NOTE: Q20-25 are the same as Q1-6 on Nov 18 Higher Paper 3
(DOESNT NEED CHECKING TWICE – CHANGE BOTH PAPERS IF THERE IS AN ERROR ON BOTH)
Question 1
Find the value of x in each calculation to make them correct.
Question 1(a) [1 mark]
42.6 + x = 90
Answer type: Simple text answer
ANSWER: 47.4
WORKING:
x = 90 - 42.6 = 47.4
Question 1(b) [1 mark]
\dfrac{3}{11} + x = 1
Answer type: Fraction
ANSWER: \dfrac{8}{11}
WORKING:
x = \dfrac{11}{11} - \dfrac{3}{11} = \dfrac{8}{11}
Question 2 [1 mark]
Write 7\% as a fraction in simplest form.
Answer type: Fraction
ANSWER: \dfrac{7}{100}
WORKING:
\% means out of 100
Question 3 [1 mark]
Find \,\,\, \sqrt{1.21}
Answer type: Simple text answer
ANSWER: 1.1
Question 4
Find \dfrac{1}{6} of 840
Answer type: Simple text answer
ANSWER: 140
WORKING:
840 \div 6 = 140
Question 5
Here is a 3D shape.
Question 5(a) [1 mark]
What is the name of this 3D shape?
Answer type: Multiple choice type 1
A: Cylinder
B: Sphere
C: Cuboid
D: Square-based pyramid
ANSWER: A
Question 5(b) [1 mark]
How many faces does this 3D shape have?
Answer type: Simple text answer
ANSWER: 3
Question 6
A fair 10 sided dice is thrown once.
Question 6(a) [1 mark]
Choose the correct probability scale that shows the probability that the dice lands on an even number, marked with a cross.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
WORKING:
The even numbers are 2,4,6,8,10
There are 5 even numbers out of 10
Probability = \dfrac{5}{10} = \dfrac{1}{2}
Question 6(b) [1 mark]
What is the probability that the dice lands on a number less than 3?
Write your answer as a fraction in simplest form.
Answer type: Fraction
ANSWER: \dfrac{1}{5}
WORKING:
Numbers less than 3 are 1 and 2
There are 2 numbers less than 3 out of 10
Probability = \dfrac{2}{10} = \dfrac{1}{5}
Question 7 [2 marks]
Harriot is 1.34 m tall.
Elise is 5 cm smaller than Harriot.
How tall is Elise, in m?
Answer type: Simple text answer
ANSWER: 1.29 m
WORKING:
5 cm = 0.05 m
Elise’s height = 1.34 - 0.05 = 1.29 m
Question 8 [4 marks]
4 rulers cost £1.88
5 protractors £1.70
Harold wants to buy 40 rulers and 40 protractors.
He only has £30 to spend.
Does Harold have enough money to buy 40 rulers and 40 protractors?
Answer type: Multiple choice type 1
A: Yes
B: No
ANSWER: B
WORKING:
Ruler cost = 10 \times £1.88 = £18.80
Protractor cost = 8 \times 1.70 = £13.60
Total cost = £18.80 + £13.60 = £32.40
Harold does not have enough money, since he only has £30 but the cost for the rulers and protractors is £32.40
Question 9
The diagram below shows seven shapes on a centimetre grid.
Question 9(a) [1 mark]
What is the name of shape G?
Answer type: Multiple choice type 1
A: Parallelogram
B: Trapezium
C: Rhombus
D: Kite
ANSWER: A
Question 9(b) [1 mark]
Two of the shapes are congruent.
Write down the letters of these two shapes (In CAPITAL LETTERS)
Answer type: Multiple answers type 2 (Can be either way around)
ANSWERS:
Shape 1 = B
Shape 2 = D
WORKING:
B and D are identical, just rotations of each other, so they are congruent.
Question 10 [1 mark]
On the grid, shape A is reflected onto shape B.
Which mirror line reflects shape A onto shape B?
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
Question 11 [3 marks]
There are men and women at a church.
There are 56 men.
20\% of the people at the church are women.
How many people are at the church in total?
Answer type: Simple text answer
ANSWER: 70
WORKING:
56 men = 80\%
Total = 56 \div 0.8 = 70 people
Question 12 [3 marks]
Jo asked each of 90 people to name their favourite type of chocolate.
Here are her results.
Choose the correct pie chart drawn using her results.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
WORKING:
Question 13 [4 marks]
Alfie sold
25 cakes at £2.40 each
42 cupcakes at £1.10 each
some buns at 60p each
He got a total of £120
How many buns did Alfie sell?
