NOTE: Q21-26 are the same as Q1-6 on June 17 Higher Paper 1
(DOESNT NEED CHECKING TWICE – CHANGE BOTH PAPERS IF THERE IS AN ERROR ON BOTH)
Question 1 [1 mark]
What is the value of 3^3?
Answer type: Simple text answer
ANSWER: 27
Question 2 [1 mark]
Write 6.28265 correct to 3 decimal places.
Answer type: Simple text answer
ANSWER: 6.283
Question 3
Answer the following questions.
Question 3(a) [1 mark]
What is 5 \times x \times y \times 11 simplified?
Answer type: Multiple choice type 1
A: 55xy
B: 16xy
C: 55x + 55y
D: 55+xy
ANSWER: A
Question 3(b) [1 mark]
Solve \dfrac{x}{3} = 5 \dfrac{1}{6}
Write your answer as an improper fraction.
Answer type: Fraction
ANSWER: \dfrac{31}{2}
WORKING:
x = 3 \times 5 \dfrac{1}{6} = 3 \times \dfrac{31}{6} = \dfrac{31}{2}
Question 4 [1 mark]
What is \dfrac{3}{4} as a percentage?
Answer type: Simple text answer
ANSWER: 75 \%
Question 5 [2 marks]
What is 40 \% of 90?
Answer type: Simple text answer
ANSWER: 36
WORKING:
10\% of 90 =9\%
So 40\% of 90 =4\times9=36\%
Question 6
Sherise spins a fair 4 sided spinner.
Question 6(a) [1 mark]
What is the probability that the spinner lands on an even number?
Answer type: Simple text answer
ANSWER: 0.5
WORKING:
Two of the four numbers on the spinner are even (2 and 4)
Question 6(b) [1 mark]
What is the probability that the spinner lands on the number 5?
Answer type: Simple text answer
ANSWER: 0
WORKING:
The number 5 doesn’t appear on the spinner.
Question 7 [3 marks]
Tamwar buys
4 packets of rice, costing 50p each
1 box of cereal costing £1.20
2 tins of beans
Tamwar pays with a £5 note.
He gets £1 change.
What is the price of one tin of beans?
Give your answer in pence.
Answer type: Simple text answer
ANSWER: 40p
WORKING:
Let the price of a tin of beans be x
4 \times £0.50 = £2.00
1 \times £1.20 = £1.20
2 \times x = 2x
Total = 2 + 1.20 + 2x = 3.20 + 2x
5.00 - 1.00 = £4.00 spent
3.20 + 2x = 4.00
2x = 0.80
x = £0.40 = 40p
Question 8
Answer the following questions.
Question 8(a) [1 mark]
Work out \dfrac{2}{9} \times \dfrac{2}{3}
Answer type: Fraction
ANSWER: \dfrac{4}{27}
WORKING:
\dfrac{2}{9} \times \dfrac{2}{3} = \dfrac{2 \times 2}{9 \times 3} = \dfrac{4}{27}
Question 8(b) [2 marks]
Work out \dfrac{7}{10} - \dfrac{2}{5}
Answer type: Fraction
ANSWER: \dfrac{3}{10}
WORKING:
\dfrac{7}{10} - \dfrac{2}{5} = \dfrac{7}{10} - \dfrac{4}{10} = \dfrac{7-4}{10} = \dfrac{3}{10}
Question 9 [4 marks]
Kimberley works for a company.
Her normal rate of pay is £13 per hour.
If she works for more than 10 hours a day, she is paid overtime for each hour she works more than 10 hours.
Kimberley’s rate of overtime is 1.5 times her normal rate of pay per hour.
On Friday, Kimberley works for 12 hours.
How much did she earn on Friday?
Answer type: Simple text answer
ANSWER: £169
WORKING:
Overtime rate = 1.5 \times £13 = £19.50 per hour
She works 10 hours at normal pay and 2 hours at overtime pay
She earns (10 \times £13) + (2 \times £19.50) = £169
Question 10 [2 marks]
Sheila has 10 packets of biscuits.
Each pack of biscuits contains 8 biscuits.
Find the ratio of the number of biscuits in 3 packets to the total number of biscuits, in its simplest form.
Choose the correct answer.
Answer type: Multiple choice type 1
A: 3:10
B: 3:1
C: 1:10
D: 4:5
ANSWER: A
WORKING:
Total: 8 \times 10 = 80
3 packets: 8 \times 3 = 24
24:80 can be simplified to 3:10
Question 11
A sequence of patterns is made from square shapes 
and triangle shapes 
Below are the first three patterns in the sequence.
Question 11(a) [2 marks]
How many square shapes are needed to make pattern 5?
Answer type: Simple text answer
ANSWER: 9
WORKING:
1, 3, 5, ...If we carry on the sequence we get 7 for pattern 4 and then 9 for pattern 5
(The nth term is 2n-1)
Question 11(b) [2 marks]
How many triangle shapes are needed for pattern 30?
