PAPER 6A
QUESTION 1 [2 marks]
Fifty students were asked how many books they each took to school on Monday.
The results are summarized in the table below.
Find the median number of books.
Answer type: Simple text answer
ANSWER: 2
WORKING:
There are 50 students in total, so the median lies between the 25\text{th} student and 26\text{th} student, where the students are ordered in order of how many books they took to school from smallest to largest.
Therefore the median is 2, because both the 25th and 26th student took 2 books to school.
QUESTION 2 [3 marks]
Spinner A has numbers 1 to 4 on it.
Spinner B has numbers 1 to 3 on it.
Both spinners are spun and the numbers on each are added together to give a score.
What is the probability that the score will be 5?
Give your answer as a decimal.
Answer type: Simple text answer
ANSWER: 0.25
WORKING:
Possible combinations that give a total score of 5:
2+3, 3+2, 4+1, so 3 combinations of scores.
Total possible combinations = 4\times3=12
Probability that the score will be 5=\dfrac{3}{12}=0.25
QUESTION 3 [1 mark]
Calculate 106.284-38.691
Answer type: Simple text answer
ANSWER: 67.593
QUESTION 4 [2 marks]
Work out 7 \times (8 \div 4)^2
Answer type: Simple text answer
ANSWER: 28
WORKING:
7 \times (8 \div 4)^2=7\times2^2=7\times4=28
QUESTION 5 [1 mark]
Find the missing angle labelled x
Answer type: Simple text answer
ANSWER: x= 48 \degree
WORKING:
Angle of a straight line is 180\degree\\
x=180\degree-132\degree=48\degree
QUESTION 6 [2 marks]
In a school, the ratio of the number of students with blonde hair to the number of students with brown hair is 4:5
If there are 450 students in the school, how many of them have brown hair?
Answer type: Simple text answer
ANSWER: 250
WORKING:
Total number of parts =4+5=9
1 part =450 \div 9 = 50
Number of students with brown hair = 50 \times 5 = 250
QUESTION 7 [1 mark]
What 3D shape can be created with the 2D net as shown above?
Answer type: Multiple choice type 1
A: Triangular Prism
B: Frustum
C: Tetrahedron
D: Square-based pyramid
ANSWER: A
QUESTION 8 [3 marks]
It took 5 and a half weeks for a team of 3 people to restore a classic car.
Assuming that everyone worked at the same rate, how long would it have taken to restore the classic car if there was an extra worker in the team?
Give your answer in weeks.
Answer type: Simple text answer
ANSWER: 4.125 weeks
WORKING:
5.5 \times 3 = 16.5 weeks of work for one person
16.5 \div 4 = 4.125 weeks for four people
PAPER 6B
QUESTION 1 [3 marks]
A conservation group try to estimate the population of different types of trees 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.
What fraction of the trees in the forest are not oak, beech or pine?
Give your answer in simplest form.
Answer type: Fraction
ANSWER: \dfrac{17}{36}
WORKING:
\dfrac{2}{36} + \dfrac{8}{36} + \dfrac{9}{36} = \dfrac{19}{36}
1-\dfrac{19}{36}=\dfrac{17}{36}
QUESTION 2 [1 mark]
Write the numbers in increasing order starting with the smallest.
1.101, \,\,\,\, 0.11, \,\,\,\, 1.10, \,\,\,\, 0.01
Answer type: Multiple choice type 1
A: 0.01, \,\,\,\, 0.11, \,\,\,\, 1.10, \,\,\,\, 1.101
B: 0.01, \,\,\,\, 0.11, \,\,\,\, 1.101, \,\,\,\, 1.10
C: 0.11, \,\,\,\, 0.01, \,\,\,\, 1.10, \,\,\,\, 1.101
D: 1.101, \,\,\,\, 1.10, \,\,\,\, 0.11, \,\,\,\, 0.01
ANSWER: A
QUESTION 3 [4 marks]
The following grouped frequency table shows the time taken (in minutes) by a class of students to complete a 1500 m race.
Estimate the mean time it took students to complete the distance.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 8.29 minutes
WORKING:
Find the midpoint of each time group, and write them in a new column.
Then calculate \text{frequency} \times \text{midpoint} for each time group, and write them in a new column.
Then, add up the frequency column, and add up the \text{frequency} \times \text{midpoint} column.
See the table below.
Estimated mean = \dfrac{373}{45}= 8.29 minutes
QUESTION 4 [6 marks]
Anna needs to be at the museum for the open evening at 18:00 h.
She will walk to the museum from the bus depot at a speed of 3 mph.
To arrive at the bus depot she will catch the bus at the stop from near her house. The bus travels at an average speed of 25 mph.
On the walk from her house to the bus stop, she will average a speed of 6 mph.
The bus depot is 0.7 miles from the museum.
The bus journey from the bus stop to bus depot is 2.2 miles.
The walk from her house to the bus stop is 0.3 miles.
Buses leave the bus stop at 15 minute intervals starting from 07:00 h.
What is the latest Anna can leave her house and still arrive at the museum on time?
Answer type: Multiple choice type 1
A: 17:27 h
B: 17:30 h
C: 17:45 h
D: 17:38 h
ANSWER: A
WORKING:
To calculate the time for the walk from the depot to the museum:
\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{0.7}{3} = 0.23 hours = 14 minutes
To calculate the time for the bus journey:
\text{Time} = \dfrac{2.2}{25} = 0.088 hours = 5.28 \approx 5 minutes
Adding the times together gives us a total of 19 minutes journey time from the bus stop to the museum.