Answer type: Simple text answer
ANSWER: 23
WORKING:
Cakes: 25 \times £2.40 = £60
Cupcakes: 42 \times £1.10 = £46.20
Buns: £120 - £60 - £46.20 = £13.80
Number of buns = 13.80 \div 0.60 = 23
Question 14
Here is a 5-sided spinner.
The table below shows the probabilities that when the spinner is spun it will land on 1, on 2, on 4 and on 5
The spinner is spun once.
Question 14(a) [1 mark]
Calculate the probability that the spinner will land on 3
Answer type: Simple text answer
ANSWER: 0.1
WORKING:
Probability of landing on 3 = 1 - 0.1 - 0.4 - 0.2 - 0.2 = 0.1
Question 14(b)
Which number is the spinner most likely to land on?
Answer type: Simple text answer
ANSWER: 2
WORKING:
2 has the greatest probability
Question 14(c) [2 marks]
Herman is going to spin the spinner 40 times.
Work out an estimate for the number of times the spinner will land on 5
Answer type: Simple text answer
ANSWER: 8
WORKING:
40 \times 0.2 = 8
Question 15 [3 marks]
Dani has a deck of 50 cards.
There is a whole number from 1 to 50 on each card, with no cards having the same number.
Dani puts a triangle on every card that has a multiple of 2 on it.
She puts a square on every card that has a multiple of 3 on it.
How many cards have both a triangle and a square on them?
Answer type: Simple text answer
ANSWER: 8
WORKING:
Cards with both are multiples of 2 \times 3 = 6
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
So, there are 8 cards with both a triangle and a square on them
Question 16 [2 marks]
What is the ratio of 350 ml to 25 ml in its simplest form?
Answer type: Multiple choice type 1
A: 14:1
B: 1:14
C: 70:5
D: 5:70
ANSWER: A
WORKING:
350:25
Divide both sides by 25 to get 14:1
Question 17
The diagram below shows a quadrilateral.
The quadrilateral has one line of symmetry.
AB = 2x
BC = 3x+1
All measurements are given in centimetres.
The perimeter of the quadrilateral is 24 cm
Question 17(a) [3 marks]
Show that ax+b = 24 by finding the values of a and b
Answer type: Multiple answers type 1
ANSWERS:
a = 10
b = 2
WORKING:
There is one line of symmetry, so AB = AD = 2x and BC = CD = 3x+1
Perimeter = (2x) + (2x) + (3x+1) + (3x+1) = 24
10x + 2 = 24
So, a = 10 and b = 2
Question 17(b) [2 marks]
Find the value of x
Answer type: Simple text answer
ANSWER: 2.2 cm
WORKING:
10x + 2 = 24
10x = 22
x = 2.2 cm
Question 18 [4 marks]
Timothy buys a motorbike.
The cost of the motorbike is £8400 plus VAT at 20 \%
Timothy pays a deposit of £3000
He pays the rest of the cost in 12 equal payments.
Calculate the cost of each of the 12 payments.
Answer type: Simple text answer
ANSWERL £590
WORKING:
Cost = £8400 \times 1.20 = £10080
Balance remaining after deposit = £10080 - £3000 = £7080
Payment cost = £7080 \div 12 = £590
Question 19
Question 19(a) [2 marks]
Which inequality is represented on the number line?
Answer type: Multiple choice type 1
A: x > -3
B: x \geq -3
C: x < -3
D: x \leq -3
ANSWER: A
WORKING:
A hollow circle means that the inequality is strict (< or >)
The arrow points to the right, to the values greater than -3
So, x>-3 is the inequality
Question 19(b) [2 marks]
-1 \leq y < 4 where y is an integer.
What are all the possible values of y?
Answer type: Multiple choice type 1
A: -1, 0, 1, 2, 3
B: -1, 0, 1, 2, 3, 4
C: 0,1,2,3,4
D: 0,1,2,3
ANSWER: A
WORKING:
-1 \leq y means that y is greater than or equal to -1
y < 4 means that y is less than 4, and not equal to it
-1 \leq y < 4 means that we can only have the numbers -1, 0, 1, 2, 3
Question 19(c) [3 marks]
Solve 4x+6 \leq x+15
Fill in the inequality.
Answer type: Simple text answer
ANSWER: x \leq 3
WORKING:
4x+6 \leq x+15
4x \leq x + 9
3x \leq 9
x \leq 3
Question 20(a) [1 mark]
Write 31897 correct to 4 significant figures
Answer type: Simple text answer
ANSWER: 31900
Question 20(b) [2 marks]
What is \dfrac{\sqrt{72 - 4^3}}{2.3^2} correct to 5 decimal places?
Answer type: Simple text answer
ANSWER: 0.53467
WORKING:
\dfrac{\sqrt{72 - 4^3}}{2.3^2} = 0.5346743146 = 0.53467 (5 dp)
Question 21 [3 marks]
Last year David paid £362 for his life insurance.
