Edexcel GCSE Higher November 2017 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)
Write 36 as a product of its prime factors.
(2 marks)
Question 2 (4 marks)
Kiaria is 7 years older than Jay.
Martha is twice as old as Kiaria.
The sum of their three ages is 77Find the ratio of Jay’s age to Kiaria’s age to Martha’s age.
(4 marks)
Question 3 (4 marks)
Diagram: Parallelogram ABCD with AD parallel to BC (double arrows) and AB parallel to DC (single arrows). The straight line from B goes through F on AD to E, which is on CD extended beyond D. Angle EFD is marked 35° and angle DCB is marked 75°.
ABCD is a parallelogram.
EDC is a straight line.
F is the point on AD so that BFE is a straight line.Angle EFD = 35°
Angle DCB = 75°Show that angle ABF = 70°
Give a reason for each stage of your working.(4 marks)
Question 4 (4 marks)
The diagram shows a logo made from three circles.
Diagram: A logo made from three circles, all with centre O. Along a radius the distances are marked 4 cm, 3 cm, 3 cm from O outwards. The ring between the smallest circle and the middle circle is shaded.
Each circle has centre O.
Daisy says that exactly 1/3 of the logo is shaded.
Is Daisy correct?
You must show all your working.(4 marks)
Question 5 (4 marks)
The table shows information about the weekly earnings of 20 people who work in a shop.
Weekly earnings (£x) Frequency 150 < x ≤ 250 1 250 < x ≤ 350 11 350 < x ≤ 450 5 450 < x ≤ 550 0 550 < x ≤ 650 3 (a)
Work out an estimate for the mean of the weekly earnings.
(3 marks)
(b)
Nadiya says,
“The mean may not be the best average to use to represent this information.”
Do you agree with Nadiya?
You must justify your answer.(1 mark)
Question 6 (4 marks)
Here is a rectangle.
Diagram: A rectangle. Its left side is labelled 2x + 6, its right side 5x – 9 and its top y.
All measurements are in centimetres.
The area of the rectangle is 48 cm².Show that y = 3
(4 marks)
Question 7 (1 mark)
Brogan needs to draw the graph of y = x² + 1
Here is her graph.
Diagram: A graph labelled y = x² + 1. Crosses are plotted at (–3, 10), (–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5), (3, 10), and each cross is joined to the next with a straight line, so the graph is made of straight line segments with sharp corners.
Write down one thing that is wrong with Brogan’s graph.
(1 mark)
Question 8 (2 marks)
Write these numbers in order of size.
Start with the smallest number.0.24̇6̇ 0.246̇ 0.2̇46̇ 0.246
(2 marks)
Question 9 (5 marks)
James and Peter cycled along the same 50 km route.
James took 21/2 hours to cycle the 50 km.
Peter started to cycle 5 minutes after James started to cycle.
Peter caught up with James when they had both cycled 15 km.
James and Peter both cycled at constant speeds.
Work out Peter’s speed.
(5 marks)
Question 10 (3 marks)
(a)
Write down the value of 100^(1/2)
(1 mark)
(b)
Find the value of 125^(2/3)
(2 marks)
Question 11 (4 marks)
3 teas and 2 coffees have a total cost of £7.80
5 teas and 4 coffees have a total cost of £14.20Work out the cost of one tea and the cost of one coffee.
(4 marks)
Question 12 (5 marks)
The table shows information about the heights, in cm, of a group of Year 11 girls.
height (cm) least height 154 median 165 lower quartile 161 interquartile range 7 range 20 (a)
Draw a box plot for this information.
Diagram: Year 11: blank grid.
(3 marks)
(b)
The box plot below shows information about the heights, in cm, of a group of Year 7 girls.
Diagram: Year 7: lowest 146, lower quartile 154.5, median 157.5, upper quartile 165, highest 170.5.
Compare the distribution of heights of the Year 7 girls with the distribution of heights of the Year 11 girls.
(2 marks)
Question 13 (4 marks)
A factory makes 450 pies every day.
The pies are chicken pies or steak pies.Each day Milo takes a sample of 15 pies to check.
The proportion of the pies in his sample that are chicken is the same as the proportion of the pies made that day that are chicken.(a)
On Monday Milo calculated that he needed exactly 4 chicken pies in his sample.
Work out the total number of chicken pies that were made on Monday.
(2 marks)
(b)
On Tuesday, the number of steak pies Milo needs in his sample is 6 correct to the nearest whole number.
Milo takes at random a pie from the 450 pies made on Tuesday.
Work out the lower bound of the probability that the pie is a steak pie.
(2 marks)
Question 14 (3 marks)
The ratio (y + x) : (y – x) is equivalent to k : 1
Show that y = (x(k + 1))/(k – 1)
(3 marks)
Question 15 (3 marks)
x = 0.43̇6̇
Prove algebraically that x can be written as 24/55
(3 marks)
Question 16 (3 marks)
y is directly proportional to 3√(x)
y = 11/6 when x = 8
Find the value of y when x = 64
(3 marks)
Question 17 (2 marks)
n is an integer.
Prove algebraically that the sum of 1/2n(n + 1) and 1/2(n + 1)(n + 2) is always a square number.
(2 marks)
Question 18 (2 marks)
Diagram: A grid with x and y from –8 to 8. Shape P is a triangle with corners at (2, 3), (2, 7) and (4, 3).
Enlarge shape P by scale factor -1/2 with centre of enlargement (0, 0).
Label your image Q.(2 marks)
Question 19 (4 marks)
Diagram: Axes with the line L sloping down from top left, through A, then E on the y-axis, to B on the x-axis. The line M slopes up steeply through D on the x-axis and A. ABCD is a rectangle with C below the x-axis.
ABCD is a rectangle.
A, E and B are points on the straight line L with equation x + 2y = 12
A and D are points on the straight line M.AE = EB
Find an equation for M.
(4 marks)
Question 20 (4 marks)
The table shows some values of x and y that satisfy the equation y = acos x° + b
x 0 30 60 90 120 150 180 y 3 1 + √3 2 1 0 1 – √3 –1 Find the value of y when x = 45
(4 marks)
Question 21 (3 marks)
Show that dfrac6 – √8√2 – 1 can be written in the form a + b√2 where a and b are integers.
(3 marks)
Question 22 (5 marks)
The two triangles in the diagram are similar.
Diagram: Triangle ACD with B on AC and E on AD, joined by BE. AB is 8 cm, BC is x cm, AE is 12 cm and ED is 3 cm.
There are two possible values of x.
Work out each of these values.
State any assumptions you make in your working.(5 marks)
Question 23 (5 marks)
Here is a rectangle and a right-angled triangle.
Diagram: A rectangle with width 3x – 2 and height x – 1, and a right-angled triangle with vertical side 2x and base x.
All measurements are in centimetres.
The area of the rectangle is greater than the area of the triangle.Find the set of possible values of x.
(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.