PAPER 6
PAPER 6A
QUESTION 1 [1 mark]
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 [1 mark]
Evaluate [(3^3 - 2^3 )+5]\div6
Answer type: Simple text answer
ANSWER: 4
WORKING:
[(3^3 - 2^3 )+5]\div6=[(27-8)+5)]\div6=[19+5]\div6=24\div6=4QUESTION 3 [1 mark]
What is 12\% of 600 GB?
Answer type: Simple text answer
ANSWER: 72 GB
WORKING:
600\text{ GB}\times0.12=72\text{ GB}QUESTION 4 [1 mark]
What is \, 5\dfrac{1}{4} - 1\dfrac{1}{5} as a mixed number fraction?
Answer type: Multiple choice type 1
A: 4\frac{1}{20}
B: 10\frac{11}{20}
C: 1\frac{1}{20}
D: 4\frac{11}{20}
ANSWER: A
5\dfrac{1}{4} - 1\dfrac{1}{5}= \dfrac{21}{4}-\dfrac{6}{5}=\dfrac{21\times5}{20}-\dfrac{6\times4}{20}=\dfrac{81}{20}=4\dfrac{1}{20}QUESTION 5 [1 mark]
This is a conversion graph between litres and pints.
Using the conversion graph, what is 5 litres in pints?
Give your answer to 1 decimal place.
Answer type: Simple text answer
ANSWER: 8.7 pints
WORKING:
QUESTION 6 [1 mark]
What is 60\times400\div30 ?
Answer type: Simple text answer
ANSWER: 800
QUESTION 7 [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 8 [1 mark]
Express 0.125 as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{1}{8}
QUESTION 9 [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 10 [1 mark]
Write the number 58051 in words.
Answer type: Multiple choice type 1
A: Fifty eight thousand and fifty one.
B: Fifty eight thousand, five hundred and one.
C: Five thousand, eight hundred and fifty one.
D: Fifty thousand, eight hundred and fifty one.
ANSWER: A
QUESTION 11 [1 mark]
Calculate 106.284-38.691
Answer type: Simple text answer
ANSWER: 67.593
QUESTION 12 [1 mark]
If 60 g of sweets cost £1.10, find the cost of 300 g of sweets.
Answer type: Simple text answer
ANSWER: £5.50
WORKING:
\dfrac{1.10}{60} \times 300 = £5.50
QUESTION 13 [1 mark]
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 black pen from the box?
Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{4}{15}
WORKING:
\dfrac{8}{8+12+10}=\dfrac{4}{15}QUESTION 14 [1 mark]
3 quarters of the 36 pupils in a class are expected to achieve a grade C or above. How many people in the class are expected to achieve a grade C or above?
Answer type: Simple text answer
ANSWER: 27
WORKING:
36\times0.75=27QUESTION 15 [1 mark]
What is the value of 12a-5ab when a=3 and b=4?
Answer type: Simple text answer
ANSWER: – 24
WORKING:
12\times3-5\times3\times4=-24
PAPER 6B
QUESTION 1 [1 mark]
Write the numbers in increasing order starting with the smallest.
968,\,\,\,\, 947,\,\,\,\, 989, \,\,\,\, 993, \,\,\,\, 998
Answer type: Multiple choice type 1
A: 947,\,\,\,\, 968,\,\,\,\, 989, \,\,\,\, 993, \,\,\,\, 998
B: 947,\,\,\,\, 968,\,\,\,\, 998, \,\,\,\, 993, \,\,\,\, 989
C: 947,\,\,\,\, 968,\,\,\,\, 989, \,\,\,\, 998, \,\,\,\, 993
D: 998,\,\,\,\, 993,\,\,\,\, 989, \,\,\,\, 968, \,\,\,\, 947
ANSWER: A
QUESTION 2 [1 mark]
Work out 2.5^2-2.1^2
Answer type: Simple text answer
ANSWER: 1.84
QUESTION 3 [1 mark]
Which of the following plan views accurately represents the 3D shapes shown?