This year he has to pay £926 for his life insurance.
What is the percentage increase in the cost of his life insurance?
Write your answer to 1 decimal place.
Answer type: Simple text answer
ANSWER: 155.8\%
WORKING:
Increase =926 - 362 = 564
\% increase = \dfrac{564}{362} \times 100 = 155.801105 = 155.8\% (1 dp)
Question 22
Question 22(a) [2 marks]
Find the values of a, b, c and d to complete this table of values for y=x^2+2x-2
Answer type: Multiple answers type 1
ANSWERS:
a = 1
b = -2
c = -2
d = 6
WORKING:
Substitute the values of x into the equation to find the values of y.
Question 22(b) [2 marks]
Choose the correct plot of y = x^2+2x-2 for values of x between -3 and 2
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
Question 22(c) [1 mark]
Use the graph to estimate a solution to x^2 + 2x - 2 = 0
Answer type: Multiple choice type 1
A: x = 0.7 or x = -2.7
B: x = 1.3 or x = -1.3
C: x = 1 or x = 3
D: x = 1.7 or x = -1.7
ANSWER: A
WORKING:
We want to find the x values where the graph crosses the x axis.
This happens at x = 0.7 or x = -2.7
Question 23
Fred asks 30 individuals how many jumpers they bought last year.
The chart below shows information about the number of jumpers bought by each of the 30 individuals.
Question 23(a) [2 marks]
What is the percentage of these individuals who bought less than 10 jumpers?
Answer type: Simple text answer
ANSWER: 40\%
WORKING:
Less than 10 jumpers =12 individuals
\dfrac{12}{30} \times 100 = 40\%
Question 23(b) [4 marks]
What is an estimate for the mean number of jumpers bought?
Answer type: Multiple choice
A: 9.3
B: 3.9
C: 10.4
D: 4.1
ANSWER: A
WORKING:
8 + 4 + 15 + 2 + 1 = 30
16 + 28 + 180 + 34 + 22 = 280
Estimated mean = \dfrac{280}{30} = 9.3
Question 24
Rita is a mountain biker.
She completed a bike race in 4 minutes 34 seconds
The race was 2.2 km in length.
Rita assumes that her average speed is the same for each race.
Question 24(a) [3 marks]
Using this assumption, calculate how long it would take Rita to complete a 4 km race.
Give your answer in minutes and seconds, to the nearest second.
Answer type: Multiple choice type 1
A: 8 minutes 18 seconds
B: 7 minutes 24 seconds
C: 9 minutes 8 seconds
D: 8 minutes 46 seconds
ANSWER: A
WORKING:
2.2 km = 2200 m
4 mins 34 seconds = 240 + 34 = 274 seconds
Average speed = \dfrac{2200}{274} = 8.029... m/s
4 km = 4000 m
Time = \dfrac{4000}{8.029...} = 498.181... seconds
498.181... seconds \div \, 60 = 8.303... minutes = 8 minutes 18 seconds (nearest second)
Question 24(b) [1 mark]
Rita’s average speed actually decreases the further she goes.
How does this affect your answer to part (a)?
Answer type: Multiple choice type 1
A: The race would take more time
B: The race would take less time
C: The race would take the same amount of time
ANSWER: A
Question 25 [4 marks]
ABC is a right-angled triangle.
AB = 6 cm
Angle C = 90 \degree
Size of angle A : Size of angle C = 1:2
Calculate the length of AC
Give your answer to 3 significant figures.
Answer type: Simple text answer
ANSWER: 6.93 cm
WORKING:
\angle A + \angle C = 180 \degree - 90 \degree = 90 \degree
Number of parts in ratio = 1 + 2 = 3
90 \div 3 = 30 \degree
So, \angle A = 30 \degree and \angle C = 2 \times 30 \degree = 60 \degree
Then, SOHCAHTOA to find AC, which we will call x
\sin \theta = \dfrac{\text{O}}{\text{H}}
\sin 60 \degree = \dfrac{6}{x}
x = \dfrac{6}{\sin 60 \degree} = 6.93 cm (3 sf)
Question 26 [2 marks]
Here are the first four terms of an arithmetic sequence.
6 \,\,\,\,\,\,\,\,\,\, 13 \,\,\,\,\,\,\,\,\,\, 20 \,\,\,\,\,\,\,\,\,\, 27
Find the nth term of the sequence, in the form an+b
Answer type: Multiple answers type 1
ANSWERS:
a = 7
b = -1
WORKING:
The difference between terms is 7, so a = 7
If you minus 7 from the first term you get 6 - 7 = -1, so b = -1
The nth term is 7n-1