Edexcel GCSE Higher November 2020 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)
The first five terms of an arithmetic sequence are
1 4 7 10 13
Write down an expression, in terms of n, for the nth term of this sequence.
(2 marks)
Question 2 (3 marks)
Show that 21/3 × 33/4 = 83/4
(3 marks)
Question 3 (2 marks)
The diagram shows four graphs.
Graph A
Diagram: Graph A: two curves, top right and bottom left, never touching the axes.
Graph B
Diagram: Graph B: an S-shaped curve through O, falling from top left to bottom right.
Graph C
Diagram: Graph C: an S-shaped curve through O, rising from bottom left to top right.
Graph D
Diagram: Graph D: a U-shaped curve with its lowest point at O.
Each of the equations in the table is the equation of one of the graphs.
Complete the table.
Equation Letter of graph y = -x³ y = x³ y = x² y = 1/x (2 marks)
Question 4 (1 mark)
The diagram shows four triangles.
Triangle A
Diagram: Triangle A: a base of 10 cm with angles of 55° and 45° at its two ends.
Triangle B
Diagram: Triangle B: a base of 8 cm with an angle of 45° at its left end; the side from the right end of the base to the top is 10 cm.
Triangle C
Diagram: Triangle C: a base of 10 cm; the right-hand side is 8 cm and the angle at the top is 55°.
Triangle D
Diagram: Triangle D: the angle at the top is 45° and the angle at the left is 80°; the right-hand side, from the top down to the bottom, is 10 cm.
Two of these triangles are congruent.
Write down the letters of these two triangles.
(1 mark)
Question 5 (3 marks)
Sean pays £10 for 24 chocolate bars.
He sells all 24 chocolate bars for 50p each.Work out Sean’s percentage profit.
(3 marks)
Question 6 (5 marks)
ADC is a triangle.
Diagram: Triangle ADC with A at the top, D at the bottom left and C at the bottom right. E is on AD and B is on AC, and EB is parallel to DC (arrows on both). Angle EBC, below EB at B, is 148°. Angle ADC is 63°.
AED and ABC are straight lines.
EB is parallel to DC.Angle EBC = 148°
Angle ADC = 63°Work out the size of angle EAB.
You must give a reason for each stage of your working.(5 marks)
Question 7 (3 marks)
The table shows information about the heights, in cm, of a group of Year 9 girls.
least height 150 cm median 165 cm greatest height 170 cm This stem and leaf diagram shows information about the heights, in cm, of a group of 15 Year 9 boys.
Diagram: Stem and leaf diagram. Stem 15, leaves 8 9 9; Stem 16, leaves 4 5 7 7 8; Stem 17, leaves 0 3 4 4 7; Stem 18, leaves 0 2. Key: 15 | 8 represents 158 cm.
Compare the distribution of the heights of the girls with the distribution of the heights of the boys.
(3 marks)
Question 8 (3 marks)
The diagram shows a prism placed on a horizontal floor.
Diagram: A prism with a hexagon at each end, standing on one hexagonal end on the floor. Its vertical height is labelled 3 m. The hidden edges at the back are dashed.
pressure = dfracforcearea The prism has height 3 m
The volume of the prism is 18 m³The pressure on the floor due to the prism is 75 newtons/m²
Work out the force exerted by the prism on the floor.
(3 marks)
Question 9 (2 marks)
Write these numbers in order of size.
Start with the smallest number.6.72 × 10⁵ 67.2 × 10⁻⁴ 672 × 10⁴ 0.000 672
(2 marks)
Question 10 (3 marks)
Given that a/b = 2/5 and b/c = 3/4
find a : b : c
(3 marks)
Question 11 (6 marks)
(a)
Find the value of 4√(81 × 10⁸)
(2 marks)
(b)
Find the value of 64^(-1/2)
(2 marks)
(c)
Write dfrac3ⁿ9ⁿ⁻¹ as a power of 3
(2 marks)
Question 12 (6 marks)
The table gives information about the weekly wages of 80 people.
Wage (£w) Frequency small 200<w≤250 5 small 250<w≤300 10 small 300<w≤350 20 small 350<w≤400 20 small 400<w≤450 15 small 450<w≤500 10 (a)
Complete the cumulative frequency table.
