Edexcel GCSE Higher June 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 (4 marks)
There are only blue cubes, red cubes and yellow cubes in a box.
The table shows the probability of taking at random a blue cube from the box.
Colour blue red yellow Probability 0.2 The number of red cubes in the box is the same as the number of yellow cubes in the box.
(a)
Complete the table.
(2 marks)
(b)
There are 12 blue cubes in the box.
Work out the total number of cubes in the box.
(2 marks)
Question 2 (5 marks)
Deon needs 50 g of sugar to make 15 biscuits.
She also needs
three times as much flour as sugar
two times as much butter as sugarDeon is going to make 60 biscuits.
(a)
Work out the amount of flour she needs.
(3 marks)
(b)
Deon has to buy all the butter she needs to make 60 biscuits.
She buys the butter in 250 g packs.How many packs of butter does Deon need to buy?
(2 marks)
Question 3 (2 marks)
Find the highest common factor (HCF) of 72 and 90
(2 marks)
Question 4 (2 marks)
The diagram shows the plan, front elevation and side elevation of a solid shape, drawn
on a centimetre grid.Diagram: A centimetre grid. The plan is a circle 4 squares across. The front elevation and the side elevation are both rectangles 4 squares wide and 5 squares tall.
In the space below, draw a sketch of the solid shape.
Give the dimensions of the solid on your sketch.(2 marks)
Question 5 (3 marks)
Diagram: A graph.
Shape A can be transformed to shape B by a reflection in the x-axis followed by a
translation ( c , d )Find the value of c and the value of d.
(3 marks)
Question 6 (4 marks)
A shop sells packs of black pens, packs of red pens and packs of green pens.
There are
2 pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pensOn Monday,
number of packs of black pens sold : number of packs of red pens sold : number of packs of green pens sold = 7 : 3 : 4
A total of 212 pens were sold.
Work out the number of green pens sold.
(4 marks)
Question 7 (4 marks)
Here are two rectangles.
Diagram: Two rectangles: ABCD, wider than it is tall, and PQRS, taller than it is wide.
QR = 10 cm
BC = PQThe perimeter of ABCD is 26 cm
The area of PQRS is 45 cm²Find the length of AB.
(4 marks)
Question 8 (4 marks)
(a)
Work out an estimate for the value of √(63.5 × 101.7)
(2 marks)
(b)
(2.3)⁶ = 148 correct to 3 significant figures.
Find the value of (0.23)⁶ correct to 3 significant figures.
(1 mark)
(c)
Find the value of 5⁻²
(1 mark)
Question 9 (3 marks)
Work out 31/2 × 13/5
Give your answer as a mixed number in its simplest form.(3 marks)
Question 10 (2 marks)
The graphs with equations 3y + 2x = 1/2 and 2y – 3x = -113/12 have been drawn on the grid below.
Diagram: Two straight lines on a grid, x from –1 to 3 and y from –3 to 1. One line slopes down gently; the other slopes up steeply. They cross once.
Using the graphs, find estimates of the solutions of the simultaneous equations
3y + 2x = 1/2
2y – 3x = -113/12(2 marks)
Question 11 (4 marks)
A bus company recorded the ages, in years, of the people on coach A and the people
on coach B.Here are the ages of the 23 people on coach A.
41 42 44 48 52 53 53 53 56 57 57 59
60 61 63 64 64 66 67 69 74 77 79(a)
Complete the table below to show information about the ages of the people on coach A.
Coach A Median Lower quartile Upper quartile Least age 41 Greatest age 79 (2 marks)
(b)
Here is some information about the ages of the people on coach B.
Coach B Median 70 Lower quartile 54 Upper quartile 73 Least age 42 Greatest age 85 Richard says that the people on coach A are younger than the people on coach B.
Is Richard correct? You must give a reason for your answer.
(1 mark)
(c)
Richard says that the people on coach A vary more in age than the people on coach B.
Is Richard correct? You must give a reason for your answer.
(1 mark)
Question 12 (3 marks)
Here are three spheres.
Diagram: Three spheres, P, Q and R, in a row. Each is bigger than the one before.
The volume of sphere Q is 50% more than the volume of sphere P.
The volume of sphere R is 50% more than the volume of sphere Q.Find the volume of sphere P as a fraction of the volume of sphere R.
(3 marks)
Question 13 (2 marks)
Given that n can be any integer such that n > 1, prove that n² – n is never an odd number.
(2 marks)
Question 14 (2 marks)
Find the exact value of tan 30° × sin 60°
Give your answer in its simplest form.(2 marks)
Question 15 (4 marks)
The diagram shows a solid shape.
The shape is a cone on top of a hemisphere.Diagram: A solid made of a cone, point up, on top of a hemisphere of the same width. The diameter across the join is labelled 6 cm and the height of the cone is labelled 10 cm.
Volume of a cone = 1/3π r²h
Diagram: A cone with its perpendicular height h and the radius r of its base marked.
Volume of a sphere = 4/3π r³
Diagram: A sphere with its radius r marked from the centre.
The height of the cone is 10 cm.
The base of the cone has a diameter of 6 cm.
The hemisphere has a diameter of 6 cm.The total volume of the shape is kπ cm³, where k is an integer.
Work out the value of k.
(4 marks)
Question 16 (4 marks)
There are three dials on a combination lock.
Each dial can be set to one of the numbers 1, 2, 3, 4, 5
The three digit number 553 is one way the dials can be set, as shown in the diagram.Diagram: A padlock with three dials. The dials show 5, 5, 3 from top to bottom.
(a)
Work out the number of different three digit numbers that can be set for the
combination lock.(2 marks)
(b)
How many of the possible three digit numbers have three different digits?
(2 marks)
Question 17 (4 marks)
Given that
x² : (3x + 5) = 1 : 2
find the possible values of x.
(4 marks)
Question 18 (5 marks)
(a)
Express √3 + √12 in the form a√3 where a is an integer.
(2 marks)
(b)
Express (dfrac1√3)⁷ in the form dfrac√bc where b and c are integers.
(3 marks)
Question 19 (3 marks)
Given that x² – 6x + 1 = (x – a)² – b for all values of x,
(i)
find the value of a and the value of b.
(2 marks)
(ii)
Hence write down the coordinates of the turning point on the graph of y = x² – 6x + 1
(1 mark)
Question 20 (4 marks)
h is inversely proportional to p
p is directly proportional to √tGiven that h = 10 and t = 144 when p = 6
find a formula for h in terms of t
(4 marks)
Question 21 (7 marks)
The functions f and g are such that
f(x) = 3x – 1 and g(x) = x² + 4
(a)
Find f⁻¹(x)
(2 marks)
(b)
Given that fg(x) = 2gf(x),
show that 15x² – 12x – 1 = 0
(5 marks)
Question 22 (5 marks)
There are only r red counters and g green counters in a bag.
A counter is taken at random from the bag.
The probability that the counter is green is 3/7
The counter is put back in the bag.2 more red counters and 3 more green counters are put in the bag.
A counter is taken at random from the bag.
The probability that the counter is green is 6/13Find the number of red counters and the number of green counters that were in the bag originally.
(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.