Answer type: Simple text answer
ANSWER: 120
WORKING:
4,8,12,...The nth term is 4n
So for pattern 30 there are 4 \times 30 = 120 triangles
Question 11(c) [2 marks]
What is the total number of shapes needed for pattern 10?
Answer type: Simple text answer
ANSWER: 59
WORKING:
If we add the nth terms together for both sequences, we get (2n-1) + (4n) = 6n-1.
So for pattern 10 there are 6 \times 10 - 1 = 59 shapes in total.
Question 12 [2 marks]
There are 5 red crayons, 10 pink crayons and 7 purple crayons in a box.
One crayon is taken at random from the box.
What is the probability that this crayon is purple?
Answer type: Fraction
ANSWER: \dfrac{7}{22}
WORKING:
Number of crayons in a the box = 5 + 10 + 7 = 22.
There are 7 purple crayons out of 22.
Probability of purple = \dfrac{7}{22}.
Question 13
The diagram shows a black ball, a grey ball and a white ball.
The diameter of the white ball is 4 cm.
All three balls are drawn to the same scale.
Question 13(a) [1 mark]
Estimate the diameter of the grey ball, giving your answer to the nearest cm.
Answer type: Simple text answer
ANSWER: 8cm
WORKING:
The diameter of the grey ball is twice the diameter of the white ball.
Question 13(b) [2 marks]
Estimate the diameter of the black ball, giving your answer to the nearest cm.
Answer type: Simple text answer
ANSWER: 16 cm
WORKING:
The diameter of the black ball is four times the diameter of the white ball.
Question 14
A group of people were surveyed about their features.
The table below shows information about their eye colours.
Question 14(a) [3 marks]
Choose the correct pie chart that represents this information.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
WORKING:
There were 25+40+15+10 = 90 people surveyed in total.
We can then calculate our angles using the following formula:
\text{angle} = \dfrac{\text{number of things in that category}}{\text{total number of things}} \times 360 \degree
The results are shown in the table below.
Question 14(b) [1 mark]
A second group of people were surveyed on their features.
The accurate pie chart below shows information about their eye colour.
Jamaal says,
“The pie chart shows that there were more people with brown eyes in the second group than the first group”
Is Jamaal correct?
Answer type: Multiple choice type 1
A: Yes
B: No
ANSWER: B
WORKING:
No, we don’t have any figures for the second group, just angles, so we don’t know how many people had brown eyes.
Question 15 [4 marks]
Below is a triangle and a square.
The area of the triangle is twice the area of the square.
Work out the length, x, of one side of the square.
Answer type: simple text
ANSWER: x= 6 cm
WORKING:
Area of triangle = \dfrac{1}{2} \times 16 \times 9 = 72 cm^2
Area of square = 72 \div 2 = 36 cm^2
Area of square = 36 = x^2
x = \sqrt{36} = 6 cm
Question 16 [2 marks]
t = \dfrac{2s}{u+v}
s = 6, u = 3, v = 1
What is the value of t?
Answer type: Simple Text
ANSWER: 3
WORKING:
t = \dfrac{2 \times 6}{3+1} = \dfrac{12}{4} = 3
Question 17 [4 marks]
6 bars of chocolate have a total weight of 900 g
4 bars of chocolate and 2 packets of chocolate have a total weight of 820 g
What is the total weight of 5 bars of chocolate and 3 packets of chocolate?
Answer type: Simple text answer
ANSWER: 1080 g
WORKING:
Let b be the weight of one bar, and p be the weight of one packet.
b = 900 \div 6 = 150 g
4b + 2p = 820
4(150) + 2p = 820
600 + 2p = 820
2p = 220
p = 110 g
5b + 3p = 5(150) + 3(110) = 1080 g
Question 18
Larissa has a garden in the shape of a circle of radius 5 m
She is going to cover the garden with lawn feed.
Lawn feed is sold in bottles.
Each bottle of lawn feed covers 20 m^2
Larissa wants to cover all of the garden with lawn feed.
Question 18(a) [4 marks]
Estimate the number of bottles of lawn feed that Larissa will need to buy.
Answer type: Simple text answer
ANSWER: 4 bottles
WORKING:
Take \pi \approx 3
Area of garden = \pi r^2 \approx 3 \times 5^2 = 3 \times 25 = 75 m^2
Number of bottles needed = \dfrac{75}{20} = 3.75 = 4 whole bottles
Question 18(b) [1 mark]
If Larissa wanted to buy enough lawn feed to cover her garden twice, how many bottles would she need?
Answer type: simple text
ANSWER: 8 bottles
WORKING:
4 \times 2 = 8 bottles.
Question 19
Answer the following questions.
Question 19(a) [2 marks]
Solve 2(x-5)=3
Answer type: Simple text answer
ANSWER: 6.5
WORKING:
2x-10=3
2x=13
x = 6.5
Question 19(b) [2 marks]
-1 \leq y < 3y is an integer.
What are the possible values of y?
Answer type: Multiple choice type 1
A: -1,0,1,2
B: 0,1,2
C: 0,1,2,3
D: -1
ANSWER: A
WORKING:
-1 is included but 3 isn’t.
All values in between are included.
