Ultimate Exam Question Finder
Every question from real past papers, each with its mark scheme, a worked solution and a shadow: the same question with new numbers.
AQA GCSE Higher November 2024 Paper 2 (calculator)
24 questions · 80 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.
Question 1 (3 marks)
Choose a word from the list below to complete each sentence.
arc centre circumference diameter radius sector segment tangent (a)
The length of the underline is double the length of the radius.
(1 mark)
(b)
A underline is a region created by drawing a chord through a circle.
(1 mark)
(c)
A radius meets a underline at a right angle.
(1 mark)
Question 2 (3 marks)
Here is a grouped frequency table.
Value, v Frequency Midpoint 0 ≤ v < 10 16 5 10 ≤ v < 20 22 15 20 ≤ v < 30 13 25 30 ≤ v < 40 9 35 Total = 60 Work out an estimate of the mean value.
(3 marks)
Question 3 (2 marks)
In the grid below, shade one quarter of the squares
so that the grid has exactly two lines of symmetry.
Shade complete squares only.Diagram: A grid of 4 by 4 squares, none shaded.
(2 marks)
Question 4 (3 marks)
A map has a scale of 1 : 4000
On the map, the distance from a station to a museum is 7 cm
Is the actual distance from the station to the museum more than 300 m?
Tick a box.
Yes square No square Show working to support your answer.
(3 marks)
Question 5 (1 mark)
X is inversely proportional to Y.
Circle the correct statement.
X is directly proportional to Y X is directly proportional to 1/Y X is directly proportional to 2Y X is directly proportional to √Y (1 mark)
Question 6 (2 marks)
Here is a right-angled triangle.
Diagram: A right-angled triangle with the right angle at the bottom left. The side going up is x cm, the side along the bottom is 1.5 cm and the sloping side is 1.7 cm.
Use Pythagoras’ theorem to show that x = 0.8
(2 marks)
Question 7 (3 marks)
Beth and Lynn each spin the same biased coin a number of times.
The table shows information about the results.Beth Lynn Number of spins 125 80 Relative frequency of Heads 0.32 0.35 (a)
How many more Heads did Beth spin than Lynn?
(2 marks)
(b)
Lynn says,
“My estimate of the probability of the coin landing on Heads must be the best,
because 0.35 is greater than 0.32”Is she correct?
Tick a box.
Yes square No square Give a reason for your answer.
(1 mark)
Question 8 (2 marks)
Some oil has
a mass of 537 g
a density of 895 000 g/m³1 m³ = 1000 litres
Work out the volume of the oil.
Give your answer in litres.(2 marks)
Question 9 (2 marks)
The length of a wall is 9 metres to the nearest metre.
Complete the error interval for the length of the wall.(2 marks)
Question 10 (3 marks)
384 000 electric cars were sold this year.
This is 20% more than last year.How many were sold last year?
(3 marks)
Question 11 (3 marks)
Here are three terms.
xy x² 5y²
Alec multiplies two of these terms.
Work out the three possible fully simplified answers.(3 marks)
Question 12 (4 marks)
At a music festival, four types of instrument are played.
guitars keyboards drums trumpets • The total number of instruments is 80
• Half of the instruments are guitars.
• keyboards : drums : trumpets = 3 : 4 : 1How many keyboards are there?
(4 marks)
Question 13 (4 marks)
Two right-angled triangles are joined to make a larger triangle.
Diagram: Two right-angled triangles joined along a shared vertical side to make one larger triangle. The left triangle has a sloping side of 14 cm and angle x at its bottom left corner. The right triangle has a base of 15 cm (an arrow under it runs from the foot of the shared side to the bottom right corner) and an angle of 38° at its bottom right corner. The right angles are at the foot of the shared side.
Work out the size of angle x.
(4 marks)
Question 14 (1 mark)
Here is a sign in a shop.
SALE
20% OFF ALL ITEMS
TODAY ONLY 10% OFF THE REDUCED PRICE
THAT MEANS YOU SAVE 30%Is the sign correct?
Tick a box.Yes square No square Give a reason for your answer.
