Edexcel GCSE Higher November 2020 Paper 2 (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)
(a)
Write 84 as a product of its prime factors.
(2 marks)
(b)
Find the lowest common multiple (LCM) of 60 and 84
(2 marks)
Question 2 (5 marks)
ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {even numbers}
B = {factors of 10}(a)
Complete the Venn diagram for this information.
Diagram: Venn diagram with sets A and B. Only A: . Both: . Only B: . Neither: .
(3 marks)
(b)
A number is chosen at random from the universal set, ℰ
Find the probability that this number is in the set A ∩ B
(2 marks)
Question 3 (5 marks)
Carlo puts tins into small boxes and into large boxes.
He puts 6 tins into each small box.
He puts 20 tins into each large box.Carlo puts a total of 3000 tins into the boxes so that
number of tins in small boxes : number of tins in large boxes = 2 : 3
Carlo says that less than 30% of the boxes filled with tins are large boxes.
Is Carlo correct?
You must show all your working.(5 marks)
Question 4 (4 marks)
(a)
Complete the table of values for y = 5 – x³
x –2 –1 0 1 2 y 6 (2 marks)
(b)
On the grid below, draw the graph of y = 5 – x³ for values of x from –2 to 2
Diagram: A blank grid with x from –2 to 2 and y from –6 to 14.
(2 marks)
Question 5 (2 marks)
Diagram: A right-angled triangle. The bottom side is horizontal, with the right angle at its right-hand end. The angle at the left-hand end is 34°. The sloping side is 178 mm. The vertical side is x mm.
Work out the value of x.
Give your answer correct to 1 decimal place.(2 marks)
Question 6 (2 marks)
mathbfa = ( 3 , 4 ) mathbfb = ( 5 , -2 )
Find 2mathbfa – 3mathbfb as a column vector.
(2 marks)
Question 7 (4 marks)
The diagram shows a right-angled triangle and a quarter circle.
Diagram: A right-angled triangle ABC: AB = 6 m along the bottom, a right angle at B, C straight above B, and AC = 9 m. A quarter circle with centre C goes from B round to D, where CD is horizontal and the angle BCD is a right angle.
The right-angled triangle ABC has angle ABC = 90°
The quarter circle has centre C and radius CB.Work out the area of the quarter circle.
Give your answer correct to 3 significant figures.
You must show all your working.(4 marks)
Question 8 (5 marks)
Tariq buys a laptop.
He gets a discount of 5% off the normal price.
Tariq pays £551 for the laptop.(a)
Work out the normal price of the laptop.
(2 marks)
(b)
Joan invests £6000 in a savings account.
The savings account pays compound interest at a rate of
2.4% for the first year
1.7% for each extra year.Work out the value of Joan’s investment at the end of 3 years.
(3 marks)
Question 9 (2 marks)
Aisha recorded the heights, in centimetres, of some girls.
She used her results to work out the information in this table.Least height 142 cm Lower quartile 154 cm Interquartile range 17 cm Median 162 cm Range 40 cm Aisha drew this box plot for the information in the table.
The box plot is not fully correct.Diagram: Box plot: lowest 142, lower quartile 154, median 161, upper quartile 172, highest 182.
Write down the two things Aisha should do to make the box plot fully correct.
(2 marks)
Question 10 (4 marks)
(a)
Simplify (1/(m²))⁰
(1 mark)
(b)
Simplify (8(x – 4))/((x – 4)²)
(1 mark)
(c)
Simplify (3n⁴w²)³
(2 marks)
Question 11 (2 marks)
Jack is in a restaurant.
There are 5 starters, 8 main courses and some desserts on the menu.Jack is going to choose one starter, one main course and one dessert.
He says there are 240 ways that he can choose his starter, his main course and his dessert.Could Jack be correct?
You must show how you get your answer.(2 marks)
Question 12 (3 marks)
The graph gives information about the volume, v litres, of petrol in the tank of Jim’s car after it has travelled a distance of d kilometres.
(a)
Diagram: A straight line graph of volume of petrol (0 to 30 litres) against distance (0 to 300 km). The line goes down from 27 litres at 0 km to 0 litres at 300 km.