Answer type: Multiple choice type 1
A: 
B: 
C: 
ANSWER: A
QUESTION 4 [2 marks]
Work out the percentage increase from 1250 to 1750
Answer type: Simple text answer
ANSWER: 40 \%
WORKING:
1750-1250=500\\ \dfrac{500}{1250}=40\%QUESTION 5 [2 marks]
What is \, \dfrac{11}{3} - \dfrac{7}{6} ?
Give your answer as an improper fraction.
Answer type: Fraction
ANSWER: \dfrac{5}{2}
\dfrac{11}{3} - \dfrac{7}{6}=\dfrac{22}{6} - \dfrac{7}{6}=\dfrac{15}{6}=\dfrac{5}{2}QUESTION 6 [2 marks]
Dani recorded the heights of members of her extended family, to the nearest cm :
163, \,\, \, 185, \,\, \, 164, \,\, \, 170, \,\, \, 188, \,\, \, 154, \,\, \, 168, \,\, \, 179
Find the median of their heights.
Answer type: Simple text answer
ANSWER: 169
WORKING:
The heights ordered smallest to largest 154, \,\, \, 163, \,\, \, 164, \,\, \, 168, \,\, \, 170, \,\, \, 179, \,\, \, 185, \,\, \, 188
\dfrac{8 + 1}{2}=4.5
The 4th value is 168 and the 5th value is 170, so the median is 169
QUESTION 7 [6 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:
Estimated mean = \dfrac{373}{45}= 8.29 minutes
QUESTION 8 [4 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 9 [2 mark]
Work out \dfrac{148.221-28.837}{81}
Give your answer as a decimal rounded to 3 decimal places.
Answer type: Simple text answer
ANSWER: 1.474
QUESTION 10 [8 mark]
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 bus Anna can catch and still arrive at the museum on time?
Answer type: Multiple choice type 1
A: 17:30 h
B: 17:45 h
C: 17:15 h
D: 17:38 h
ANSWER: A
WORKING:
Walk from the depot to the museum:
\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{0.7}{3} = 0.23 hours = \, 14 minutes
Bus journey:
\text{Time} = \dfrac{2.2}{25} = 0.088 hours = \, 5 minutes
Walk from her house to the bus stop:
\text{Time} = \dfrac{0.3}{6} = 0.05 hours = \, 3 minutes
22 minutes journey time. Subtracting this from 18:00 gives 17:38 but, because the buses go every 15 minutes, the last bus she can get is 17:30
QUESTION 11 [5 marks]
The diagram shows a parallelogram and two triangles within a rectangle, ADEB.
CD = x, DE = x, FE = 2 cm
If x = 4 cm, work out the area of the rectangle ADEB.
Answer type: Simple text answer
ANSWER: 24 cm^2
WORKING:
AD = 4 + 2 = 6 cm
DE = 4 cm
Area = 6 \times 4 = 24 cm^2
QUESTION 12 [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 4:1, how much commission did the four team members earn between them in total? Give your answer in pounds.
Answer type: Simple text answer
ANSWER: £911
WORKING:
Total wage for all 4 employees =\text{£}1200+\text{£}1000+\text{£}1300+\text{£}1055=\text{£}4555
Total wage for all employees earned by commission by all 4 employees = \dfrac{\text{£}4555}{5}=\text{£}911
QUESTION 13 [2 marks]
A grain of rice weighs approximately 0.015 g
Work out how many grains of rice are in a 600 g bag of rice.
Answer type: Simple text answer
ANSWER: 40000
WORKING:
600 \div 0.015 = 40000 grains
QUESTION 14 [3 marks]
A plane flies between two airports that are 7130 km apart.
Given that the plane travels at a constant speed of 920 km/h, determine the time the journey took in hours and minutes.
Answer type: Multiple choice type 1
A: 7 hours and 45 minutes
B: 7 hours and 15 minutes
C: 8 hours and 15 minutes
D: 7 hours and 48 minutes
ANSWER: A
WORKING:
\text{time }=\dfrac{\text{distance}}{\text{speed}}=\dfrac{7130}{920}=7.75 hours
So, we have 7 hours and 0.75 hours (7 hours and 45 minutes)
QUESTION 15 [2 marks]
32\% of people voted for the green party in a local election.
What fraction of people voted for the green party?
Write the fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{8}{25}