Paper 1A
QUESTION 1 [1 mark]
Write the following numbers in order of size.
3.2, \,\ 3.27, \, 3.72, \, 3.702, \, 3.02
Start with the smallest number.
Answer type: Multiple choice type 2
A: 3.02, \, 3.2, \, 3.27, \, 3.702, \, 3.72
B: 3.02, \, 3.2, \, 3.27, \, 3.72, \, 3.702
C: 3.72, \, 3.702, \, 3.27, \, 3.2, \, 3.02
D: 3.2, \, 3.02, \, 3.27, \, 3.702, \, 3.72
ANSWER: A
QUESTION 2 [3 marks]
A printer charges 10p to print one black and white page, and 15p to print one colour page.
The ratio of black and white pages to colour pages is 4:1
A student pays £5.50 to print their project.
How many pages is the student’s project?
Answer type: Simple text answer
ANSWER: 50
WORKING:
The ratio of black and white pages to colour pages in pence is 40p :15p
Total: 40 + 15 = 55p
1 part: 550 \div 55 = 10 pages
There are 4 + 1 = 5 parts
So, there are 5 \times 10 pages in total
QUESTION 3 [2 marks]
When Jimmy decides to go to the cinema, he will either go to watch a sci-fi movie, a horror movie, or a romantic comedy.
The probability he chooses a romantic comedy is 0.56. There is an equal chance that he picks a horror movie or a sci-fi movie.
Find the probability Jimmy choose a sci-fi movie or a romantic comedy.
Answer type: Simple text answer
ANSWER: 0.78
WORKING:
1 - 0.56 = 0.44
0.44 \div2 = 0.22
The probability of watching a sci-fi movie is 0.22
The probability of watching a romantic comedy is 0.56
0.22 + 0.56 = 0.78
QUESTION 4 [2 marks]
The distance between two towns on a map measures 8 cm.
The map has a scale of 1:25 000
What is the actual distance between the two towns in km?
Answer type: Simple text answer
ANSWER: 2 km
WORKING:
8 \text{ cm} \times 25000 = 200000 \text{ cm} = 2000\text{ m} = 2\text{ km}
QUESTION 5 [2 marks]
It takes 6 people 2 days to build a shed.
Assuming everyone works at the same rate, how long would it take for 4 people to build the same shed?
Give your answer in days.
Answer type: Simple text answer
ANSWER: 3 days
6 people \times \, 2 days = 12 days of work
12 \div 4 = 3 days
QUESTION 6 [1 mark]
Calculate 6.402+3.545
Answer type: Simple text answer
ANSWER: 9.947
Question 7 [1 mark]
What are the coordinates of the point shown on this grid?
Answer type: Multiple choice type 1
A: (4,3)
B: (3,4)
C: (1,5)
D: (4,4)
ANSWER: A
QUESTION 8 [3 marks]
The mean length of 7 planks of wood is 1.4 m. When an extra plank of wood is added, the mean length of a plank of wood increased to 1.5 m.
What is the length of the extra plank of wood that was added?
Answer type: Simple text answer
ANSWER: 2.2 m
WORKING:
7 \times 1.4 m = 9.8 m
8 \times 1.5 m = 12 m
12 m - \, 9.8 m = 2.2 m
Paper 1B
QUESTION 1 [4 marks]
A pizza with the size of 12 inches in diameter has been cut into 8 slices.
You are given that \pi = 3.14
What is the area of of each slice of pizza?
Give your answer correct to 2 decimal places.
Answer type: Simple text answer
ANSWER: 14.13 inches^2
WORKING:
r = 12\div 2 = 6 inches
Area = 3.14 \times 6^2=113.04 inches^2
For the area of the Slice:
113.04 \div 8 = 14.13 inches^2
QUESTION 2 [2 marks]
John is paid on the first day of every month.
He aims to spend \dfrac{1}{3} of his pay on food and \dfrac{1}{4} of his pay on rent.
What fraction of his pay will John have left? Write your answer in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{5}{12}
WORKING:
\dfrac{1}{4}+\dfrac{1}{3} = \bigg(\dfrac{1}{4}\times \dfrac{3}{3} \bigg)+ \bigg(\dfrac{1}{3}\times \dfrac{4}{4} \bigg)=\dfrac{4}{12}+\dfrac{3}{12}=\dfrac{7}{12}
1-\dfrac{7}{12}=\dfrac{5}{12}
QUESTION 3 [3 marks]
Fifty students were asked how many books they each took to school on Monday.
The results are summarized in the table below.
Calculate the mean number of books that students took to school.
Answer type: Simple text answer
ANSWER: 2.52
WORKING:
\dfrac{(0\times10)+(1\times11)+(2\times8)+(3\times3)+(4\times6)+(5\times7)+(6\times4)+(7\times1)}{50}=2.52
QUESTION 4 [1 mark]
Choose the correct plan view that accurately represents the 3D shape shown.
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A
QUESTION 5 [1 mark]
Peter rolls an ordinary 6 sided dice.
It has faces marked 1, 2, 3, 4, 5 and 6
Write down the probability that he rolls an even number. Give your answer as a decimal.
Answer type: Simple text answer
ANSWER: 0.5
WORKING:
Even numbers: 2, 4 and 6
\dfrac{3}{6} = 0.5
QUESTION 6 [2 marks]
Savannah has an annual income of £19410
She has a personal allowance of £11850, for which doesn’t pay any tax. She pays 20\% tax on the rest of her income.
