 # Edexcel GCSE Mathematics November 2017 - Paper 3H

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Edexcel GCSE November 2017 Paper 3H (Calculator) Solutions
1. The table shows information about the heights of 80 children.
(a) Find the class interval that contains the median.
(b) Draw a frequency polygon for the information in the table.

2. In London, 1 litre of petrol costs 108.9p
In New York, 1 US gallon of petrol costs \$2.83
1 US gallon = 3.785 litres
£1 = \$1.46
In which city is petrol better value for money, London or New York?

3. 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.

4. 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 : 1
There are less than 100 pens in the box.
What is the greatest possible number of red pens in the box?

5. (a) Find the value of the reciprocal of 1.6
Jess rounds a number, x, to one decimal place.
The result is 9.8
(b) Write down the error interval for x.

6. Here is a rectangle.
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.
The perimeter of the 8-sided shape is 70 cm.
Work out the area of the 8-sided shape.

7. Work out (13.8 × 107) × (5.4 × 10-12)

8. 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.
Rachael is going to drop the drawing pin once.
(a) Whose results will give the best estimate for the probability that the drawing pin will land point up?
Stuart is going to drop the drawing pin twice.
(b) 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.

9. 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 formula
V = 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?
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 £79.20
(b) Work out the value of R.

10. 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.
(a) Work out the probability of getting a red counter.
(b) What is the least possible number of counters in the bag?

11. The cumulative frequency graph shows information about the weights of 60 potatoes.
(a) Use the graph to find an estimate for the median weight.
Jamil says,
"80 - 40 = 40 so the range of the weights is 40 g"
(b) Is Jamil correct?
(c) Show that less than 25% of the potatoes have a weight greater than 65 g.

12. 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 0.6
The probability tree diagram shows this information.
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.

13. Write x2 + 6x - 7 in the form (x + a)2 + b where a and b are integers.

14. Cone A and cone B are mathematically similar.
The ratio of the volume of cone A to the volume of cone B is 27 : 8
The surface area of cone A is 297 cm2
Show that the surface area of cone B is 132 cm2

15. (a) Show that the equation x3 + 7x - 5 = 0 has a solution between x = 0 and x = 1
(b) Show that the equation x3 + 7x - 5 = 0 can be arranged to give x = 5/(x2 + 7)
(c) Starting with x0 = 1, use the iteration formula xn+1 = 5/(xn)2 three times to find an estimate for the solution of x3 + 7x - 5 = 0
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

16. The petrol consumption of a car, in litres per 100 kilometres, is given by the formula
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?

17. ABC and ADC are triangles.
The area of triangle ADC is 56 m2
Work out the length of AB.

18. Here is a speed-time graph for a train.
(a) Work out an estimate for the distance the train travelled in the first 20 seconds. Use 4 strips of equal width.
(b) Is your answer to (a) an underestimate or an overestimate of the actual distance the train travelled?

19. Prove algebraically that the straight line with equation x - 2y = 10 is a tangent to the circle with equation x2 + y2 = 20

20. 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.

21. OAN, OMB and APB are straight lines.
AN = 2OA.
M is the midpoint of OB.
OA = a
OB = b
AP = k AB where k is a scalar quantity.
Given that MPN is a straight line, find the value of k

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