Edexcel GCSE Higher June 2017 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 (5 marks)
The scatter graph shows the maximum temperature and the number of hours of sunshine
in fourteen British towns on one day.
Diagram: A scatter graph of maximum temperature (°C) against the number of hours of sunshine for fourteen towns. Most crosses go up from bottom left to top right; one cross, at (10, 19), is well above the others.
One of the points is an outlier.
(a)
Write down the coordinates of this point.
(1 mark)
(b)
For all the other points write down the type of correlation.
(1 mark)
(c)
On the same day, in another British town, the maximum temperature was 16.4°C.
Estimate the number of hours of sunshine in this town on this day.
(2 marks)
(d)
A weatherman says,
“Temperatures are higher on days when there is more sunshine.”
Does the scatter graph support what the weatherman says?
Give a reason for your answer.
(1 mark)
Question 2 (2 marks)
Express 56 as the product of its prime factors.
(2 marks)
Question 3 (3 marks)
Work out 54.6 × 4.3
(3 marks)
Question 4 (3 marks)
Diagram: A square ABCD. Above the top side, double-headed arrows mark 3 cm from A, then x cm to B. Beside the left side, arrows mark 3 cm down from A, then x cm to D. Dashed lines across the square mark these lengths.
The area of square ABCD is 10 cm².
Show that x² + 6x = 1
(3 marks)
Question 5 (5 marks)
This rectangular frame is made from 5 straight pieces of metal.
Diagram: A rectangle 12 m long and 5 m high, with right angles marked at the top left and bottom right, and a diagonal from the bottom left corner to the top right corner.
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
(5 marks)
Question 6 (2 marks)
The equation of the line mathbfL_1 is y = 3x – 2
The equation of the line mathbfL_2 is 3y – 9x + 5 = 0
Show that these two lines are parallel.
(2 marks)
Question 7 (3 marks)
There are 10 boys and 20 girls in a class.
The class has a test.
The mean mark for all the class is 60
The mean mark for the girls is 54
Work out the mean mark for the boys.
(3 marks)
Question 8 (3 marks)
(a)
Write 7.97 × 10⁻⁶ as an ordinary number.
(1 mark)
(b)
Work out the value of (2.52 × 10⁵) ÷ (4 × 10⁻³)
Give your answer in standard form.
(2 marks)
Question 9 (2 marks)
Jules buys a washing machine.
20% VAT is added to the price of the washing machine.
Jules then has to pay a total of £600
What is the price of the washing machine with no VAT added?
(2 marks)
Question 10 (3 marks)
Show that (x + 1)(x + 2)(x + 3) can be written in the form ax³ + bx² + cx + d
where a, b, c and d are positive integers.
(3 marks)
Question 11 (3 marks)
The graph of y = f(x) is drawn on the grid.
Diagram: A U-shaped curve on a grid with x from –2 to 4 and y from –4 to 6. It crosses the y-axis at –2, has its lowest point at (1, –3), and crosses the x-axis between –1 and 0 and between 2 and 3.
(a)
Write down the coordinates of the turning point of the graph.
(1 mark)
(b)
Write down estimates for the roots of f(x) = 0
(1 mark)
(c)
Use the graph to find an estimate for f(1.5)
(1 mark)
Question 12 (4 marks)
(a)
Find the value of 81^(-1/2)
(2 marks)
(b)
Find the value of (64/125)^(2/3)
(2 marks)
Question 13 (4 marks)
The table shows a set of values for x and y.
x 1 2 3 4
y 9 21/4 1 9/16
y is inversely proportional to the square of x.
(a)
Find an equation for y in terms of x.
(2 marks)
(b)
Find the positive value of x when y = 16
(2 marks)
Question 14 (4 marks)
White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 3 : 7
The ratio of the number of white circles to the number of white squares is 4 : 5
The ratio of the number of black circles to the number of black squares is 2 : 5
Work out what fraction of all the shapes are circles.
(4 marks)
Question 15 (4 marks)
A cone has a volume of 98 cm³.
The radius of the cone is 5.13 cm.
Volume of cone = 1/3π r² h
Diagram: A sketch of a cone, with its perpendicular height h and the radius r of its base marked.
(a)
Work out an estimate for the height of the cone.
(3 marks)
(b)
John uses a calculator to work out the height of the cone to 2 decimal places.
Will your estimate be more than John’s answer or less than John’s answer?
Give reasons for your answer.
(1 mark)
Question 16 (4 marks)
n is an integer greater than 1
Prove algebraically that n² – 2 – (n – 2)² is always an even number.
(4 marks)
Question 17 (4 marks)
There are 9 counters in a bag.
7 of the counters are green.
2 of the counters are blue.
Ria takes at random two counters from the bag.
Work out the probability that Ria takes one counter of each colour.
You must show your working.
(4 marks)
Question 18 (4 marks)
Diagram: Axes with the origin O at the bottom left. Above them is a rhombus ABCD, with A at the top left, B at the top right, C at the bottom right and D at the bottom left. AB and DC are level.
ABCD is a rhombus.
The coordinates of A are (5, 11)
The equation of the diagonal DB is y = 1/2x + 6
Find an equation of the diagonal AC.
(4 marks)
Question 19 (4 marks)
Diagram: Parallelogram OABC, with O at the bottom left, A at the top left, B at the top right and C at the bottom right. An arrow on OA is labelled a and an arrow on OC is labelled c.
OABC is a parallelogram.
overrightarrowOA = mathbfa and overrightarrowOC = mathbfc
X is the midpoint of the line AC.
OCD is a straight line so that OC : CD = k : 1
Given that overrightarrowXD = 3mathbfc – 1/2mathbfa
find the value of k.
(4 marks)
Question 20 (5 marks)
Solve algebraically the simultaneous equations
x² + y² = 25
y – 3x = 13
(5 marks)
Question 21 (4 marks)
ABCD is a quadrilateral.
Diagram: Quadrilateral ABCD with A at the bottom left, B at the top left, C at the top right and D at the bottom right. BC is shorter than AD. AB and CD are marked equal, and the angles at B and C are marked equal.
AB = CD.
Angle ABC = angle BCD.
Prove that AC = BD.
(4 marks)
Question 22 (5 marks)
The diagram shows a hexagon ABCDEF.
Diagram: A hexagon ABCDEF shaped like an arrowhead pointing up: B at the top, A and C below it on either side, F and D at the bottom, and E inside, below B. A dashed line joins B to E. P is marked on AF and Q on CD.
ABEF and CBED are congruent parallelograms where AB = BC = x cm.
P is the point on AF and Q is the point on CD such that BP = BQ = 10 cm.
Given that angle ABC = 30°,
⁠prove that cos PBQ = 1 – dfrac(2 – √3)200x²
(5 marks)

x	1	2	3	4
y	9	21/4	1	9/16

Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.

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Edexcel GCSE Higher June 2017 Paper 1 (non-calculator)

Question 1 (5 marks)

Question 2 (2 marks)

Question 3 (3 marks)

Question 4 (3 marks)

Question 5 (5 marks)

Question 6 (2 marks)

Question 7 (3 marks)

Question 8 (3 marks)

Question 9 (2 marks)

Question 10 (3 marks)

Question 11 (3 marks)

Question 12 (4 marks)

Question 13 (4 marks)

Question 14 (4 marks)

Question 15 (4 marks)

Question 16 (4 marks)

Question 17 (4 marks)

Question 18 (4 marks)

Question 19 (4 marks)

Question 20 (5 marks)

Question 21 (4 marks)

Question 22 (5 marks)