How much tax will she pay in a year?
Answer type: Simple text answer
ANSWER: £1512
WORKING:
Income that gets taxed = £19410 - £11850 = £7560
20\% of £7560 = £7560 \times 0.2 = £1512
QUESTION 7 [4 marks]
Harry’s electric car has a range of 380 miles when fully charged.
The car has 30\% battery charge remaining.
Harry then travels from Warrington to Birmingham, which is a distance of 128 km.
1 mile = 1.6 km
What percentage of the battery will remain after this journey?
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 8.95 \%
WORKING:
Miles remaining before journey = 0.3 \times 380 = 114
Miles travelled = 128 \div 1.6 = 80 miles
Miles remaining after journey = 114 - 80 = 34 miles
Remaining battery = \dfrac{34}{380} \times 100 = 8.95 \%
QUESTION 8 [5 marks]
Wall tiles are sold either as a single tile or as a box.
Brian needs enough tiles to cover a wall of 4 m^2.
Boxes of tiles are sold full.
Which option should he choose?
Answer type: Multiple choice type 1
A: Single
B: Box
ANSWER: A
WORKING:
Area single =200 cm^3, Area box =3200 cm^3
Area of wall =40000 cm^3
\dfrac{40000}{200} = 200 tiles, \dfrac{40000}{3200} = 12.5 boxes = \, 13 full boxes
Single tile cost: 200 \times £0.49 = £98
Cost of the box of tiles: 13 \times £7.99 = £103.87
Single tiles are better value.
QUESTION 9 [3 marks]
1 cm=0.394 inches
Find the perimeter of the isosceles triangle, in inches.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 8.94 inches
WORKING:
Perimeter in cm =5.6 + 5.6 + 11.5 = 22.7 cm
Perimeter in inches = 22.7 \times 0.394 = 8.94 inches
QUESTION 10 [3 marks]
Nabeel travelled to London by train, her journey was made up of two parts.
One train into York and then another train into London.
The first train departed at 07:05 and the journey lasted for 12 minutes.
The second train departed at 07:27 and the journey lasted for 122 minutes.
The total distance travelled was 197 miles.
What was Nabeela’s average speed for the entire journey in mph to 2 decimal places?
Answer type: Simple text answer
ANSWER: 82.08 mph
WORKING:
Journey time = 12+10+122 = 144 minutes = \, 2.4 hours
\text{Speed} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{197}{2.4} = 82.08 mph
QUESTION 11 [5 marks]
The diagram below shows a cylinder.
The radius of the cylinder is 3 cm and the height is 12 cm.
\dfrac{1}{3} the total surface area of the cylinder is coloured red.
Given that \pi = 3.14
Find the surface area of the cylinder that is coloured red.
Give your answer to 1 decimal place
Answer type: Simple text answer
ANSWER: 94.2 cm^2
WORKING:
Area of top = 3.14 \times3^2=28.26
Area of base = 3.14 \times3^2=28.26
Area of curved surface =12\times6\times3.14=226.08
Surface Area = 28.26 + 28.26 + 226.08 = 282.6 cm^2
Red surface area =\dfrac{1}{3} \times 282.6 = 94.2 cm^2
QUESTION 12
The table gives information about the number of girls and boys in Years 9 and 10.
Question 12(a) [3 marks]
Find the values of a, b, c, d and e from the two-way table above.
Answer type: Multiple answers type 1
ANSWER:
a = 62
b = 159
c = 84
d = 181
e = 355
WORKING:
Question 12(b) [1 mark]
Find the probability that a student selected at random is a boy.
Give your answer to 3 decimal places.
Answer type: Simple text answer
ANSWER: 0.448
WORKING:
Probability of selecting a boy = \dfrac{159}{355} = 0.448
QUESTION 13 [3 marks]
Lucy has £5000. She is looking for the best savings account to save her money for one year.
Bank A pays 2\% compound interest. It adds interest every 6 months.
Bank B pays 3.15\% annual interest rate.
Which bank should the Lucy choose?
Answer type: Multiple choice type 1
A: Bank A
B: Bank B
ANSWER: A
WORKING:
Bank A: £5000 \times 1.02^2 = £5202
Bank B: £5000 \times 1.0315 = £5157.50
Lucy should choose Bank A.
QUESTION 14 [2 marks]
A science experiment takes 1 hour and 20 minutes for a teacher to perform in front of a class. With the aid of an assistant, he can complete the experiment in 40\% less time. How long does it take him to complete the experiment with the help of an assistant?
Give your answer in minutes.
Answer type: Simple text answer
ANSWER: 48 minutes
WORKING:
1 hour and 20 minutes =80 minutes
80 \times 0.6 =48 minutes
QUESTION 15 [3 marks]
The diagram below shows a cuboid, with the following dimensions
Width is 6 cm
Height is 3 cm
Length is 10 cm
The cuboid is made from wood and has a mass of 234 g.
Calculate the density of the cuboid.
Answer type: Simple text answer
ANSWER: 1.3 g/cm^3
WORKING:
Volume = 10 \times 3 \times 6 = 180 cm^3
Density = 234 \div 180 = 1.3 g/cm^3