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Edexcel GCSE Mathematics May 2019 - Paper 1H

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Edexcel GCSE May 2019 Paper 1H (No Calculator) Solutions
1. There are only blue cubes, red cubes and yellow cubes in a box.
The table shows the probability of taking at random a blue cube from the box.
The number of red cubes in the box is the same as the number of yellow cubes in the box.
(a) Complete the table.
There are 12 blue cubes in the box.
(b) Work out the total number of cubes in the box.

2. Deon needs 50 g of sugar to make 15 biscuits.
She also needs
three times as much flour as sugar
two times as much butter as sugar
Deon is going to make 60 biscuits.
(a) Work out the amount of flour she needs.
Deon has to buy all the butter she needs to make 60 biscuits.
She buys the butter in 250 g packs.
(b) How many packs of butter does Deon need to buy?

3. Find the highest common factor (HCF) of 72 and 90

4. The diagram shows the plan, front elevation and side elevation of a solid shape, drawn on a centimetre grid.
In the space below, draw a sketch of the solid shape.
Give the dimensions of the solid on your sketch.



5. Shape A can be transformed to shape B by a reflection in the x-axis followed by a translation.
Find the value of c and the value of d.

6. A shop sells packs of black pens, packs of red pens and packs of green pens.
There are
2 pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pens
On Monday,
number of packs of black pens sold : number of packs of red pens sold : number of packs of green pens sold = 7:3:4
A total of 212 pens were sold.
Work out the number of green pens sold.

7. Here are two rectangles.
QR = 10 cm
BC = PQ
The perimeter of ABCD is 26 cm
The area of PQRS is 45 cm2
Find the length of AB.

8. (a) Work out an estimate for the value of √(63.5 x 101.7)
(2.3)6 = 148 correct to 3 significant figures.
(b) Find the value of (0.23)6 correct to 3 significant figures.
(c) Find the value of 5–2
Give your answer in standard form.

9. Work out 3 1/2 × 1 3/5
Give your answer as a mixed number in its simplest form.

10. The graphs with equations 3y + 2x = 1/2 and 2y – 3x = –113/12 have been drawn on the grid below.
Using the graphs, find estimates of the solutions of the simultaneous equations

11. A bus company recorded the ages, in years, of the people on coach A and the people on coach B.
Here are the ages of the 23 people on coach A.
(a) Complete the table below to show information about the ages of the people on coach A.
Here is some information about the ages of the people on coach B.
Richard says that the people on coach A are younger than the people on coach B.
(b) Is Richard correct?
You must give a reason for your answer.
Richard says that the people on coach A vary more in age than the people on coach B.
(c) Is Richard correct?
You must give a reason for your answer.

12. Here are three spheres.
The volume of sphere Q is 50% more than the volume of sphere P.
The volume of sphere R is 50% more than the volume of sphere Q.
Find the volume of sphere P as a fraction of the volume of sphere R.

13. Given that n can be any integer such that n > 1, prove that n2 – n is never an odd number.

14. Find the exact value of tan 30° × sin 60°
Give your answer in its simplest form.



15. The diagram shows a solid shape.
The shape is a cone on top of a hemisphere.
The height of the cone is 10 cm.
The base of the cone has a diameter of 6 cm.
The hemisphere has a diameter of 6 cm.
The total volume of the shape is kπ cm3, where k is an integer.
Work out the value of k.

16. There are three dials on a combination lock.
Each dial can be set to one of the numbers 1, 2, 3, 4, 5
The three digit number 553 is one way the dials can be set, as shown in the diagram.
(a) Work out the number of different three digit numbers that can be set for the combination lock.
(b) How many of the possible three digit numbers have three different digits?

17. Given that
x2 : (3x + 5) = 1 : 2
find the possible values of x.

18. (a) Express √3 + √12 + in the form a√3 where a is an integer.
(b) Express (1/√3)7 in the form √b/c where b and c are integers.
Find an equation of the diagonal AC.

19. Given that x2 – 6x + 1 = (x – a)2 – b for all values of x,
(i) find the value of a and the value of b.
(ii) Hence write down the coordinates of the turning point on the graph of y = x2 – 6x + 1

20. h is inversely proportional to p
p is directly proportional to √t
Given that h = 10 and t = 144 when p = 6
find a formula for h in terms of t

21. The functions f and g are such that f(x) = 3x – 1 and g(x) = x2 + 4 (a) Find f–1(x)
Given that fg(x) = 2gf(x),
(b) show that 15x2 – 12x – 1 = 0

22. There are only red counters and g green counters in a bag.
A counter is taken at random from the bag.
The probability that the counter is green is 3/7
The counter is put back in the bag.
2 more red counters and 3 more green counters are put in the bag.
A counter is taken at random from the bag.
The probability that the counter is green is 6/13
Find the number of red counters and the number of green counters that were in the bag originally.

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