Edexcel GCSE Higher November 2019 Paper 2 (calculator)
25 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)
The table shows some information about the weights of 50 potatoes.
Weight (w grams) Frequency 10 < w ≤ 20 6 20 < w ≤ 30 21 30 < w ≤ 40 13 40 < w ≤ 50 7 50 < w ≤ 60 3 Iveta drew this frequency polygon for the information in the table.
The frequency polygon is not fully correct.Diagram: A grid with weight (w grams) from 10 to 60 across and numbers from 0 to 30 up the side; the vertical axis has no label. Crosses at (15, 8), (25, 21), (35, 13), (45, 7), (55, 3) are joined in order with straight lines, and the last cross is joined back to the first.
Write down two things that are wrong with the frequency polygon.
(2 marks)
Question 2 (2 marks)
The length of a pencil is 128 mm correct to the nearest millimetre.
Complete the error interval for the length of the pencil.
(2 marks)
Question 3 (4 marks)
Tom and Adam have a total of 240 stamps.
The ratio of the number of Tom’s stamps to the number of Adam’s stamps is 3 : 7Tom buys some stamps from Adam.
The ratio of the number of Tom’s stamps to the number of Adam’s stamps is now 3 : 5How many stamps does Tom buy from Adam?
You must show all your working.(4 marks)
Question 4 (3 marks)
Each person in a fitness club is going to get a free gift.
Stan is going to order the gifts.Stan takes a sample of 50 people in the fitness club.
He asks each person to tell him the gift they would like.The table shows information about his results.
Gift Number of people sports bag 17 gym towel 7 headphones 11 voucher 15 There are 700 people in the fitness club.
(i)
Work out how many sports bags Stan should order.
(2 marks)
(ii)
Write down any assumption you made and explain how this could affect your answer.
(1 mark)
Question 5 (2 marks)
Here are six graphs.
A
Diagram: Graph A: a U-shaped curve with its lowest point at O.
B
Diagram: Graph B: a cubic curve through O, rising from bottom left, with a maximum then a minimum, crossing the x-axis three times.
C
Diagram: Graph C: two curves, top left and bottom right, never touching the axes.
D
Diagram: Graph D: two curves, top right and bottom left, never touching the axes.
E
Diagram: Graph E: a straight line with positive gradient, crossing the y-axis above O.
F
Diagram: Graph F: an S-shaped curve through O, rising from bottom left to top right and flattening at O.
Write down the letter of the graph that could have the equation
(a)
y = x³
(1 mark)
(b)
y = 1/x
(1 mark)
Question 6 (3 marks)
The nth term of a sequence is 2n² – 1
The nth term of a different sequence is 40 – n²
Show that there is only one number that is in both of these sequences.
(3 marks)
Question 7 (2 marks)
Work out (3.42 × 10⁻⁷) ÷ (7.5 × 10⁻⁶)
Give your answer in standard form.
(2 marks)
Question 8 (3 marks)
The number of days, d, that it will take to build a house is given by
d = 720/n
where n is the number of workers used each day.
Ali’s company will take 40 days to build the house.
Hayley’s company will take 30 days to build the house.Hayley’s company will have to use more workers each day than Ali’s company.
How many more?
(3 marks)
Question 9 (5 marks)
The diagram shows a cube and a cuboid.
Diagram: A cube with no lengths labelled, and a cuboid 8 cm across the front, 6 cm high and 18 cm long going back.
The total surface area of the cube is equal to the total surface area of the cuboid.
Janet says,
“The volume of the cube is equal to the volume of the cuboid.”
Is Janet correct?
You must show how you get your answer.(5 marks)
Question 10 (2 marks)
Make k the subject of the formula y = √(2m – k)
(2 marks)
Question 11 (3 marks)
Megan grows potatoes.
The box plot below shows information about the weights of Megan’s potatoes.
Diagram: Megan: lowest 23, lower quartile 39, median 57, upper quartile 65, highest 72.
Megan says that half of her potatoes weigh less than 50 grams each.
(a)
Is Megan correct?
Give a reason for your answer.(1 mark)
(b)
Amy also grows potatoes.
The box plot below shows information about the weights of Amy’s potatoes.
Diagram: Amy: lowest 23, lower quartile 35, median 42, upper quartile 51, highest 70.
Compare the distribution of the weights of Megan’s potatoes with the distribution of
the weights of Amy’s potatoes.(2 marks)
Question 12 (4 marks)
The diagram shows triangle ABC.
Diagram: Triangle ABC with AC along the bottom. D is on AC and BD is vertical, at right angles to AC. E is on DB and A is joined to E. AD is labelled 4.4 cm, BC is labelled 8.6 cm and angle DCB is marked 40°.
ADC and DEB are straight lines.
AD = 4.4 cm
BC = 8.6 cm
E is the midpoint of DB.Angle CDB = 90°
Angle DCB = 40°Work out the size of angle EAD.
Give your answer correct to 1 decimal place.
