PAPER 10
PAPER 10A
(Q1) QUESTION 1 [1 mark]
Estimate \dfrac{22.38\times3.1}{3.19\times2.1}
Answer type: Multiple choice type 1
A: 10
B: 12
C: 5
D: 8
ANSWER: A
WORKING:
\dfrac{20\times3}{3\times2}=\dfrac{60}{6}=10(Q2) QUESTION 2 [1 mark]
What is \dfrac{14}{5} - \dfrac{8}{3} ?
Give your answer as an improper fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{2}{15}
WORKING:
\dfrac{14}{5} - \dfrac{8}{3}=(\dfrac{14}{5}\times\dfrac{3}{3}) - (\dfrac{8}{3}\times\dfrac{5}{5})=\dfrac{42}{15}-\dfrac{40}{15}=\dfrac{2}{15}(Q3) QUESTION 3 [1 mark]
What is 15\% of 300 kg?
Answer type: Simple text answer
ANSWER: 45 kg
300\text{ kg}\times0.15=45\text{ kg}(Q4) QUESTION 4 [1 mark]
Find the median of the following set of values
20.21, 44.82, 27.64, 41.29, 10.74
Answer type: Simple text answer
ANSWER: 27.64
(Q5) QUESTION 5 [1 mark]
Describe the nature of the correlation shown in the scatter graph.
Answer type: Multiple choice type 1
A: Weak negative correlation
B: Weak positive correlation
C: Strong positive correlation
D: No correlation
ANSWER: A
(Q6) QUESTION 6 [1 mark]
A car hire firm charges a fixed £50 fee then charges per mile driven.
Using the conversion graph, how much would it cost to drive 300 miles?
Answer type: Simple text answer
ANSWER: £170
WORKING:
(Q7) QUESTION 8 [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: Triangular prism
ANSWER: A
(Q8) QUESTION 9 [2 marks]
Find the perimeter of the rectangle.
Answer type: Simple text answer
ANSWER: 39.8 cm
WORKING:
Perimeter =14.3+14.3+5.6+5.6 =39.8 cm
(Q9) QUESTION 10 [1 mark]
What is \dfrac{32}{50} as a percentage?
Simple text answer
ANSWER: 64 \%
(Q10) QUESTION 11 [1 mark]
What is the value of \dfrac{8a}{2b}-5ab when a=3 and b=-4 ?
Answer type: Simple text answer
ANSWER: 57
WORKING:
\dfrac{8a}{2b}-5ab=\dfrac{8\times3}{2\times-4}-5\times3\times-4=\dfrac{24}{-8}+60=57(Q11) QUESTION 12 [1 mark]
Choose the correct plot of the coordinate (10,3) on the graph below.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: C
(Q12) QUESTION 13 [1 mark]
Lily has 296 guests, and each requires one glass of juice each.
Estimate how many cartons of juice she will need if each carton has enough to fill 9.5 glasses.
Answer type: Multiple choice type 1
A: 30 cartons
B: 35 cartons
C: 3000 cartons
D: 40 cartons
ANSWER: A
WORKING:
300\div10=30(Q13) QUESTION 14 [1 mark]
What is \dfrac{1}{3} of 27?
Answer type: Simple text answer
ANSWER: 9
(Q14) QUESTION 15 [1 mark]
Evaluate (3\times5^2)\div5-20\times4+75
Answer type: Simple text answer
ANSWER: 10
PAPER 10B
QUESTION 1 [2 marks]
The price of a chocolate box has increased by 25\%. The box of chocolate now costs £17.25
How much did it cost originally?
Answer type: Simple text answer
ANSWER: £13.80
WORKING:
£17.25 \div 1.25 = £13.80
QUESTION 2 [1 mark]
Work out 13.5^2-11.5^2
Answer type: Simple text answer
ANSWER: 50
QUESTION 3 [2 marks]
A school pays for the costumes for a school concert.
There are 30 children in the concert and they each require 3 separate costumes.
The costumes cost the school £14 each.
How much does it cost the school in total to purchase the costumes for its children?
Answer type: Simple text answer
ANSWER: £1260
WORKING:
30 children needing 3 costumes each, so there are 90 costumes required in total.
90\times\text{£}14=\text{£}1260QUESTION 4 [2 marks]
The probability of a badminton player winning a match is \dfrac{1}{4}
The player is competing in two matches over the weekend.
What is the probability of the player winning neither of those games?
Give your answer as a decimal.
Answer type: Simple text answer
ANSWER: 0.5625
WORKING:
0.75\times 0.75 = 0.5625
QUESTION 5 [1 mark]
Calculate the value of [(x+11-9)^2+8.5\times2]\div 7 when x = 3
Answer type: Simple text answer
ANSWER: 6
WORKING:
[(3+11-9)^2+8.5\times2]\div 7=[latex][5^2+8.5\times2]\div 7=[25+17]\div7=42\div7=6QUESTION 6 [3 marks]
A conservation group try to estimate the population of different types of tress that are found in a nearby forest:
\dfrac{1}{18} of the trees are oak
\dfrac{2}{9} of the trees are beech
and \dfrac{1}{4} of the trees are pine.
The group estimates there are 720 trees in the forest. How many of these trees are not oak or pine?
Answer type: Simple text answer
ANSWER: 500
WORKING:
\dfrac{1}{18} are oak hence \dfrac{40}{720} of the trees are oak.
