Edexcel GCSE Higher November 2022 Paper 3 (calculator)
26 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)
Make a the subject of the formula p = 3a – 9
(2 marks)
Question 2 (1 mark)
Rob has been asked to divide 120 in the ratio 3 : 5
Here is his working.
120 ÷ 3 = 40
120 ÷ 5 = 24Rob’s working is not correct.
Describe what Rob has done wrong.
(1 mark)
Question 3 (3 marks)
200 students chose one language to study.
Each student chose one language from French or Spanish or German.Of the 200 students,
90 are boys and the rest of the students are girls
70 chose Spanish
60 of the 104 students who chose French are boys
18 girls chose German.Work out how many boys chose Spanish.
(3 marks)
Question 4 (4 marks)
Karina has 4 tanks on her tractor.
Each tank is a cylinder with diameter 80 cm and height 160 cm.Diagram: A cylinder standing on its end. An arrow across the top shows the diameter, 80 cm; an arrow down the right side shows the height, 160 cm.
The 4 tanks are to be filled completely with a mixture of fertiliser and water.
The fertiliser has to be mixed with water in the ratio 1 : 100 by volume.
Karina has 32 litres of fertiliser.1 litre = 1000 cm³
Has Karina enough fertiliser for the 4 tanks?
You must show how you get your answer.(4 marks)
Question 5 (4 marks)
Triangle ABC and triangle DEF are similar.
Diagram: A diagram.
Diagram: A diagram.
(a)
Work out the length of EF.
(2 marks)
(b)
Work out the length of AB.
(2 marks)
Question 6 (4 marks)
One weekend the Keddie family is going to do a sports quiz and a music quiz.
The probability that the family will win the sports quiz is 0.3
The probability that the family will win the music quiz is 0.35(a)
Complete the probability tree diagram.
Diagram: Probability tree diagram. Sports quiz: win 0.3, do not win a gap. Music quiz after win: win 0.35, do not win a gap; after do not win: win 0.35, do not win a gap.
(2 marks)
(b)
Work out the probability that the Keddie family will win both the sports quiz and the
music quiz.(2 marks)
Question 7 (4 marks)
(a)
Change 8000 cm³ to m³
(1 mark)
(b)
Change a speed of 180 km per hour to metres per second.
(3 marks)
Question 8 (3 marks)
There are 30 women and 20 men at a gym.
The mean height of all 50 people is 167.6 cm
The mean height of the 20 men is 182 cmWork out the mean height of the 30 women.
(3 marks)
Question 9 (3 marks)
(a)
Write 6.75 × 10⁻⁴ as an ordinary number.
(1 mark)
(b)
Work out dfrac2.56 × 10⁶ × 4.12 × 10⁻³ 1.6 × 10⁻²
Give your answer in standard form.(2 marks)
Question 10 (1 mark)
Peter has to subtract (x² – 2x – 4) from (x² + 3x + 5)
Here is his working
(x² + 3x + 5) – (x² – 2x – 4)
= x² + 3x + 5 – x² – 2x – 4
= x + 1Explain what is wrong with Peter’s working.
(1 mark)
Question 11 (2 marks)
x and y are integers such that
3 < x < 8
4 < y < 10
and x + y = 14Find all the possible values of x.
(2 marks)
Question 12 (2 marks)
Martin used his calculator to work out the value of a number P.
He wrote down the first two digits of the answer on his calculator.
He wrote down 1.2Complete the error interval for P.
ldotsldots ≤ P < ldotsldots
(2 marks)
Question 13 (2 marks)
Chen has this information about the time that it took an operator at a call centre to answer each of 90 calls.
Time (t seconds) Cumulative frequency 0 < t ≤ 10 4 0 < t ≤ 20 25 0 < t ≤ 30 70 0 < t ≤ 40 88 0 < t ≤ 50 90 Chen draws this cumulative frequency graph for the information in the table.
Diagram: Chen’s graph: cumulative frequency (0 to 100) up, and a scale from 0 to 50 across with no label. Crosses at (5, 4), (10, 25), (15, 70), (20, 88) and (25, 90), joined to (0, 0) with a smooth S-shaped curve.
Write down two different things that are wrong with this graph.
(2 marks)
Question 14 (5 marks)
(a)
Simplify fully (3x⁵y⁶)⁴
(2 marks)
(b)
Expand and simplify (x + 2)(x – 3)(x + 4)
(3 marks)
Question 15 (2 marks)
A pet shop has
7 guppy fish
13 tetra fish
5 angel fish.David is going to choose one of the following combinations of fish
a guppy fish and an angel fish
or a tetra fish and an angel fish
or a guppy fish, a tetra fish and an angel fish.Show that there are 555 different ways for David to choose his fish.