Subtracting this from 18:00 gives 17:41 but, because the buses go every 15 minutes, the last bus she can get is 17:30 to get her there before 18:00
To calculate the time of the walk from her house to the bus stop:
\text{Time} = \dfrac{0.3}{6} = 0.05 hours = 3 minutes
So, she needs to leave 3 minutes before 17:30, at 17:27, to catch the bus.
QUESTION 5 [4 marks]
A carpet-fitter is laying carpet tiles in a rectangular floor which measures 7.5 m by 4.5 m.
Each carpet tile measures 50 cm by 50 cm.
The carpet fitter already has 100 of these carpet tiles in his van.
How many more carpet tiles will the carpet fitter need to get to be able to cover the whole floor?
Answer type: Simple text answer
ANSWER: 35
WORKING:
750 \times 450 = 337500 cm^2
50 \times 50 = 2500 cm^2
337500 \div 2500 = 135 tiles to cover the whole floor
135 - 100 = 35 carpet tiles needed
QUESTION 6 [4 marks]
Four sales employees from different companies collect their monthly wages. The total monthly wage is comprised of a fixed service wage plus sales related commission.
If the ratio between the service wage and commission is 3:2, how much commission did the four team members earn between them in total? Give your answer in pounds.
Answer type: Simple text answer
ANSWER: £1822
WORKING:
Total wage for all 4 employees =\text{£}1200+\text{£}1000+\text{£}1300+\text{£}1055=\text{£}4555
Number of parts in ratio = 3 + 2 = 5
1 part = \dfrac{\text{£}4555}{5}=\text{£}911
Total wage for all employees earned by commission by all 4 employees = 2 \times £911 = £1822
QUESTION 7 [2 marks]
Two football teams have a head to head of five matches won by the first team, to ten draws, to twenty-five matches won by the second team.
Write this ratio in its simplest form where the first number in the ratio is the amount of matches the first team has won and the last number is the amount of matches won by the second team.
Answer type: Multiple choice type 1
A: 1:2:5
B: 5:2:1
C: 1:5
D: 1:2:10
ANSWER: A
QUESTION 8 [3 marks]
Alex opened an account with £1150 at the Bank.
After one year, with the the bank paying interest there was £1165 in his account.
Work out, as a percentage, the interest rate.
Give your answer to 3 decimal places.
Answer type: Simple text answer
ANSWER: 1.304 \%
WORKING:
x=\dfrac{1165-1150}{1150} \times 100 = 1.304\%
QUESTION 9 [1 mark]
Choose the front elevation of the 3D shape shown.
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A
QUESTION 10 [4 marks]
A form group of 24 Spanish students decide to purchase costumes for an end-of-term party. They all decide to purchase the same outfit from a popular online UK retailer as one order. The costumes are £7.50 each and there is a delivery charge of £18 for the entire order. The group apply a promotional code that gives them 30\% off the price of the costumes.
£1 = €1.10
The group split the total cost between them evenly. How much did each person pay individually, in Euros (€)?
Answer type: Simple text answer
ANSWER: €6.60
WORKING:
Total costume cost = 24\times£7.50=£180
Total costume cost after discount = £180\times0.7=£126
Total cost = £126+£18=£144
Cost per person = \dfrac{£144}{24}=£6
Cost per person in Euros = 6 \times 1.10 = €6.60
QUESTION 11 [3 marks]
John scored 27 out of 42 in a Maths test, 39 out of 61 in a Science test and 50 out of 78 in an English test.
Which subject did John score a higher percentage in?
Answer type: Multiple choice type 1
A: Maths
B: Science
C: English
ANSWER: A
WORKING:
Maths score = \dfrac{27}{42}\times100= 64.3\%
Science score = \dfrac{39}{61}\times100=63.9\%
English score = \dfrac{50}{78} \times 100 = 64.1 \%
So John did better in Maths.
QUESTION 12 [2 marks]
Below is a diagram of a bangle.
You are given that \pi = 3.14
Find the circumference of the bangle.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 13.82 cm
WORKING:
Circumference =2\pi r=2 \times 3.14 \times 2.2 =13.82 cm (2 dp)
QUESTION 13 [2 marks]
10 grains of rice weighs approximately 0.15 g
Work out how many grains of rice are in a 600 g bag of rice.
Answer type: Simple text answer
ANSWER: 40000
WORKING:
1 grain =0.15 \div 10 = 0.015 g
Number of grains in bag = 600 \div 0.015 = 40000 grains
QUESTION 14 [2 marks]
This is a conversion graph between litres and pints.
Using the conversion graph, estimate how many litres there are in 4350 pints.
Answer type: Multiple choice type 1
A: 2500 litres
B: 25 litres
C: 7569 litres
D: 5 litres
ANSWER: A
WORKING:
5 litres =8.7 pints
4350 pints = 4350 \div 8.7 = 500 litres
500 \times 5 = 2500 litres in 4350 pints
QUESTION 15 [4 marks]
The diagram shows a glass in the shape of a cylinder.
The radius of the glass is 5 cm, and the height of the glass is 15 cm
70\% of the glass is filled with water.
Calculate the volume of water in the glass, to 2 decimal places.
Answer type: Simple text answer
ANSWER:
WORKING:
Area of base = 3.14 \times 3^2 = 28.26 cm^2
Volume of glass = 28.26 \times 15 = 423.9 cm^3
Volume of water = 0.7 \times 423.9 = 296.73 cm^3