\dfrac{9}{36} are pine hence \dfrac{180}{720} of the trees are pine.
There are a total of 220 oak and pine trees.
So 500 trees in the forest that are not oak or pine.
QUESTION 7 [5 marks]
At the store, cola is sold in a multipack of cans or in a single bottle.
Which option is the better value for money?
Answer type: Multiple choice type 1
A: Multipack
B: Single
ANSWER: A
WORKING:
Single = 1500 ml
\dfrac{150}{1500} = 1 ml = \, 0.1p
Multipack = 6 \times 330 = 1980 ml
\dfrac{170}{1980} = 1 ml = \, 0.086p
Multipack is cheaper
QUESTION 8
Christopher has seven rabbits in his garden. Their weights in kilograms are listed below.
1.1, 1.9, 1.5, 1.3, 2.0, 1.3, 1.7
Question 8(a) [2 marks]
What is the mean for the weight of the rabbits?
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 1.54 kg
WORKING:
Mean = 10.8 \div 7 = 1.54 kg
Question 8(b) [1 mark]
What is the mode for the weight of the rabbits?
Give your answer to 1 decimal place.
Answer type: Simple text answer
ANSWER: 1.3 kg
Question 8(c) [1 mark]
What is the median for the weight of the rabbits?
Give your answer to 1 decimal place.
Answer type: Simple text answer
ANSWER: 1.5 kg
QUESTION 9 [6 marks]
A carpenter plans to carve a doorstop out of a block of wood that has a density of 5 g/cm^3.
Calculate the mass of the doorstop, in g, if this is the design:
You are given that the volume, V = \text{Area of cross-section} \times \text{Length}
Answer type: Simple text answer
ANSWER: 75 g
WORKING:
Volume = \dfrac{1}{2} \times 3 \times 5 \times 2 = 15 cm^3
Mass = \text{Density}\times\text{Volume}=5 \times 15 = 75 g
QUESTION 10 [6 marks]
The diagram below shows a representation of a small USB drive consisting of two cuboids, ABCDEFGH and IJKLMNOP attached together.
AC=12 mm, BH=3 mm, GF=9 mm, IL=3 mm, KO=1 mm, IJ=e
Calculate the total surface area of the USB drive, if e = 2.5 mm
Answer type: Simple text answer
ANSWER: 362 mm^2
WORKING:
Big cuboid:
(12\times3)\times2=72,
(9\times12 )\times2=216,
(3\times9 )\times2=54
Total =342 mm^2
Small cuboid:
(3\times 2.5)\times2=15,
(1\times 2.5)\times2=5,
(3\times1)\times2=6
Total =15+5+6 = 26 mm^2
Overlapping surface area =(3\times1)\times2=6 mm^2
Total Area of USB = 342+26-6=362 mm^2
QUESTION 11 [4 marks]
A school is purchasing stationary before the new term commences. The school requires 126 pencils, 48 books and 80 crayons.
In pounds, how much does it cost the school in total to buy the stationary?
Answer type: Simple text answer
ANSWER: £159.65
WORKING:
126 pencils with the promotion of 5 for the price of 4, means the school pays for 101.
101\times\text{£}0.25=\text{£25.25}48 books with the promotion of 8 for the price of 7, means the school pays for 42 books.
48\times\text{£}2=\text{£}9680 crayons with the promotion of 30\% off the unit price, means the school pays \text{£}0.63 per unit.
80\times \text{£}0.63=\text{£}50.4\\ \text{£}25.25+\text{£}84+\text{£}50.4=\text{£}159.65QUESTION 12 [3 marks]
Edith starts on a salary of £23800 and gets a raise of 6\% every year.
What will her salary be in 2 years time?
Give your answer to the nearest pound.
Answer type: Simple text answer
ANSWER: £26742
WORKING:
Year 1: £23800 \times 1.06 = £25228
Year 2: £25228 \times 1.06 = £26742 (nearest pound)
QUESTION 13 [2 marks]
12 students need to drink 3 litres of water over the course of the day.
How much water would be needed for 20 students?
Give your answer in litres.
Answer type: Simple text answer
ANSWER: 5 litres
WORKING:
3 litres \div \, 12 students = \, 0.25 litres per student
for 20 students they would need 5 litres
QUESTION 14
Data set A has a median value of 18.6
Data set B is comprised of 7 data points:
12, 17, 29, 16, 33, 8, 22
Question 14(a) [1 mark]
Calculate the median of set B.
Answer type: Simple text answer
ANSWER: 17
Question 14(b) [1 mark]
Which data set has a higher median?
Answer type: Multiple choice type 1
A: Data set A
B: Data set B
ANSWER: A
QUESTION 15 [2 marks]
Holly is deciding what colour trousers and what colour jumper to wear. Her choices are given below.
Trouser colours: black, navy, purple
Jumper colours: orange, yellow, white
If she chooses to wear black trousers and a yellow jumper, that would be denoted as BY.
List all other possible outcomes for Macy’s choice of outfit.
Answer type: Multiple choice type 1
A: BO, BW, NO, NY, NW, PO, PY, PW
B: BO, BW, NO, NW, PO, PW
C: BO, BW, NO, NY, NW
D: NO, NY, NW, PO, PY, PW
ANSWER: A