10,11,12,12,12,13,149, 10, 10, 10, 11, 12, 12, 12, 13, 14

 

The median is the n+12=5.5\dfrac{n+1}{2} = 5.5th value, so lies half way between the 55th and 66th value.

Median =11+122=11.5= \dfrac{11+12}{2} = 11.5

 

 

QUESTION 5 [2 marks]

Ruth is on holiday in Spain.

She spends €85.50€85.50 in a restaurant.

The exchange rate is £1=€1.20£1 = €1.20

Calculate how much she spends in pounds (£)(£).

 

Answer type: Simple text answer

ANSWER: £71.25

WORKING:

85.50÷1.20=£71.2585.50 \div 1.20 = £71.25

 

 

QUESTION 6 [3 marks]

If 55 housemates get through 1.51.5 litres of milk per day, how much milk will they need for 22 days when 33 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:

2×1.55×8=35×8=4.82 \times \dfrac{1.5}{5} \times 8 = \dfrac{3}{5} \times 8 = 4.8 litres

 

 

QUESTION 7 [1 mark]

Calculate the following: 56.21−9.73156.21-9.731

 

Answer type: Simple text answer

ANSWER: 46.479

 

 

QUESTION 8 [2 marks]

AB=ACAB = AC

Find the missing angle labelled xx.

 

Answer type: Simple text answer

ANSWER: 45 °\degree

WORKING:

Triangles with 22 sides the same length are isosceles triangles, therefore triangle ABC has 22 equal angles.

All angles in a triangle add up to 180°,  180°−90°=90°180\degree,\,\, 180\degree-90\degree=90\degree

x=90°2=45°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)(8,2)

B: (2,8)(2,8)

C: (0,10)(0,10)

D: (10,0)(10,0)

 

ANSWER: A

 

 

QUESTION 2 [2 marks]

Wayde van Niekerk set the world record for the 400400 m with a time of 4343 seconds.

Determine his average speed over the course of the race.

Give your answer to 11 decimal place.

 

Answer type: Simple text answer

ANSWER: 9.3 m/s

WORKING:

speed=distancetime=40043=9.3\text{speed}=\dfrac{\text{distance}}{\text{time}}=\dfrac{400}{43}=9.3 m/s (11 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 =79500=0.158= \dfrac{79}{500} = 0.158p per gram

Shop B =0.158= 0.158p per gram

Shop C =0.099= 0.099p per gram

Shop D =1291250=0.1032= \dfrac{129}{1250} = 0.1032p per gram

 

Shop C is the cheapest.

 

 

QUESTION 4 [4 marks]

In 20162016, there were 1000010000 electric cars in the United Kingdom.

In 20172017, there were 2500025000 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 20192019?

 

Answer type: Simple text answer

ANSWER: 156250

WORKING:

10000×r=2500010000 \times r =25000

r=2500010000=2.5r= \dfrac{25000}{10000} = 2.5

 

20182018:    25000×2.5=62500\,\,\, 25000\times 2.5 = 62500

20192019:    62500×2.5=156250\,\,\, 62500 \times 2.5 = 156250

 

 

QUESTION 5 [5 marks]

Laura used to earn £200£200 per week. She was given a pay rise equal to 25\dfrac{2}{5} of her weekly income at the start of the year.

Laura earns £3000£3000 in bonuses over the next year, which is added to her annual income.

The first £12500£12500 of her annual income is tax-free.

20%20\% tax is deducted on any annual earnings over £12500£12500

Given that there are 5252 weeks in a year, calculate Laura’s income this year after tax.

 

Answer type: Simple text answer

ANSWER: £16548

WORKING:

25\dfrac{2}{5} of £200=£80£200 = £80

Weekly income =£200+£80=£280= £200 + £80 = £280

 

Yearly income before bonuses =£280×52=£14560= £280 \times 52 = £14560

Yearly income including bonuses =£14560+£3000=£17560= £14560 + £3000 = £17560

 

£17560−12500=£5060£17560 - 12500 = £5060 over £12500£12500 that gets taxed

£5060×0.8=£4048£5060 \times 0.8 = £4048 earned over £12500£12500

 

Final yearly income =£12500+£4048=£16548= £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 = (19×0)+(1×5)+(2×4)+(3×2)=19= (19\times0)+(1\times5)+(2\times4)+(3\times2) = 19

Total frequency =30= 30

Mean =1930=0.63= \dfrac{19}{30}=0.63 (22 dp)

 

 

QUESTION 7 [4 marks]

300300 students are asked to choose between strawberry and chocolate ice-cream.

