Edexcel GCSE Higher June 2018 Paper 1 (non-calculator)
20 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 (4 marks)
(a)
Work out 21/7 + 11/4
(2 marks)
(b)
Work out 11/5 ÷ 3/4
Give your answer as a mixed number in its simplest form.
(2 marks)
Question 2 (3 marks)
In a village
the number of houses and the number of flats are in the ratio 7 : 4
the number of flats and the number of bungalows are in the ratio 8 : 5There are 50 bungalows in the village.
How many houses are there in the village?
(3 marks)
Question 3 (4 marks)
Renee buys 5 kg of sweets to sell.
She pays £10 for the sweets.Renee puts all the sweets into bags.
She puts 250 g of sweets into each bag.
She sells each bag of sweets for 65p.Renee sells all the bags of sweets.
Work out her percentage profit.
(4 marks)
Question 4 (4 marks)
A cycle race across America is 3069.25 miles in length.
Juan knows his average speed for his previous races is 15.12 miles per hour.
For the next race across America he will cycle for 8 hours per day.(a)
Estimate how many days Juan will take to complete the race.
(3 marks)
(b)
Juan trains for the race.
The average speed he can cycle at increases.
It is now 16.27 miles per hour.How does this affect your answer to part (a)?
(1 mark)
Question 5 (6 marks)
Here is a solid square-based pyramid, VABCD.
Diagram: A solid square-based pyramid VABCD. The base ABCD is a square with A and B at the front and D and C at the back; V is the vertex at the top. AB is marked 6 cm. A dotted line from V down to the centre of the base is marked 4 cm. M is the midpoint of BC, and the dotted line VM is marked 5 cm. An arrow labelled Front view points at the face VAB from the front.
The base of the pyramid is a square of side 6 cm.
The height of the pyramid is 4 cm.
M is the midpoint of BC and VM = 5 cm.(a)
Draw an accurate front elevation of the pyramid from the direction of the arrow.
Diagram: A blank centimetre grid, 14 squares across and 12 squares up.
(2 marks)
(b)
Work out the total surface area of the pyramid.
(4 marks)
Question 6 (5 marks)
A pattern is made from four identical squares.
The sides of the squares are parallel to the axes.
Diagram: A pair of axes with a pattern of four identical squares, sides parallel to the axes, going up to the right. A (6, 7) is the bottom left corner of the first square and B (38, 36) the top right corner of the last square. The second square starts at the top right corner of the first, and the fourth at the top right corner of the third; the third square is lower: its bottom left corner, C, is on the right side of the second square. C is marked with a cross but its coordinates are not given.
Point A has coordinates (6, 7)
Point B has coordinates (38, 36)
Point C is marked on the diagram.Work out the coordinates of C.
(5 marks)
Question 7 (2 marks)
Diagram: A grid with x from –6 to 6 and y from –7 to 6. Shape T is a shaded triangle with corners (1, 1), (3, 1) and (2, 3).
Shape T is reflected in the line x = -1 to give shape R.
Shape R is reflected in the line y = -2 to give shape S.Describe the single transformation that will map shape T to shape S.
(2 marks)
Question 8 (4 marks)
The perimeter of a right-angled triangle is 72 cm.
The lengths of its sides are in the ratio 3 : 4 : 5Work out the area of the triangle.
(4 marks)
Question 9 (4 marks)
(a)
Write down the value of 36^(1/2)
(1 mark)
(b)
Write down the value of 23⁰
(1 mark)
(c)
Work out the value of 27^(-2/3)
(2 marks)
Question 10 (5 marks)
The table gives some information about the heights of 80 girls.
Least height 133 cm Greatest height 170 cm Lower quartile 145 cm Upper quartile 157 cm Median 151 cm (a)
Draw a box plot to represent this information.
Diagram: A squared grid with a horizontal scale of height in centimetres from 120 to 180.
(3 marks)
(b)
Work out an estimate for the number of these girls with a height between 133 cm and
157 cm.(2 marks)
Question 11 (5 marks)
Diagram: A circle with centre O. A is on the circle at the left, a little above O; B is the lowest point of the circle. The straight line from A passes through O and leaves the circle on the right, meeting C. BC is a horizontal line touching the circle at B. A is joined to B.
A and B are points on a circle, centre O.
BC is a tangent to the circle.
AOC is a straight line.
Angle ABO = x°.Find the size of angle ACB, in terms of x.
Give your answer in its simplest form.
Give reasons for each stage of your working.(5 marks)
Question 12 (4 marks)
Prove that the square of an odd number is always 1 more than a multiple of 4
(4 marks)
Question 13 (3 marks)
√5(√8 + √18) can be written in the form a√10 where a is an integer.
Find the value of a.
(3 marks)
Question 14 (5 marks)
y is inversely proportional to d²
When d = 10, y = 4d is directly proportional to x²
When x = 2, d = 24Find a formula for y in terms of x.
Give your answer in its simplest form.(5 marks)
Question 15 (4 marks)
(a)
Factorise a² – b²
(1 mark)
(b)
Hence, or otherwise, simplify fully (x² + 4)² – (x² – 2)²
(3 marks)
Question 16 (3 marks)
There are only red counters, blue counters and purple counters in a bag.
The ratio of the number of red counters to the number of blue counters is 3 : 17Sam takes at random a counter from the bag.
The probability that the counter is purple is 0.2Work out the probability that Sam takes a red counter.
(3 marks)
Question 17 (3 marks)
Simplify fully (3x² – 8x – 3)/(2x² – 6x)
(3 marks)
Question 18 (2 marks)
Here is the graph of y = sin x° for -180 ≤ x ≤ 180
Diagram: A grid with x from –210 to 210 and y from –5 to 5, labelled every 90 across and every 2 up. The graph of y = sin x goes from (–180, 0) down to (–90, –1), up through (0, 0) to (90, 1) and back down to (180, 0).
On the grid, sketch the graph of y = sin x° – 2 for -180 ≤ x ≤ 180
(2 marks)
Question 19 (5 marks)
The point P has coordinates (3, 4)
The point Q has coordinates (a, b)A line perpendicular to PQ is given by the equation 3x + 2y = 7
Find an expression for b in terms of a.
(5 marks)
Question 20 (5 marks)
n is an integer such that 3n + 2 ≤ 14 and 6n/(n² + 5) > 1
Find all the possible values of n.
(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.