Edexcel GCSE Higher November 2018 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 (2 marks)
Work out the value of dfrac3⁷ × 3⁻² 3³
(2 marks)
Question 2 (4 marks)
v² = u² + 2a s
u = 12 a = -3 s = 18
(a)
Work out a value of v.
(2 marks)
(b)
Make s the subject of v² = u² + 2a s
(2 marks)
Question 3 (5 marks)
A bonus of £2100 is shared by 10 people who work for a company.
40% of the bonus is shared equally between 3 managers.
The rest of the bonus is shared equally between 7 salesmen.One of the salesmen says,
“If the bonus is shared equally between all 10 people I will get 25% more money.”
Is the salesman correct?
You must show how you get your answer.(5 marks)
Question 4 (3 marks)
It would take 120 minutes to fill a swimming pool using water from 5 taps.
(a)
How many minutes will it take to fill the pool if only 3 of the taps are used?
(2 marks)
(b)
State one assumption you made in working out your answer to part (a).
(1 mark)
Question 5 (4 marks)
A plane travels at a speed of 213 miles per hour.
(a)
Work out an estimate for the number of seconds the plane takes to travel 1 mile.
(3 marks)
(b)
Is your answer to part (a) an underestimate or an overestimate?
Give a reason for your answer.(1 mark)
Question 6 (3 marks)
Solve the simultaneous equations
5x + y = 21
x – 3y = 9(3 marks)
Question 7 (4 marks)
The diagram shows a square ABCD with sides of length 20 cm.
It also shows a semicircle and an arc of a circle.Diagram: A square ABCD with sides of 20 cm, A at the bottom left and B at the bottom right. A semicircle with diameter AB is drawn inside the square, and an arc of the circle centred at B goes from A up to C. The region between the arc and the semicircle is shaded.
AB is the diameter of the semicircle.
AC is an arc of a circle with centre B.Show that dfracarea of shaded regionarea of square = (π)/8
(4 marks)
Question 8 (3 marks)
(a)
Write down the exact value of tan 45°
(1 mark)
(b)
Here is a right-angled triangle.
Diagram: A right-angled triangle with the right angle at the bottom left. The vertical side is 4 cm. The angle at the top is 60°. The sloping side, opposite the right angle, is x cm.
cos 60° = 0.5
Work out the value of x.
(2 marks)
Question 9 (6 marks)
The times that 48 trains left a station on Monday were recorded.
The cumulative frequency graph gives information about the numbers of minutes the trains were delayed, correct to the nearest minute.
The shortest delay was 0 minutes. The longest delay was 42 minutes.Diagram: A cumulative frequency graph for the delays of 48 trains, with an empty box plot grid for Monday underneath on the same delay scale. The curve starts at (0, 0) and rises steeply at first, through about (4, 12), (10, 24), (20, 36), (30, 44) and (40, 47), levelling off to 48 at 50 minutes.
(a)
On the grid below, draw a box plot for the information about the delays on Monday.
(3 marks)
(b)
48 trains left the station on Tuesday. The box plot below gives information about the delays on Tuesday.
Diagram: Tuesday: lowest 0, lower quartile 6, median 9, upper quartile 17, highest 33.
Compare the distribution of the delays on Monday with the distribution of the delays on Tuesday.
(2 marks)
(c)
Mary says, “The longest delay on Tuesday was 33 minutes.
This means that there must be some delays of between 25 minutes and 30 minutes.”
Is Mary right? You must give a reason for your answer.(1 mark)
Question 10 (3 marks)
(a)
Simplify (x – 1)/(5(x – 1)²)
(1 mark)
(b)
Factorise fully 50 – 2y²
(2 marks)
Question 11 (3 marks)
Jack and Sadia work for a company that sells boxes of breakfast cereal.
The company wants to have a special offer.Here is Jack’s idea for the special offer.
Put 25% more cereal into each box and do not change the price. Here is Sadia’s idea.
Reduce the price and do not change the amount of cereal in each box. Sadia wants her idea to give the same value for money as Jack’s idea.
