Edexcel GCSE Higher November 2017 Paper 3 (calculator)
21 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 (3 marks)
The table shows information about the heights of 80 children.
Height (h cm) Frequency 130 < h ≤ 140 4 140 < h ≤ 150 11 150 < h ≤ 160 24 160 < h ≤ 170 22 170 < h ≤ 180 19 (a)
Find the class interval that contains the median.
(1 mark)
(b)
Draw a frequency polygon for the information in the table.
Diagram: A blank grid. Height (h cm) from 130 to 180 across, frequency from 0 to 30 up.
(2 marks)
Question 2 (3 marks)
In London, 1 litre of petrol costs 108.9p
In New York, 1 US gallon of petrol costs ＄2.831 US gallon = 3.785 litres
£1 = ＄1.46In which city is petrol better value for money, London or New York?
You must show your working.(3 marks)
Question 3 (3 marks)
A gold bar has a mass of 12.5 kg.
The density of gold is 19.3 g/cm³
Work out the volume of the gold bar.
Give your answer correct to 3 significant figures.(3 marks)
Question 4 (3 marks)
There are only blue pens, green pens and red pens in a box.
The ratio of the number of blue pens to the number of green pens is 2 : 5
The ratio of the number of green pens to the number of red pens is 4 : 1There are less than 100 pens in the box.
What is the greatest possible number of red pens in the box?
(3 marks)
Question 5 (3 marks)
(a)
Find the value of the reciprocal of 1.6
Give your answer as a decimal.(1 mark)
(b)
Jess rounds a number, x, to one decimal place.
The result is 9.8Write down the error interval for x.
(2 marks)
Question 6 (5 marks)
Here is a rectangle.
Diagram: A rectangle, longer than it is wide.
The length of the rectangle is 7 cm longer than the width of the rectangle.
4 of these rectangles are used to make this 8-sided shape.
Diagram: An 8-sided shape made from four of the rectangles: one lying flat at the bottom left, one standing up to its right, one standing up above the first, and one lying flat at the top right.
The perimeter of the 8-sided shape is 70 cm.
Work out the area of the 8-sided shape.
(5 marks)
Question 7 (2 marks)
Work out (13.8 × 10⁷) × (5.4 × 10⁻¹²)
Give your answer as an ordinary number.(2 marks)
Question 8 (3 marks)
When a drawing pin is dropped it can land point down or point up.
Lucy, Mel and Tom each dropped the drawing pin a number of times.
The table shows the number of times the drawing pin landed point down and the number
of times the drawing pin landed point up for each person.Lucy Mel Tom point down 31 53 16 point up 14 27 9 (a)
Rachael is going to drop the drawing pin once.
Whose results will give the best estimate for the probability that the drawing pin will
land point up?
Give a reason for your answer.(1 mark)
(b)
Stuart is going to drop the drawing pin twice.
Use all the results in the table to work out an estimate for the probability that the
drawing pin will land point up the first time and point down the second time.(2 marks)
Question 9 (5 marks)
Jack bought a new boat for £12 500
The value, £V, of Jack’s boat at the end of n years is given by the formulaV = 12 500 × (0.85)ⁿ
(a)
At the end of how many years was the value of Jack’s boat first less than 50% of the
value of the boat when it was new?(2 marks)
(b)
A savings account pays interest at a rate of R% per year.
Jack invests £5500 in the account for one year.At the end of the year, Jack pays tax on the interest at a rate of 40%.
After paying tax, he gets £79.20Work out the value of R.
(3 marks)
Question 10 (3 marks)
There are only blue counters, yellow counters, green counters and red counters in a bag.
A counter is taken at random from the bag.The table shows the probabilities of getting a blue counter or a yellow counter or a green counter.
Colour blue yellow green red Probability 0.2 0.35 0.4 (a)
Work out the probability of getting a red counter.
(1 mark)
(b)
What is the least possible number of counters in the bag?
You must give a reason for your answer.(2 marks)
Question 11 (4 marks)
The cumulative frequency graph shows information about the weights of 60 potatoes.
Diagram: A cumulative frequency graph for the weights of 60 potatoes. Weight goes from 30 to 85 g and cumulative frequency from 0 to 65. The S-shaped curve starts at 40 g with a cumulative frequency of 2, rises slowly to 50 g, then steeply to about 60 g, and then levels off to end at 80 g with a cumulative frequency of 60.
(a)
Use the graph to find an estimate for the median weight.