(1 mark)
Question 15 (4 marks)
AB and CD are straight, parallel lines.
P is a point on AB.
Q is a point on CD.
AP = AQDiagram: Two parallel horizontal lines, AB above CD. P is on AB and Q is on CD, below and to the left of P. AP and AQ are marked equal. The line from Q through P carries on above AB. The angle PAQ at A is marked 2x and the angle between QD and QP at Q is marked 5x + 6.
Work out the value of x.
(4 marks)
Question 16 (4 marks)
Solve (x + 2)(x – 5) = 6x
(4 marks)
Question 17 (2 marks)
Straight line LM has equation y = 4x – 7
Straight line ST has equation y = (9 – x)/4
Are the lines LM and ST perpendicular?
Tick a box.Yes square No square Give a reason for your answer.
(2 marks)
Question 18 (7 marks)
Two types of battery, P and Q, were tested.
100 of each type were put into clocks.
The number of days each battery lasted was recorded.(a)
The frequency table represents the results for type P.
Number of days, d Frequency 0 ≤ d < 40 2 40 ≤ d < 80 9 80 ≤ d < 120 26 120 ≤ d < 160 45 160 ≤ d < 200 18 On the grid, draw a cumulative frequency diagram to represent the data.
Diagram: An empty grid: number of days, d, from 0 to 200 across and cumulative frequency from 0 to 100 up.
(3 marks)
(b)
For type Q, the median was 126 days the interquartile range was 57 days.
Compare the number of days that types P and Q lasted.
Make one statement about the average and one statement about the spread.
Use statistical measures to support your statements.(4 marks)
Question 19 (5 marks)
A phone screen is similar to a tablet screen.
Diagram: Two similar rectangles. The phone screen on the left has height 6 cm. The tablet screen on the right has height 15 cm.
The area of the tablet screen is 420 cm²
A screen costs £7000 per square metre.Work out the cost of a screen for the phone.
(5 marks)
Question 20 (3 marks)
Here is a formula for an iterative process.
u_n + 1 = 24/u_n + 4
u_2 = 8
Work out the values of u_1 and u_3
(3 marks)
Question 21 (6 marks)
The graph represents the velocity of a ball as it rolls along the ground.
Diagram: A velocity-time graph. The velocity starts at 0 and curves up, less and less steeply, to 8 m/s at 4 seconds. It stays at 8 m/s until 10 seconds, then falls in a straight line to 0 at 16 seconds.
(a)
Work out an estimate for the acceleration of the ball, in m/s², after 2 seconds.
You must show your working.(2 marks)
(b)
Work out an estimate for the total distance covered by the ball.
(3 marks)
(c)
Is your estimate from part (b) an overestimate or underestimate?
Tick a box.Overestimate square Underestimate square Give a reason for your answer.
(1 mark)
Question 22 (3 marks)
The nth term of a sequence is n² – 30n + 236
By completing the square,
show that all the terms of the sequence have two or more digits.(3 marks)
Question 23 (6 marks)
(a)
Diagram: A circle with centre O. A, B and C are on the circle, with chords CA, CB and AB and radii OA and OB. The line DAE touches the circle at A. Angle AOB at the centre is marked x. The angle between AE and AB is 53°.
Line DAE is a tangent at A to the circle with centre O.
Work out the size of angle x.
(2 marks)
(b)
Here is a cyclic quadrilateral.
Diagram: A quadrilateral with all four corners on a circle. The angle at the top corner is f, at the left corner g, at the bottom left corner h, and at the bottom right corner 63°. The 63° angle is opposite g, and f is opposite h.
f : g = 2 : 3
Work out f : h
Give your answer in its simplest form.(4 marks)
Question 24 (4 marks)
In the diagram,
ABCD and AEFG are congruent rectangles
D lies on EF
angle ADE = xDiagram: Two congruent rectangles, ABCD and AEFG, sharing the corner A. AD is the top side of ABCD. The second rectangle is tilted so that D lies on its side EF, with E below AD and G above it. Angle ADE is marked x. A dashed line joins G to D.
Prove that GD bisects angle ADF.
(4 marks)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.