Edexcel GCSE Higher November 2021 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 (6 marks)
(a)
Work out 3.67 × 4.2
(3 marks)
(b)
Work out 59.84 ÷ 1.6
(3 marks)
Question 2 (3 marks)
ℰ = {even numbers less than 19}
A = {6, 12, 18}
B = {2, 6, 14, 18}Complete the Venn diagram for this information.
Diagram: Venn diagram with sets A and B. Only A: . Both: . Only B: . Neither: .
(3 marks)
Question 3 (3 marks)
Work out 41/5 – 22/3
Give your answer as a mixed number.
(3 marks)
Question 4 (4 marks)
At the end of 2017
the value of Tamara’s house was £220 000
the value of Rahim’s house was £160 000At the end of 2019
the value of Tamara’s house had decreased by 20%
the value of Rahim’s house had increased by 30%At the end of 2019, whose house had the greater value?
You must show how you get your answer.(4 marks)
Question 5 (3 marks)
Rosie, Matilda and Ibrahim collect stickers.
number of stickers Rosie has : number of stickers Matilda has : number of stickers Ibrahim has = 4 : 7 : 15
Ibrahim has 24 more stickers than Matilda.
Ibrahim has more stickers than Rosie.
How many more?(3 marks)
Question 6 (3 marks)
The diagram shows a prism.
Diagram: A triangular prism. Its end is a right-angled triangle with the right angle at the bottom left; the base of the triangle is labelled 5 cm and the length of the prism is labelled 25 cm.
The cross section of the prism is a right-angled triangle.
The base of the triangle has length 5 cmThe prism has length 25 cm
The prism has volume 750 cm³Work out the height of the prism.
(3 marks)
Question 7 (4 marks)
The diagram shows a cube with edges of length x cm and a sphere of radius 3 cm.
Cube
Diagram: A cube. One edge is labelled x cm.
Sphere
Diagram: A sphere with its centre marked. A radius from the centre is labelled 3 cm.
Surface area of sphere = 4π r²
The surface area of the cube is equal to the surface area of the sphere.
Show that x = √(kπ) where k is an integer.
(4 marks)
Question 8 (3 marks)
Solve x² = 5x + 24
(3 marks)
Question 9 (4 marks)
(a)
Write down the value of 7⁰
(1 mark)
(b)
Find the value of 3 × 3⁶ × 3⁻⁶
(1 mark)
(c)
Find the value of 2⁻⁴
(1 mark)
(d)
Find the value of 27^(1/3)
(1 mark)
Question 10 (4 marks)
The diagram shows a shape made from 6 identical squares.
Diagram: A shape made from 6 identical squares: 3 in the top row, 2 under them and 1 at the bottom, lined up on the left.
The total area of the shape is 5406 cm²
(a)
Find an estimate for the length of one side of each square.
Give your answer correct to the nearest whole number.(3 marks)
(b)
Is your answer to part (a) an underestimate or an overestimate?
You must give a reason for your answer.(1 mark)
Question 11 (4 marks)
The diagram shows two rectangles, A and B.
Diagram: Two rectangles, A and B, with their sides labelled.
All measurements are in centimetres.
The area of rectangle A is equal to the area of rectangle B.
Find an expression for y in terms of w.
(4 marks)
Question 12 (3 marks)
The cumulative frequency table gives information about the heights, in cm, of 40 plants.
Height (h cm) Cumulative Frequency 0 < h ≤ 5 4 0 < h ≤ 10 11 0 < h ≤ 15 24 0 < h ≤ 20 34 0 < h ≤ 25 38 0 < h ≤ 30 40 (a)
On the grid, draw a cumulative frequency graph for this information.
Diagram: A graph.
(2 marks)
(b)
Use the graph to find an estimate for the median height of the plants.
(1 mark)
Question 13 (1 mark)
Ted is trying to change 0.4̇3̇ to a fraction.
Here is the start of his method.
x = 0.4̇3̇
10x = 4.3̇4̇
10x – x = 4.3̇4̇ – 0.4̇3̇Evaluate Ted’s method so far.
(1 mark)
Question 14 (3 marks)
Here is a shape with all its measurements in centimetres.
Diagram: An L-shaped figure: a narrow part at the top left above a wider rectangle, with right angles marked.
The area of the shape is A cm²
Show that A = 2x² + 24x + 46
(3 marks)
Question 15 (3 marks)
Show that (4x + 3)/2x + 3/5 can be written in the form (ax + b)/cx where a, b and c are integers.
(3 marks)
Question 16 (4 marks)
There are only 3 red counters and 5 yellow counters in a bag.
Jude takes at random 3 counters from the bag.
Work out the probability that he takes exactly one red counter.
(4 marks)
Question 17 (3 marks)
On the grid show, by shading, the region that satisfies all of these inequalities.
2y + 4 < x x < 3 y < 6 – 3x
Label the region R.
Diagram: A graph.
(3 marks)
Question 18 (5 marks)
Here is trapezium ABCD.
Diagram: Trapezium ABCD with AB parallel to DC, side BC labelled and the angle at C marked 30°.
The area of the trapezium is 66 cm²
the length of AB : the length of CD = 2 : 3
Find the length of AB.
(5 marks)
Question 19 (4 marks)
Show that dfrac8 + √125 + √3 can be written in the form dfraca + √3b, where a and b are integers.
(4 marks)
Question 20 (3 marks)
The diagram shows the graph of x² + y² = 30.25
Diagram: The circle x² + y² = 30.25, centre O, on a grid from –7 to 7.
Use the graph to find estimates for the solutions of the simultaneous equations
x² + y² = 30.25
y – 2x = 1(3 marks)
Question 21 (6 marks)
The functions f and g are such that
f(x) = 3x² + 1 for x > 0 and g(x) = 4/(x²) for x > 0
(a)
Work out gf(1)
(2 marks)
(b)
The function h is such that h = (fg)⁻¹
Find h(x)
(4 marks)
Question 22 (4 marks)
Find the coordinates of the turning point on the curve with equation y = 9 + 18x – 3x²
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.