Wage (£w) Cumulative frequency small 200<w≤250 small 200<w≤300 small 200<w≤350 small 200<w≤400 small 200<w≤450 small 200<w≤500 (1 mark)
(b)
On the grid, draw a cumulative frequency graph for your completed table.
(2 marks)
(c)
Juan says
“60% of this group of people have a weekly wage of £360 or less.”
Is Juan correct?
You must show how you get your answer.Diagram: A graph.
(3 marks)
Question 13 (3 marks)
Liquid A and liquid B are mixed to make liquid C.
Liquid A has a density of 70 kg/m³
Liquid A has a mass of 1400 kgLiquid B has a density of 280 kg/m³
Liquid B has a volume of 30 m³Work out the density of liquid C.
(3 marks)
Question 14 (3 marks)
Sally plays two games against Martin.
In each game, Sally could win, draw or lose.In each game they play,
the probability that Sally will win against Martin is 0.3
the probability that Sally will draw against Martin is 0.1Work out the probability that Sally will win exactly one of the two games against Martin.
(3 marks)
Question 15 (3 marks)
The straight line mathbfL_1 has equation y = 3x – 4
The straight line mathbfL_2 is perpendicular to mathbfL_1 and passes through the point (9, 5)
Find an equation of line mathbfL_2
(3 marks)
Question 16 (4 marks)
Shirley wants to find an estimate for the number of bees in her hive.
On Monday she catches 90 of the bees.
She puts a mark on each bee and returns them to her hive.On Tuesday she catches 120 of the bees.
She finds that 20 of these bees have been marked.(a)
Work out an estimate for the total number of bees in her hive.
(3 marks)
(b)
Shirley assumes that none of the marks had rubbed off between Monday and Tuesday.
If Shirley’s assumption is wrong, explain what effect this would have on your answer to part (a).
(1 mark)
Question 17 (4 marks)
Make f the subject of the formula d = (3(1 – f))/(f – 4)
(4 marks)
Question 18 (3 marks)
x is proportional to √y where y > 0
y is increased by 44%
Work out the percentage increase in x.
(3 marks)
Question 19 (5 marks)
f and g are functions such that
f(x) = dfrac12√x and g(x) = 3(2x + 1)
(a)
Find g(5)
(1 mark)
(b)
Find gf(9)
(2 marks)
(c)
Find g⁻¹(6)
(2 marks)
Question 20 (4 marks)
Show that dfrac√180 – 2√55√5 – 5 can be written in the form a + dfrac√5b where a and b are integers.
(4 marks)
Question 21 (4 marks)
DEF is a triangle.
Diagram: Triangle DEF with D at the top, F at the bottom left and E at the bottom right. P is the midpoint of FD and Q is the midpoint of DE. Straight lines join P to E and F to Q.
P is the midpoint of FD.
Q is the midpoint of DE.overrightarrowFD = mathbfa and overrightarrowFE = mathbfb
Use a vector method to prove that PQ is parallel to FE.
(4 marks)
Question 22 (5 marks)
The diagram shows two shaded shapes, A and B.
Shape A is formed by removing a sector of a circle with radius (3x – 1) cm from a sector of the circle with radius (5x – 1) cm.
Shape B is a circle of diameter (2 – 2x) cm.Diagram: Shape A: a sector with angle 45° and a smaller sector with the same centre and angle cut out of it, leaving a shaded band. Along its upper straight edge the inner radius is labelled (3x – 1) cm and the rest of the edge 2x cm. Shape B: a shaded circle with its diameter labelled (2 – 2x) cm.
The area of shape A is equal to the area of shape B.
Find the value of x.
You must show all your working.(5 marks)
Question 23 (3 marks)
There are four types of cards in a game.
Each card has a black circle or a white circle or a black triangle or a white triangle.
Diagram: Four cards in a row, each a square box: a black circle, a white circle, a black triangle and a white triangle.
number of cards with a black shape : number of cards with a white shape = 3 : 5
number of cards with a circle : number of cards with a triangle = 2 : 7
Express the total number of cards with a black shape as a fraction of the total number of cards with a triangle.
(3 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.