Edexcel GCSE Higher November 2023 Paper 1 (non-calculator)
22 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)
Work out 6.3 × 2.4
(3 marks)
Question 2 (4 marks)
(a)(i)
Write down the value of 5⁰
(1 mark)
(ii)
Write down the value of 5⁻²
(1 mark)
(b)
Write (2⁵ × 2⁴)/(2^text3) in the form 2ⁿ where n is an integer.
(2 marks)
Question 3 (4 marks)
(a)
Write 156 as a product of its prime factors.
(2 marks)
(b)
Find the highest common factor (HCF) of 156 and 130
(2 marks)
Question 4 (4 marks)
The mean length of 5 sticks is 4.2 cm.
Nawal measured the length of one of the sticks as 7 cm.
(a)
Work out the mean length of the other 4 sticks.
(3 marks)
(b)
Nawal made a mistake.
The stick was not 7 cm long.
It was 17 cm long.How does this affect your answer to part (a)?
(1 mark)
Question 5 (2 marks)
The point P lies on the line AB.
Use ruler and compasses to construct an angle of 90° at P.
You must show all your construction lines.Diagram: A horizontal line AB, 11 cm long, with the point P marked on it 4.5 cm from A.
(2 marks)
Question 6 (4 marks)
The diagram shows an isosceles triangle ABD and the straight line ABC.
Diagram: Triangle ABD with BA = BD (marked with dashes). The line CBA is straight, with C beyond B. Angle DAB is x°, angle ABD is y° and angle DBC is w°.
BA = BD
x : y = 2 : 1
Work out the value of w.
(4 marks)
Question 7 (5 marks)
Mano has three shelves of books.
There are x books on shelf A.
There are (3x + 1) books on shelf B.
There are (2x – 5) books on shelf C.There is a total of 44 books on the three shelves.
All the books have the same mass.
The books on shelf B have a total mass of 7500 g.Work out the total mass of the books on shelf A.
(5 marks)
Question 8 (2 marks)
The normal price of a mattress is reduced by 40% in a sale.
The price of the mattress in the sale is £660Work out the normal price of the mattress.
(2 marks)
Question 9 (4 marks)
To cook rice
the number of cups of rice (x) : the number of cups of water (y) = 4 : 5
(a)
Use this information to draw a graph to show the relationship between the number of cups of rice and the number of cups of water needed to cook rice.
Diagram: A blank grid: number of cups of rice (x) from 0 to 10 across, number of cups of water (y) from 0 to 10 up.
(2 marks)
(b)(i)
Find the gradient of the line drawn in part (a).
(1 mark)
(ii)
Explain what this gradient represents.
(1 mark)
Question 10 (3 marks)
The circumference of a circle is 10 m.
Work out the area of the circle.
Give your answer in terms of π.(3 marks)
Question 11 (5 marks)
Alice recorded the number of cars going into a village on each of 80 days.
The incomplete table and the incomplete box plot give information about her results.
Number of cars Least number 300 Lower quartile Median 900 Upper quartile Range 1000 Diagram: An incomplete box plot on a scale from 200 to 1400 cars: only the box is drawn, from 780 to 1200, with no median line and no whiskers.
(a)
(i) Use the information in the table to complete the box plot.
(ii) Use the information in the box plot to complete the table.
(3 marks)
(b)
On some of these 80 days Alice saw fewer than 1200 cars going into the village.
Work out an estimate for the number of days Alice saw fewer than 1200 cars going into the village.
(2 marks)
Question 12 (3 marks)
The straight line L has equation 2y = 3x – 7
Find an equation of the straight line perpendicular to L that passes through (6, –5)
(3 marks)
Question 13 (3 marks)
Solid A and solid B are similar.
The ratio of the height of solid A to the height of solid B is 2 : 5
The volume of solid A is 12 cm³Work out the volume of solid B.
(3 marks)
Question 14 (3 marks)
Work out the value of 27^(2/3) + (1/2)⁻³
(3 marks)
Question 15 (3 marks)
An object falls from rest.
Here is the distance-time graph for the distance (d metres) fallen by the object t seconds after it starts to fall.
Diagram: A curve starting at (0, 0) and getting steeper: about 22 metres at 2 seconds, 72 at 4 seconds, 111 at 5 seconds and 223 at 7 seconds.
Work out an estimate for the gradient of the graph at t = 3
You must show how you get your answer.(3 marks)
Question 16 (4 marks)
At the start of year n the population of a species is P_n
At the start of the following year the population of the species is given by
P_n + 1 = kP_n where k is a positive constant.The population of the species at the start of year 1 is 8 million.
The population of the species at the start of year 2 is 6 million.(a)
Work out the population of the species at the start of year 3
(3 marks)
(b)
At the start of year 5 the value of k is increased by 0.3 to a new constant value.
Louise thinks that from the start of year 5 the population of the species would increase year on year.
Is Louise correct?
You must give a reason for your answer.(1 mark)
Question 17 (4 marks)
(a)
Factorise 6x² – 5x – 4
(2 marks)
(b)
Hence, or otherwise, solve 6x² – 5x – 4 < 0
(2 marks)
Question 18 (4 marks)
Spinner A and spinner B are each spun once.
The probability that spinner A lands on red is 1/4
The probability that both spinner A and spinner B land on red is 1/24Work out the probability that one spinner lands on red and the other spinner does not land on red.
(4 marks)
Question 19 (3 marks)
Here is the graph of y = sin x° for -180 ≤ x ≤ 180
Diagram: The graph of y = sin x for x from –180 to 180: it goes down from 0 at –180 to –1 at –90, up through 0 at 0 to 1 at 90, and back down to 0 at 180.
(a)
Use the graph to find estimates for the solutions of
sin x° = 0.3 for -180 ≤ x ≤ 180
(2 marks)
(b)
Write down a value of x such that
sin(x + 20)° = 0 for -180 ≤ x ≤ 180
(1 mark)
Question 20 (4 marks)
Here is triangle ABC.
Diagram: A diagram.
Find the size of angle ABC.
You must show all your working.(4 marks)
Question 21 (5 marks)
(a)
On the grid, draw the graph of x² + y² = 169
Diagram: A blank grid, x and y each from –14 to 14.
(2 marks)
(b)
Use your graph to find estimates for the solutions of the simultaneous equations
x² + y² = 169
2y = 3x(3 marks)
Question 22 (4 marks)
The 2nd term of a geometric sequence is 3 + 2√2
The 3rd term of the sequence is 13 + 9√2Find the value of the common ratio of the sequence.
Give your answer in the form a + √b where a and b are integers.
You must show all your working.(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.