Edexcel GCSE Higher November 2019 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)
Find the Lowest Common Multiple (LCM) of 108 and 120
(3 marks)
Question 2 (4 marks)
There are 60 people in a choir.
Half of the people in the choir are women.The number of women in the choir is 3 times the number of men in the choir.
The rest of the people in the choir are children.the number of children in the choir : the number of men in the choir = n : 1
Work out the value of n.
You must show how you get your answer.(4 marks)
Question 3 (3 marks)
Work out 13/4 × 11/3
Give your answer as a mixed number.
(3 marks)
Question 4 (2 marks)
Use a ruler and compasses to construct the line from the point P perpendicular to the line CD.
You must show all construction lines.Diagram: A horizontal line CD and a point P, marked with a cross, above the line and nearer to D.
(2 marks)
Question 5 (4 marks)
The diagram shows triangle ABC.
Diagram: Triangle ABC with B at the bottom left, C at the bottom right and A at the top. D is on AB and a line joins D to C. Angle BAC is marked 75° and angle ABC is marked 51°.
ADB is a straight line.
the size of angle DCB : the size of angle ACD = 2 : 1
Work out the size of angle BDC.
(4 marks)
Question 6 (3 marks)
4 red bricks have a mean weight of 5 kg.
5 blue bricks have a mean weight of 9 kg.
1 green brick has a weight of 6 kg.Donna says,
“The mean weight of the 10 bricks is less than 7 kg.”Is Donna correct?
You must show how you get your answer.(3 marks)
Question 7 (3 marks)
(a)
Simplify (p²)⁵
(1 mark)
(b)
Simplify 12x⁷y³ ÷ 6x³y
(2 marks)
Question 8 (5 marks)
The accurate scale drawing shows the positions of port P and a lighthouse L.
Diagram: An accurate scale drawing of port P and lighthouse L, each marked with a cross and a north line. L is to the right of P and a little lower. A centimetre scale bar, 0 to 3 cm, is drawn underneath so lengths can be measured on screen.
Scale: 1 cm represents 4 km.
Aleena sails her boat from port P on a bearing of 070°
She sails for 11/2 hours at an average speed of 12 km/h to a port Q.Find
(i) the distance, in km, of port Q from lighthouse L,
(ii) the bearing of port Q from lighthouse L.(5 marks)
Question 9 (4 marks)
A car travels for 18 minutes at an average speed of 72 km/h.
(a)
How far will the car travel in these 18 minutes?
(2 marks)
(b)
David says,
“72 kilometres per hour is faster than 20 metres per second.”
Is David correct?
You must show how you get your answer.(2 marks)
Question 10 (6 marks)
The cumulative frequency table shows information about the times, in minutes, taken by 40 people to complete a puzzle.
Time (m minutes) Cumulative frequency 20 < m ≤ 40 5 20 < m ≤ 60 25 20 < m ≤ 80 35 20 < m ≤ 100 38 20 < m ≤ 120 40 (a)
On the grid below, draw a cumulative frequency graph for this information.
Diagram: A blank grid for a cumulative frequency graph: Time (m minutes) from 0 to 120 across, cumulative frequency from 0 to 45 up.
(2 marks)
(b)
Use your graph to find an estimate for the interquartile range.
(2 marks)
(c)
One of the 40 people is chosen at random.
Use your graph to find an estimate for the probability that this person took between 50 minutes and 90 minutes to complete the puzzle.
(2 marks)
Question 11 (2 marks)
There are p counters in a bag.
12 of the counters are yellow.Shafiq takes at random 30 counters from the bag.
5 of these 30 counters are yellow.Work out an estimate for the value of p.
(2 marks)
Question 12 (1 mark)
T = q/2 + 5
Here is Spencer’s method to make q the subject of the formula.
2 × T = q + 5
q = 2T – 5What mistake did Spencer make in the first line of his method?
(1 mark)
Question 13 (3 marks)
(a)
Write 5/(x + 1) + 2/3x as a single fraction in its simplest form.
(2 marks)
(b)
Factorise (x + y)² + 3(x + y)
(1 mark)
Question 14 (4 marks)
The diagram shows a right-angled triangle.
Diagram: A right-angled triangle with the right angle at the top left. The top side is labelled x + 4 and the left side is labelled x – 2. The third side slopes from the bottom left to the top right corner.
All the measurements are in centimetres.
The area of the triangle is 27.5 cm²
Work out the length of the shortest side of the triangle.
You must show all your working.(4 marks)
Question 15 (3 marks)
Express 0.41̇8̇ as a fraction.
You must show all your working.(3 marks)
Question 16 (5 marks)
(a)
Rationalise the denominator of dfrac22√11
Give your answer in its simplest form.
(2 marks)
(b)
Show that dfrac√32√3 – 1 can be written in the form dfraca + √3b where a and b are integers.
(3 marks)
Question 17 (4 marks)
A and B are two similar cylindrical containers.
Diagram: Two cylinders standing side by side, each taller than it is wide: cylinder A on the left and a larger cylinder B on the right.
the surface area of container A : the surface area of container B = 4 : 9
Tyler fills container A with water.
She then pours all the water into container B.
Tyler repeats this and stops when container B is full of water.Work out the number of times that Tyler fills container A with water.
You must show all your working.(4 marks)
Question 18 (6 marks)
The function f is given by
f(x) = 2x³ – 4
(a)
Show that f⁻¹(50) = 3
(2 marks)
(b)
The functions g and h are given by
g(x) = x + 2 and h(x) = x²
Find the values of x for which
hg(x) = 3x² + x – 1
(4 marks)
Question 19 (3 marks)
Given that 9^(-1/2) = 27^(1/4) ÷ 3^(x + 1)
find the exact value of x.
(3 marks)
Question 20 (3 marks)
The graph of y = f(x) is shown on the grid.
(a)
Diagram: A grid with x and y from –6 to 6. The graph of y = f(x) is made of straight lines: level from (–4, 3) to (–3, 3), down to A(–2, 1), up to (1, 4), then level to (3, 4).
On the grid, draw the graph with equation y = f(x + 1) – 3
(2 marks)
(b)
Point A(-2, 1) lies on the graph of y = f(x).
When the graph of y = f(x) is transformed to the graph with equation y = f(-x), point A is mapped to point B.
Write down the coordinates of point B.
(1 mark)
Question 21 (5 marks)
Sketch the graph of
y = 2x² – 8x – 5
showing the coordinates of the turning point and the exact coordinates of any intercepts with the coordinate axes.
(5 marks)
Question 22 (4 marks)
A, B, C and D are four points on a circle.
Diagram: A circle with four points on it: A at the top, D on the left, B on the right and C at the bottom right. Chords AD, AB, AC, DB, DC and BC are drawn. AC and DB cross at E, inside the circle.
AEC and DEB are straight lines.
Triangle AED is an equilateral triangle.
Prove that triangle ABC is congruent to triangle DCB.
(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.