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Edexcel GCSE Mathematics November 2019 - Paper 1H

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More Questions and Worked Solutions for Edexcel GCSE Exams

1. Find the Lowest Common Multiple (LCM) of 108 and 120
2. There are 60 people in a choir.
Half of the people in the choir are women.
The number of women in the choir is 3 times the number of men in the choir.
The rest of the people in the choir are children.
the number of children in the choir : the number of men in the choir = n : 1
Work out the value of n.
You must show how you get your answer.
3. Work out 1 3/4 x 1 1/3
Give your answer as a mixed number.
4. Use a ruler and compasses to construct the line from the point P perpendicular to the line CD.
You must show all construction lines.
5. The diagram shows triangle ABC
ADB is a straight line.
the size of angle DCB : the size of angle ACD = 2 : 1
Work out the size of angle BDC.
6. 4 red bricks have a mean weight of 5kg.
5 blue bricks have a mean weight of 9kg.
1 green brick has a weight of 6kg.
Donna says,
“The mean weight of the 10 bricks is less than 7kg.”
Is Donna correct?
You must show how you get your answer.
7. (a) Simplify (p2)5
(b) Simplify 12x7y3 ÷ 6x3y
8. The accurate scale drawing shows the positions of port P and a lighthouse L
Aleena sails her boat from port P on a bearing of 070°
She sails for 1 1/2 hours at an average speed of 12km/h to a port Q.
Find
(i) the distance, in km, of port Q from lighthouse L,
(ii) the bearing of port Q from lighthouse L.
9. A car travels for 18 minutes at an average speed of 72km/h.
(a) How far will the car travel in these 18 minutes?
David says,
“72 kilometres per hour is faster than 20 metres per second.”
(b) Is David correct?
You must show how you get your answer.
10. The cumulative frequency table shows information about the times, in minutes, taken by 40 people to complete a puzzle.
(a) On the grid below, draw a cumulative frequency graph for this information.
(b) Use your graph to find an estimate for the interquartile range.
One of the 40 people is chosen at random.
(c) Use your graph to find an estimate for the probability that this person took between 50 minutes and 90 minutes to complete the puzzle.
11. There are p counters in a bag.
12 of the counters are yellow.
Shafiq takes at random 30 counters from the bag.
5 of these 30 counters are yellow.
Work out an estimate for the value of p.
12. T = q/2 + 5
Here is Spencer’s method to make q the subject of the formula.
2 x T = q + 5
q = 2T – 5
What mistake did Spencer make in the first line of his method?
13. (a) Write 5/(x + 1) + 2/(3x) as a single fraction in its simplest form
(b) Factorise (x + y)2 + 3(x + y)
14. The diagram shows a right-angled triangle.
All the measurements are in centimetres.
The area of the triangle is 27.5cm2
Work out the length of the shortest side of the triangle.
You must show all your working
15. Express 0.418 as a fraction.
You must show all your working.
16. (a) Rationalise the denominator of 22/√11
Give your answer in its simplest form
(b) Show that √3/(2√3 - 1) can be written in the form a (a + √3)/b where a and b are integers.
17. A and B are two similar cylindrical containers.
the surface area of container A : the surface area of container B = 4 : 9
Tyler fills container A with water.
She then pours all the water into container B.
Tyler repeats this and stops when container B is full of water.
Work out the number of times that Tyler fills container A with water.
You must show all your working
18. The function f is given by
f(x) = 2x3 – 4
(a) Show that f–1(50) = 3
The functions g and h are given by
g(x) = x + 2 and h(x) = x2 (b) Find the values of x for which
hg(x) = 3x2 + x – 1
19. Given that 91/2 = 271/4 ÷ 3x + 1
find the exact value of x.
20. The graph of y = f(x) is shown on the grid.
(a) On the grid, draw the graph with equation y = f(x + 1) - 3
Point A(–2, 1) lies on the graph of y = f(x).
When the graph of y = f(x) is transformed to the graph with equation y = f(–x), point A is mapped to point B.
(b) Write down the coordinates of point B.
21. Sketch the graph of
y = 2x2 – 8x – 5
showing the coordinates of the turning point and the exact coordinates of any intercepts with the coordinate axes.
22. A, B, C and D are four points on a circle.
AEC and DEB are straight lines.
Triangle AED is an equilateral triangle.
Prove that triangle ABC is congruent to triangle DCB.


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