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AQA GCSE Higher November 2024 Paper 1 (non-calculator)
23 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 (2 marks)
Work out the value of 1.5²
(2 marks)
Question 2 (3 marks)
(a)
Complete this number machine so that y = 4x + 5
Diagram: A number machine. Input x goes into the first box, then the second box, then comes out as output y. First box: empty. Second box: empty.
(1 mark)
(b)
Complete this number machine so that y = 3x – 24
Diagram: A number machine. Input x goes into the first box, then the second box, then comes out as output y. First box: empty. Second box: × 3.
(1 mark)
(c)
Complete this number machine so that y = x
Diagram: A number machine. Input x goes into the first box, then the second box, then comes out as output y. First box: × 6. Second box: empty.
(1 mark)
Question 3 (3 marks)
Each number in a list is increased by 10
Tick one box for each statement.
True False Cannot tell The mode is increased by 10 The median is increased by 10 The range is increased by 10 (3 marks)
Question 4 (3 marks)
(a)
Write the missing term in the geometric progression.
1 4 16 …… 256
(1 mark)
(b)
A Fibonacci-type sequence begins
5 –9
The sequence is continued by adding the previous two terms.
Work out the next two terms.(2 marks)
Question 5 (3 marks)
Here is a solid prism.
Diagram: A solid prism lying on its side. Its cross-section, at the front left, is a hexagon, and the prism runs back to the right. Hidden edges are dashed.
(a)
How many faces does the prism have?
(1 mark)
(b)
The prism has
volume = 3500 cm³
and
length = 20 cmWork out the area of the cross-section of the prism.
(2 marks)
Question 6 (2 marks)
Work out 11/5 – 3/10
Give your answer as a fraction.(2 marks)
Question 7 (4 marks)
A large circle and a small circle are shown.
The radius of the large circle is 12 cmradius of large circle : radius of small circle = 4 : 1 Diagram: A large circle with a small circle inside it, touching it at the top left. The region inside the large circle and outside the small circle is shaded.
Work out the shaded area.
Give your answer in terms of π(4 marks)
Question 8 (3 marks)
(a)
In this part, assume that each person works at the same rate.
10 people can complete a job in 9 hours.If 15 people work on the same job, how many hours will it take to complete the job?
(2 marks)
(b)
In fact, of the 15 people
6 work at a slower rate
9 work at a faster rate.What does this mean about the number of hours it will take to complete the job?
Tick one box.It is greater than the answer to (a) It is the same as the answer to (a) It is less than the answer to (a) It is not possible to say (1 mark)
Question 9 (3 marks)
( a , 2 ) + ( 1 , 3b ) = ( 5 , 20 )
Work out the values of a and b.
(3 marks)
Question 10 (4 marks)
Clive owns two coffee shops, A and B.
Out of 150 people
• 18 people use both shops
• 46% use shop A
• 2/5 use shop B only.Complete the Venn diagram to represent the information.
ξ = 150 people
A = people who use shop A
B = people who use shop BDiagram: A blank Venn diagram: two overlapping circles A and B inside a rectangle labelled ξ.
(4 marks)
Question 11 (3 marks)
Construct the region that lies within 4 cm of the line.
Diagram: A straight line 6 cm long.
(3 marks)
Question 12 (5 marks)
(a)
Convert 27/11 to a recurring decimal.
(2 marks)
(b)
Convert 0.15̇ to a fraction.
(3 marks)
Question 13 (5 marks)
(a)
By rounding each number to one significant figure,
estimate the value of dfrac√401 + 1.9³cos 58.7°
You must show your working.
(3 marks)
(b)
Here is a triangle.
Diagram: A triangle with sides 7 cm and 3 cm meeting at the angle x, and 5 cm opposite x.
Sam attempts to find the value of cos x using the cosine rule.
Here is his working.5² = 3² + 7² + 2 × 3 × 7 × cos x
5² = 10² + 42 × cos x
25 = 142 cos x
Therefore cos x = 25/142Identify two errors Sam has made.
(2 marks)
Question 14 (3 marks)
Enlarge triangle PQR by scale factor -1/3 with centre (0, 0)
Diagram: A grid with x and y from –5 to 10. Triangle PQR has P at (0, 9), Q at (9, 9) and R at (9, 3).
(3 marks)
Question 15 (4 marks)
(a)
Solve the inequality 20 – 5x ≤ 30
(3 marks)
(b)
Represent x > -1 on the number line.
Diagram: A number line from –5 to 6, marked every 1, labelled x.
(1 mark)
Question 16 (2 marks)
When w is truncated the answer is 8
Sacha writes the error interval due to truncation as 7.5 ≤ w < 8.5
Give a reason why Sacha is wrong and state the correct error interval for w.
(2 marks)
Question 17 (6 marks)
(a)
A circle has centre (0, 0) and circumference 36π
Work out the equation of the circle.
(2 marks)
(b)
Point J has coordinates (15, 0) and point K has coordinates (30, -5)
Work out the equation of the straight line through J and K.
(4 marks)
Question 18 (4 marks)
(a)
Express x² + 8x – 5 in the form (x + a)² – b where a and b are integers.
(2 marks)
(b)
A curve has the equation y = (x – 7)² + 8
Write down the coordinates of the turning point of the curve.
(2 marks)
Question 19 (5 marks)
(a)
Expand and simplify fully (x + 2)(2x + 3)(3x + 4)
(3 marks)
(b)
Use your answer from part (a) to work out 102 × 203 × 304
(2 marks)
Question 20 (4 marks)
(a)
Show that dfrac√363√3 simplifies to an integer.
(2 marks)
(b)
Rationalise the denominator and simplify dfrac20√5
(2 marks)
Question 21 (3 marks)
Here is a sketch of the graph of y = tan x where 0° ≤ x ≤ 360°
Diagram: A sketch of y = tan x for x from 0 to 360 degrees, marked every 90 degrees, with y marked at –10, –5, 5 and 10. The curve is 0 at 0, 180 and 360 and rises from left to right in each branch, getting closer and closer to the dashed vertical asymptotes at x = 90 and x = 270.
You are given that tan 78.69° = 5
(a)
Work out the other value of x where tan x = 5 and 0° ≤ x ≤ 360°
(1 mark)
(b)
Work out the two values of x where tan x = -5 and 0° ≤ x ≤ 360°
(2 marks)
Question 22 (3 marks)
7ⁿ = x
Match each expression on the left to the correct expression on the right.
One has been done for you.
Diagram: Two columns of boxes. On the left, top to bottom: 7^–n, 7^2n, 7^n + 1, 7^½n. On the right, top to bottom: 7x, 1/x, ½x, square root of x, x². A line joins 7^–n to 1/x.
(3 marks)
Question 23 (3 marks)
In each part, the graph shown is a transformation of the graph y = x²
(a)
Diagram: A curve on a grid with x from –3 to 3 and y from 0 to 7: a U-shaped parabola with its lowest point at (0, 2), passing through (1, 3), (–1, 3), (2, 6) and (–2, 6).
(b)
Diagram: A curve on a grid with x from –3 to 3 and y from –5 to 0: an upside-down parabola with its highest point at (0, 0), passing through (1, –1), (–1, –1), (2, –4) and (–2, –4).
(c)
Diagram: A curve on a grid with x from 0 to 5 and y from 0 to 5: a U-shaped parabola with its lowest point at (3, 0), passing through (2, 1), (4, 1), (1, 4) and (5, 4).
(a)
Write down the equation of the graph shown.
(1 mark)
(b)
Write down the equation of the graph shown.
(1 mark)
(c)
Write down the equation of the graph shown.
(1 mark)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.