You must show all your working.(4 marks)
Question 13 (3 marks)
Sakira invested £3550 in a savings account for 3 years.
She was paid 2.6% per annum compound interest for each of the first 2 years.
She was paid R% interest for the third year.Sakira had £3819.21 in her savings account at the end of the 3 years.
Work out the value of R.
Give your answer correct to 1 decimal place.(3 marks)
Question 14 (2 marks)
Sadia is going to buy a new car.
For the car, she can choose one body colour, one roof colour and one wheel type.She can choose from
19 different body colours
25 different wheel typesThe total number of ways Sadia can choose the body colour and the roof colour and the
wheel type is 3325Work out the number of different roof colours that Sadia can choose from.
(2 marks)
Question 15 (3 marks)
Expand and simplify (3x + 2)(2x + 1)(x – 5)
(3 marks)
Question 16 (3 marks)
Marek has 9 cards.
There is a number on each card.Diagram: 9 cards in a row, numbered 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Marek takes at random two of the cards.
He works out the product of the numbers on the two cards.Work out the probability that the product is an even number.
(3 marks)
Question 17 (3 marks)
Diagram: A circle with centre O, marked with a dot. A is at the bottom of the circle and CAD is a horizontal line touching the circle at A, with C to the left and D to the right, outside the circle. B is on the circle at the upper left, and BOD is a straight line. OA and BA are drawn. Angle ODA is marked 32°.
A and B are points on a circle with centre O.
CAD is the tangent to the circle at A.
BOD is a straight line.Angle ODA = 32°
Work out the size of angle CAB.
You must show all your working.(3 marks)
Question 18 (3 marks)
The histogram gives information about the heights, in metres, of the trees in a park.
The histogram is incomplete.Diagram: An incomplete histogram of the heights of the trees, with no bar from 10 to 12.5 metres. Bars: 0 to 2.5 metres, frequency density 1.2; 2.5 to 5 metres, frequency density 2; 5 to 10 metres, frequency density 2.8; 12.5 to 25 metres, frequency density 0.8.
20% of the trees in the park have a height between 10 metres and 12.5 metres.
None of the trees in the park have a height greater than 25 metres.Complete the histogram.
(3 marks)
Question 19 (2 marks)
The diagram shows a hemisphere with diameter 8.4 cm.
Diagram: A hemisphere with its flat circular face at the top. A line with arrows at both ends goes across the diameter of the flat face, labelled 8.4 cm.
Diagram: A sphere with its centre marked and a radius r drawn from the centre to the surface.
Volume of sphere = 4/3π r³
Work out the volume of the hemisphere.
Give your answer correct to 3 significant figures.(2 marks)
Question 20 (4 marks)
d = 1/8c³
c = 10.9 correct to 3 significant figures.
By considering bounds, work out the value of d to a suitable degree of accuracy.
Give a reason for your answer.(4 marks)
Question 21 (5 marks)
Here is a speed-time graph for a train journey between two stations.
The journey took 100 seconds.Diagram: A speed-time graph for a train journey. The speed rises steadily from 0 at 0 seconds to 12 m/s at 30 seconds, stays at 12 m/s until 80 seconds, then falls steadily to 0 at 100 seconds.
(a)
Calculate the time taken by the train to travel half the distance between the two stations.
You must show all your working.(4 marks)
(b)
Compare the acceleration of the train during the first part of its journey with the
acceleration of the train during the last part of its journey.(1 mark)
Question 22 (4 marks)
The number of rabbits on a farm at the end of month n is P_n
The number of rabbits at the end of the next month is given by P_n + 1 = 1.2P_n – 50At the end of March there are 200 rabbits on the farm.
(a)
Work out how many rabbits there will be on the farm at the end of June.
(3 marks)
(b)
Considering your results in part (a), suggest what will happen to the number of
rabbits on the farm after a long time.(1 mark)
Question 23 (6 marks)
The diagram shows a parallelogram.
Diagram: A parallelogram leaning to the right. The top side is labelled (2x – 1) cm and the left side is labelled (10 – x) cm. The angle between them, at the top left, is marked 150°.
The area of the parallelogram is greater than 15 cm²
(a)
Show that 2x² – 21x + 40 < 0
(3 marks)
(b)
Find the range of possible values of x.
(3 marks)
Question 24 (2 marks)
Diagram: A grid with x and y from –6 to 6. Square ABCD is shaded, with A at (1, 4), B at (3, 4), C at (3, 2) and D at (1, 2).
Square ABCD is transformed by a combined transformation of a reflection in the line x = -1
followed by a rotation.Under the combined transformation, two vertices of the square ABCD are invariant.
Describe fully one possible rotation.
(2 marks)
Question 25 (5 marks)
The straight line L has equation 3x + 2y = 17
The point A has coordinates (0, 2)
The straight line M is perpendicular to L and passes through A.Line L crosses the y-axis at the point B.
Lines L and M intersect at the point C.Work out the area of triangle ABC.
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.