(1 mark)
(b)
Jamil says,
“80 – 40 = 40 so the range of the weights is 40 g.”
Is Jamil correct?
You must give a reason for your answer.(1 mark)
(c)
Show that less than 25% of the potatoes have a weight greater than 65 g.
(2 marks)
Question 12 (3 marks)
Alan has two spinners, spinner A and spinner B.
Each spinner can land on only red or white.The probability that spinner A will land on red is 0.25
The probability that spinner B will land on red is 0.6The probability tree diagram shows this information.
Diagram: A probability tree diagram. Spinner A: red 0.25, white 0.75. Spinner B, after each: red 0.6, white 0.4.
Alan spins spinner A once and he spins spinner B once.
He does this a number of times.The number of times both spinners land on red is 24
Work out an estimate for the number of times both spinners land on white.
(3 marks)
Question 13 (2 marks)
Write x² + 6x – 7 in the form (x + a)² + b where a and b are integers.
(2 marks)
Question 14 (3 marks)
Cone A and cone B are mathematically similar.
The ratio of the volume of cone A to the volume of cone B is 27 : 8The surface area of cone A is 297 cm²
Show that the surface area of cone B is 132 cm²
(3 marks)
Question 15 (9 marks)
(a)
Show that the equation x³ + 7x – 5 = 0 has a solution between x = 0 and x = 1
(2 marks)
(b)
Show that the equation x³ + 7x – 5 = 0 can be arranged to give x = 5/(x² + 7)
(2 marks)
(c)
Starting with x_0 = 1, use the iteration formula x_n + 1 = 5/(x_n² + 7) three times to find
an estimate for the solution of x³ + 7x – 5 = 0(3 marks)
(d)
By substituting your answer to part (c) into x³ + 7x – 5,
comment on the accuracy of your estimate for the solution to x³ + 7x – 5 = 0(2 marks)
Question 16 (3 marks)
The petrol consumption of a car, in litres per 100 kilometres, is given by the formula
Petrol consumption = dfracbeginmatrix 100 × Number of litres \\ of petrol used endmatrixbeginmatrix Number of kilometres \\ travelled endmatrix
Nathan’s car travelled 148 kilometres, correct to 3 significant figures.
The car used 11.8 litres of petrol, correct to 3 significant figures.Nathan says,
“My car used less than 8 litres of petrol per 100 kilometres.”
Could Nathan be wrong?
You must show how you get your answer.(3 marks)
Question 17 (5 marks)
ABC and ADC are triangles.
Diagram: Two triangles ABC and ADC that share the side AC. B is above AC and D is below it. AD is 11 m, angle ADC is 105°, angle ABC is 118° and angle BCA is 48°.
The area of triangle ADC is 56 m²
Work out the length of AB.
Give your answer correct to 1 decimal place.(5 marks)
Question 18 (4 marks)
Here is a speed-time graph for a train.
Diagram: A speed-time graph. Time is from 0 to 25 seconds and speed from 0 to 25 m/s. The curve starts at (0, 0) and gets steeper and steeper: through 5 m/s at 10 seconds and 10 m/s at 15 seconds, leaving the top of the grid at 25 m/s just before 23 seconds.
(a)
Work out an estimate for the distance the train travelled in the first 20 seconds.
Use 4 strips of equal width.(3 marks)
(b)
Is your answer to (a) an underestimate or an overestimate of the actual distance the
train travelled?
Give a reason for your answer.(1 mark)
Question 19 (5 marks)
Prove algebraically that the straight line with equation x – 2y = 10 is a tangent to the
circle with equation x² + y² = 20(5 marks)
Question 20 (4 marks)
Diagram: A circle with centre O. A and B are at the ends of a diameter through O, A on the left and B on the right. C is at the top of the circle. The chords AC and CB are drawn.
A, B and C are points on the circumference of a circle, centre O.
AOB is a diameter of the circle.Prove that angle ACB is 90°
You must not use any circle theorems in your proof.(4 marks)
Question 21 (5 marks)
Diagram: Triangle OAB with OA carried on in a straight line to N, so that AN is twice OA. M is the midpoint of OB and P is a point on AB.
OAN, OMB and APB are straight lines.
AN = 2OA.
M is the midpoint of OB.overrightarrowOA = mathbfa overrightarrowOB = mathbfb
overrightarrowAP = koverrightarrowAB where k is a scalar quantity.
Given that MPN is a straight line, find the value of k.
(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.