Question 20 [2 marks]
Donald’s wage is £1800 per month.
He is going to get a 5 \% increase in his wage.
What is Donald’s new wage per month after the increase?
Answer type: Simple text answer
ANSWER: £1890
WORKING:
10\% of 1800=180
So 5\% of 1800=\dfrac{180}{2}=90
£1800+£90=£1890
Question 21
The scatter graph shows the maximum temperature and the number of hours of sunshine in fourteen German Cities on one day.
Question 21(a) [1 mark]
One of the points is an outlier.
What are the coordinates of this point?
Answer type: Multiple choice type 1
A: (10, 18)
B: (15, 20)
C: (18, 10)
D: (20, 15)
Answer type: Simple text answer
ANSWER: A
Question 21(b) [1 mark]
For all the other points, what is the type of correlation?
Answer type: Multiple choice type 1
A: Positive correlation
B: Negative correlation
C: No correlation
ANSWER: A
Question 21(c) [2 marks]
On the same day, in another German City, the maximum temperature was 17.2 \degree C.
Choose the closest estimate for the number of hours of sunshine in this City on this day.
Answer type: Multiple choice type 1
A: 13 hours
B: 15 hours
C: 11 hours
D: 18 hours
ANSWER: A
Question 21(d) [1 mark]
A weatherman says,
“Temperatures are higher on days when there is more sunshine.”
Does the scatter graph support what the weatherman says?
Answer type: Multiple choice type 1
A: Yes
B: No
ANSWER: A
WORKING:
Yes, as the majority of points for high temperatures appear when there are more hours of sunshine (i.e. there is a positive correlation)
Question 22 [2 marks]
Express 48 as the product of its prime factors in index form.
Choose the correct expression.
Answer type: Multiple choice type 1
A: 2^4 \times 3
B: 2^3 \times 3
C: 2^3 \times 3^2
D: 2 \times 3^3
ANSWER: A
WORKING:
Use a prime factor tree:
48 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3
Question 23 [3 marks]
Work out 46.3 \times 5.2
Answer type: Simple text answer
ANSWER: 240.76
WORKING:
Move the decimal places on each number, to make them easier to use to calculate.
20000 + 3000 + 150 = 23150
800 + 120 + 6 = 926
23150 + 926 = 24076
Now move the decimal place back, to get 240.76
Question 24 [3 marks]
The area of the square ABCD is 12 cm^2.
What is the correct equation formed from this information?
Answer type: Multiple choice type 1
A: x^2 + 4x = 8
B: x^2 + 2x = 8
C: x^2 + 4x = 12
D: x^2 + 4x = 4
ANSWER: A
WORKING:
(x+2)^2 = 12
x^2 + 4x + 4 = 12
x^2 + 4x = 8
Question 25 [5 marks]
A rectangular frame is made from 5 straight pieces of metal, as seen below.
The mass of the metal is 2.5 kg per metre.
What is the total mass of the metal in this frame?
Answer type: Simple text answer
ANSWER: 95 kg
WOKRING:
Calculate the length of the diagonal by using Pythagoras’ theorem:
\sqrt{6^2 + 8^2} = \sqrt{100} = 10 m
Add together the lengths of all five pieces of metal:
6+6+8+8+10 = 38 m
Multiply this by 2.5 kg to calculate the total mass of the frame:
38 \times 2.5 = 95 kg
Question 26 [2 marks]
The equation of line A is y = 4x - 1
The equation of line B is 2y - 8x - 9 = 0
Are these two lines parallel, perpendicular or neither?
Answer type: Multiple choice type 1
A: Parallel
B: Perpendicular
C: Neither
ANSWER: A
WORKING:
Rearrange the equation of line B:
2y - 8x - 9 = 0
2y = 8x + 9
y = 4x + \dfrac{9}{2}
Line A and Line B have the same gradient, so are parallel.
Question 27
ABCD is a rectangle.
The diagonals of the rectangle intersect at O.
\overrightarrow{OA} = \textbf{a} and \overrightarrow{OB} = \textbf{b}
Question 27(a) [1 mark]
What is the vector \overrightarrow{CA} in terms of \textbf{a} and \textbf{b}?
Answer type: Multiple choice type 1
A: 2\textbf{a}
B: \textbf{a} + \textbf{b}
C: 2\textbf{b}
D: -2\textbf{a}
ANSWER: A
Question 27(b) [1 mark]
What is the vector \overrightarrow{BA} in terms of \textbf{a} and \textbf{b}?
Answer type: Multiple choice type 1
A: \textbf{a} - \textbf{b}
B: \textbf{a} + \textbf{b}
C: \textbf{b} - \textbf{a}
D: 2\textbf{a} - \textbf{b}
ANSWER: A
Question 27(c) [1 mark]
What is the vector \overrightarrow{BC} in terms of \textbf{a} and \textbf{b}?
Answer type: Multiple choice type 1
A: - \textbf{a} - \textbf{b}
B: \textbf{a} - \textbf{b}
C: \textbf{b} - \textbf{a}
D: 2\textbf{a} - \textbf{b}
ANSWER: A