Find the gradient of the graph.
(2 marks)
(b)
Interpret what the gradient of the graph represents.
(1 mark)
Question 13 (3 marks)
Here is triangle ABC.
Diagram: Triangle ABC with AB along the bottom and C above and to the left of A. CB is 23.8 cm, angle ACB is 34° and angle ABC is 26°.
Work out the length of AB.
Give your answer correct to 1 decimal place.(3 marks)
Question 14 (4 marks)
Here are two squares, A and B.
Diagram: Two squares side by side with their tops level: a smaller square A on the left and a larger square B on the right.
The length of each side of square B is 4 cm greater than the length of each side of square A.
The area of square B is 70 cm² greater than the area of square A.Find the area of square B.
Give your answer correct to 3 significant figures.
You must show all your working.(4 marks)
Question 15 (2 marks)
Diagram: A grid with x from –6 to 7 and y from –8 to 6. Triangle A has corners (3, 3), (5, 3) and (5, 5). Triangle B has corners (–2, –2), (–5, –2) and (–5, –5).
Describe fully the single transformation that maps triangle A onto triangle B.
(2 marks)
Question 16 (3 marks)
Here are the first five terms of a quadratic sequence.
10 21 38 61 90
Find an expression, in terms of n, for the nth term of this sequence.
(3 marks)
Question 17 (1 mark)
Write down the coordinates of the turning point on the graph of y = (x + 12)² – 7
(1 mark)
Question 18 (4 marks)
The diagram represents a solid cone.
Diagram: A cone with base diameter 20 cm and slant height 25 cm. A circle is drawn around the cone 10 cm up the slant from the base, and the part of the cone above the circle is shaded grey.
Diagram: A box with the formula: curved surface area of cone = πrl. Beside it, a cone with slant height l, perpendicular height h and base radius r.
The cone has a base diameter of 20 cm and a slant height of 25 cm.
A circle is drawn around the surface of the cone at a slant height of 10 cm above the base.
The curved surface of the cone above the circle is painted grey.Work out the area of the curved surface of the cone that is not painted grey.
Give your answer as a multiple of π
You must show all your working.(4 marks)
Question 19 (4 marks)
A hot air balloon is descending.
The height of the balloon n minutes after it starts to descend is h_n metres.
The height of the balloon (n + 1) minutes after it starts to descend, h_n + 1 metres, is given byh_n + 1 = K × h_n + 20 where K is a constant.
The balloon starts to descend from a height of 1200 metres at 09 15
At 09 16 the height of the balloon is 1040 metres.Work out the height of the balloon at 09 18
(4 marks)
Question 20 (8 marks)
There are only red sweets and yellow sweets in a bag.
There are n red sweets in the bag.
There are 8 yellow sweets in the bag.Sajid is going to take at random a sweet from the bag and eat it.
He says that the probability that the sweet will be red is 7/10
(a)
Show why the probability cannot be 7/10
(3 marks)
(b)
After Sajid has taken the first sweet from the bag and eaten it, he is going to take at random a second sweet from the bag.
Given that the probability that both the sweets he takes will be red is 3/5
work out the number of red sweets in the bag.
You must show all your working.(5 marks)
Question 21 (4 marks)
The graph of the curve with equation y = f(x) is shown on the grid below.
(a)
Diagram: A grid with x from –4 to 4 and y from –3 to 3. The curve y = f(x) starts at (–4, 2), goes down to touch the x-axis at (–3, 0), up through (–2, 1) to a highest point at (–1, 2), then down to the origin.
On the grid above, sketch the graph of the curve with equation y = f(-x)
(2 marks)
(b)
Diagram: A sketch of two n-shaped curves of the same shape. Curve C has its highest point at (1, 6). Curve S is curve C moved to the right, with its highest point at (4, 6).
The curve C with equation y = 5 + 2x – x² is transformed by a translation to give the curve S such that the point (1, 6) on C is mapped to the point (4, 6) on S.
Find an equation for S.
(2 marks)
Question 22 (5 marks)
C is a circle with centre the origin.
A tangent to C passes through the points (–20, 0) and (0, 10)Work out an equation of C.
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.