(2 marks)
Question 16 (4 marks)
Diagram: A circle with A at the top, B on the right, D at the bottom right and E at the bottom left, all on the circle. AE and BD are chords. AB is extended to C outside the circle and ED is extended to C, so ABC and EDC are straight lines meeting at C. Angle DBC is marked 60°.
ABDE is a cyclic quadrilateral.
ABC and EDC are straight lines.
Angle DBC = 60°Given that
size of angle EAB : size of angle BCD = 2 : 1work out the size of angle BCD.
You must show all your working.(4 marks)
Question 17 (4 marks)
There are four boxes on a shelf, A, B, C and D.
The total weight of A and B is 3 times the total weight of C and D.
The weight of A is 2/3 of the weight of B.
The weight of C is 75% of the weight of D.
Find the ratio
weight of A : weight of B : weight of C : weight of D(4 marks)
Question 18 (2 marks)
Shape A is reflected in the line with equation x = 2 to give shape B.
Shape B is reflected in the line with equation x = 6 to give shape C.Describe fully the single transformation that maps shape A onto shape C.
(2 marks)
Question 19 (3 marks)
There are only blue counters, red counters and green counters in a box.
The probability that a counter taken at random from the box will be blue is 0.4
The ratio of the number of red counters to the number of green counters is 7 : 8
Sameena takes at random a counter from the box.
She records its colour and puts the counter back in the box.
Sameena does this a total of 50 times.Work out an estimate for the number of times she takes a green counter.
(3 marks)
Question 20 (3 marks)
The diagram shows a triangle ADE.
Diagram: Triangle ADE with AD across the top and E at the bottom. B and C are on AD, with B nearer A and C nearer D. Lines are drawn from E to B and from E to C.
AE = DE
AB : BC : CD = 1 : 2 : 1Prove that triangle ACE is congruent to triangle DBE.
(3 marks)
Question 21 (3 marks)
The equation of a curve is y = 4x² – 56x
The curve has one turning point.By completing the square, show that the coordinates of the turning point are (7, -196)
You must show all your working.(3 marks)
Question 22 (3 marks)
(2x + 3)/(x – 5) + (x – 4)/(x + 5) – 3 can be written in the form
(ax + b)/(x² – 25) where a and b are integers.
Work out the value of a and the value of b.
You must show all your working.(3 marks)
Question 23 (2 marks)
The graph of y = f(x) is shown on the grid below.
Diagram: A grid with x from –5 to 5 and y from –4 to 5. A cubic curve rises steeply from the bottom of the grid, crosses the x-axis at –1, turns at about (0, 2), crosses the x-axis at 1, dips just below it, then crosses again at 2 and rises steeply off the top.
(a)
On the grid above, sketch the graph of y = f(x + 2)
(1 mark)
(b)
Diagram: A grid with x from –4 to 4 and y from –3 to 3. Graph A (solid) comes down steeply from the top left, touches the x-axis at about –1.2, makes a small hump just above the axis, touches the axis again at the origin and rises steeply. Graph B (dashed) is graph A turned upside down: the same shape below the x-axis.
On this grid, graph A has been reflected to give graph B.
The equation of graph A is y = g(x)Write down an equation of graph B.
(1 mark)
Question 24 (4 marks)
CDEF is a quadrilateral.
Diagram: Quadrilateral CDEF with CD along the top and FE along the bottom, parallel to CD and half as long. Arrows show the vectors 2a from C to D, a from F to E, and b from E to D.
overrightarrowFE = mathbfa overrightarrowED = mathbfb overrightarrowCD = 2mathbfa
The point P is such that CEP is a straight line and that CE = EP
Use a vector method to prove that CF is parallel to DP.
(4 marks)
Question 25 (5 marks)
The pyramid P is formed from two parts made of different materials.
Diagram: A square-based pyramid cut by a plane parallel to its base, shown with dashed lines. The small pyramid above the cut is labelled top; the piece below it is labelled bottom.
The top part of P has a mass of 92.8 g and is made from material with a density of 2.9 g/cm³
The bottom part of P has a mass of 972.8 g
The average density of P is 4.7 g/cm³Calculate the volume of the top part of P as a percentage of the total volume of P.
Give your answer correct to 1 decimal place.
You must show all your working.(5 marks)
Question 26 (5 marks)
ABCDEFG is a regular heptagon.
Diagram: A regular heptagon ABCDEFG with A at the top and the letters going clockwise. The line GB is drawn, cutting off triangle ABG at the top.
The area of triangle ABG is 30 cm²
Calculate the length of GB.
Give your answer correct to 3 significant figures.
You must show all your working.(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.