By what percentage does she need to reduce the price?
(3 marks)
Question 12 (3 marks)
Diagram: A circle with centre O. A, B and C are on the circle, with B at the top, C at the lower left and A at the right. The chords BA, BC and CA and the radii OB and OA are drawn. The line DAE touches the circle at A, with E above A and D below. Angle BAE is marked 56° and angle CBO is marked 35°.
A, B and C are points on the circumference of a circle, centre O.
DAE is the tangent to the circle at A.Angle BAE = 56°
Angle CBO = 35°Work out the size of angle CAO.
You must show all your working.(3 marks)
Question 13 (2 marks)
Diagram: A grid with x and y from –6 to 6. Triangle A has corners (–4, –1), (–4, –4) and (2, –4). Triangle B has corners (4, 3), (4, 4) and (2, 4).
Describe fully the single transformation that maps triangle A onto triangle B.
(2 marks)
Question 14 (4 marks)
(a)
Work out the value of (16/81)^(3/4)
(2 marks)
(b)
3^a = 1/9 3^b = 9√3 3^c = dfrac1√3
Work out the value of a + b + c
(2 marks)
Question 15 (4 marks)
Three solid shapes A, B and C are similar.
The surface area of shape A is 4 cm²
The surface area of shape B is 25 cm²The ratio of the volume of shape B to the volume of shape C is 27 : 64
Work out the ratio of the height of shape A to the height of shape C.
Give your answer in its simplest form.(4 marks)
Question 16 (3 marks)
Prove algebraically that 0.25̇6̇ can be written as 127/495
(3 marks)
Question 17 (4 marks)
Here is a sketch of a curve.
Diagram: A sketch of a U-shaped curve on x and y axes with no scale. It crosses the x-axis once to the left of O and once to the right, crosses the y-axis below O, and its lowest point is below the x-axis, to the right of the y-axis.
The equation of the curve is y = x² + ax + b where a and b are integers.
The points (0, -5) and (5, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
(4 marks)
Question 18 (2 marks)
The graph of y = f(x) is shown on the grid below.
(a)
Diagram: A grid with x from –4 to 6 and y from –3 to 3. The graph of y = f(x) is a U-shaped curve from (–1, 3) down through O to its lowest point (1, –1), then up through (2, 0) to (3, 3).
On the grid above, sketch the graph of y = f(x – 2)
(1 mark)
(b)
Diagram: A grid with x from –4 to 6 and y from –3 to 3. Graph A comes down from (–3.5, 3), crosses the x-axis at about –1.2, crosses the y-axis at about –0.6, then falls steeply to (1, –3). Graph B is its mirror image in the y-axis: it rises steeply from (–1, –3) through the same point on the y-axis, crosses the x-axis at about 1.2 and goes up to (3.5, 3).
On the grid, graph A has been reflected to give graph B.
The equation of graph A is y = g(x)
Write down the equation of graph B.
(1 mark)
Question 19 (4 marks)
For all values of x
f(x) = (x + 1)² and g(x) = 2(x – 1)
(a)
Show that gf(x) = 2x(x + 2)
(2 marks)
(b)
Find g⁻¹(7)
(2 marks)
Question 20 (3 marks)
Show that dfrac(√18 + √2)²√8 – 2 can be written in the form a(b + √2) where a and b are integers.
(3 marks)
Question 21 (5 marks)
Diagram: Triangle OAB, with O at the bottom left, B at the bottom right and A at the top. M is the midpoint of AB. The line OM and the line from A to N on OB cross at P.
OAB is a triangle.
OPM and APN are straight lines.
M is the midpoint of AB.overrightarrowOA = mathbfa overrightarrowOB = mathbfb
OP : PM = 3 : 2
Work out the ratio ON : NB
(5 marks)
Question 22 (6 marks)
There are only green pens and blue pens in a box.
There are three more blue pens than green pens in the box.
There are more than 12 pens in the box.Simon is going to take at random two pens from the box.
The probability that Simon will take two pens of the same colour is 27/55
Work out the number of green pens in the box.
(6 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.