54%54\% of the students picked chocolate.

48%48\% of the students are girls.

26%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:

300×0.54=162300\times0.54=162 (Total number of students who picked chocolate)

300×0.48=144300\times0.48=144 (Total number of girl students)

300×0.26=78300\times0.26=78 (Total number of girls who picked chocolate)

7272 boys selected strawberry.

 

 

QUESTION 8 [1 mark]

A multivitamin contains 16.216.2 mg of vitamin C. This is 24%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÷0.24=67.5 16.2 \div 0.24 = 67.5 mg

 

 

QUESTION 9 [5 marks]

A shape is made from a cylinder of radius 55 cm and height 44 cm.

A cuboid measuring 66 cm wide, 11 cm long and 44 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 π=3.14\pi = 3.14

Give your answer as a decimal to 11 decimal place.

 

Answer type: Simple text answer

ANSWER: 326.6 cm2^2

WORKING:

Surface area of cylinder =2πr2+2πrh = 2 \pi r^2 + 2 \pi rh

(2×3.14×52)+(2×3.14×5×4)=282.6 (2 \times 3.14 \times 5^2) + (2 \times 3.14 \times 5 \times 4) = 282.6

 

Surface area of cylinder – 22 cuboid faces:

282.6−(2×6×1)=270.6282.6 -(2\times6\times1)=270.6

 

Inside faces: (6×4)×2=48,   (6\times4)\times2 =48, \,\,\,    (4×1)×2=8 \,\,\, (4\times1)\times2=8

 

Total: 270.6+48+8=326.6270.6+48+8=326.6 cm2^2

 

 

QUESTION 10 [3 marks]

A person wishes to post a package that weighs 6.56.5 lb.

When they get to the post office, they’re told that the first 22 kg cost £10£10 to post, and every interval of 500500 g over will cost an additional £2£2

If 11 lb =453= 453 g, how much will it cost to post the package?

 

Answer type: Simple text answer

ANSWER: £14

WORKING:

6.5×453=2944.56.5 \times 453 = 2944.5 g

The first 22 kg costs £10£10

Then there are 22 intervals of 500500 g over, which costs £4£4

Total =£14= £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 0.80.8 of a pizza

Lily eats 34\dfrac{3}{4} of a pizza

George eats 77%77\% of a pizza

Sam eats 82%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%0.8 = 80\% and 34=75%\dfrac{3}{4} = 75\%

Sam eats the most, since 82%82\% is the biggest.

 

 

QUESTION 12 [2 marks]

Choose the correct drawing of the shape on the 11 cm by 11 cm grid at a scale of 1:301 : 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, ABCDEFGHABCDEFGH.

The cuboid has a mass of 300300 g

Given that: AB=3AB=3 cm, BC=12BC=12 cm, and CF=16CF=16 cm.

Find the density of the cuboid.

Give your answer to 22 decimal places.

 

Answer type: Simple text answer

ANSWER: 0.52 g/cm3^3

WORKING:

Volume=3×12×16=576\text{Volume} = 3\times12 \times16=576 cm3^3

Density=Mass÷Volume=300÷576=0.52\text{Density} = \text{Mass} \div \text{Volume} = 300 \div 576 = 0.52 g/cm3^3 (22 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 22 minutes or under?

Give your answer as a decimal correct to two decimal places.

 

Answer type: Simple text answer

ANSWER: 0.47

WORKING:

0+2+11+320+2+11+32+33+18=0.46875=0.47\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 7:47:4

The diameter of a cricket ball is 2.82.8 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, 44 inches =10=10 cm

 

11 part of ratio: 2.8÷7=0.42.8 \div 7 = 0.4 inches

Diameter of table tennis ball in inches =4×0.4=1.6= 4 \times 0.4 = 1.6 inches

Diameter of table tennis ball in cm =1.64×10=4= \dfrac{1.6}{4} \times 10 = 4 cm