IGCSE Edexcel Paper 3H Janaury 2013 Quiz

1) Here is a biased 5-sided spinner.


When the spinner is spun, it can land on red, blue, black, white or green.
The probability that it lands on red, blue, black or white is given in the table.



George spins the spinner once.
(a) Work out the probability that the spinner lands on green.

Heena spins the spinner 40 times.
(b) Work out an estimate for the number of times the spinner lands on blue.

2) Rectangle A has a width of x metres and a height of (x + 2) metres.
Rectangle B has a width of 2x metres and a height of 4x metres.

The perimeter of rectangle A is equal to the perimeter of rectangle B.
(i) Use this information to write down an equation in x.

(ii) Find the value of x.

3) Joseph travels to work each day by train.
The weekly cost of his train journey is £45
Joseph’s weekly pay is £625
(a) Work out 45 as a percentage of 625

(b) The weekly cost of his train journey increases by 8%.
Increase £45 by 8%.

(c) Joseph’s weekly pay increases to £640
Calculate the percentage increase from 625 to 640

(d) Joseph decides to cycle to work.
He cycles 18 km to work.
His journey to work takes 1 hour 20 minutes.
Calculate his average speed in kilometres per hour.

4)

(a) On the grid, enlarge shape P with scale factor 3 and centre (-8, 7)
Label the new shape Q.

(b) On the grid, rotate shape P through 90º clockwise about the point (-8, 7)
Label the new shape R.

5) Solve the simultaneous equations
y - 2x = 6
y + 2x = 0
Show clear algebraic working.

6) A school has 60 teachers.
The table shows information about the distances, in km, the teachers travel to school
each day

(a) Write down the modal class.

(b) Work out an estimate for the total distance travelled to school by the 60 teachers
each day.

7) (i) Solve the inequalities –2 < x + 2 ≤ 5

(ii) On the number line, represent the solution to part (i).

8)

ABC is a triangle.
AC = 7.9cm
Angle B = 90°
Angle C = 38°
(a) Calculate the length of BC.
Give your answer correct to 3 significant figures

(b) The size of angle C is 38°, correct to 2 significant figures.
(i) Write down the lower bound of the size of angle C.

(ii) Write down the upper bound of the size of angle C.

9) The table shows the diameters, in kilometres, of five planets.



(a) Which of these planets has the smallest diameter?

(b) Calculate the difference, in kilometres, between the diameter of Saturn and the
diameter of Neptune.
Give your answer in standard form.

The diameter of the Moon is 3.5 × 10³ km.
The diameter of the Sun is 1.4 × \[10^{6}\] km.
(c) Calculate the ratio of the diameter of the Moon to the diameter of the Sun.
Give your answer in the form 1 : n

10) The points (0, –1) and (4, 5) lie on the straight line L.

(a) Work out the gradient of L.

(b) Write down an equation of L.

(c) Find an equation of the line which is parallel to L and passes through the point (– 2, 0)

11) A washing line is attached at points A and B on two vertical posts standing on horizontal
ground.
Point A is 2.1 metres above the ground on one post.
Point B is 1.7 metres above the ground to the other post
The horizontal distance between the two posts is 6 metres.

Calculate the distance AB.
Give your answer correct to 3 significant figures.

12) Make h the subject of the formula A = + 2πr(r + h)

13) The incomplete table and histogram show information about the lengths of time,
t minutes, students spent waiting for their school bus one morning.

(i) Use the histogram to complete the table.

(ii) Use the table to complete the histogram.

14) A target has a black circle and a white region.
Arrows can hit the black circle, the white region or miss the target.
Peter shoots two arrows at the target.
On each shot, the probability that Peter’s arrow misses the target is 0.1
On each shot, the probability that Peter’s arrow hits the white region is twice the
probability that it hits the black circle.
(a) Complete the probability tree diagram for Peter’s two arrows.

(b) An arrow which hits the black circle scores 10 points.
An arrow which hits the white region scores 5 points.
An arrow which misses the target scores 0 points.
Calculate the probability that Peter scores exactly 10 points with his 2 arrows.

15) The Venn diagram shows a universal set E and three sets A, B and C.



7,6,3,2 and 10 represent the numbers of elements.
Find
(i) n (A ∪ B)

(ii) n ( A′ )

(iii) n ( B ∩ C′ )

(iv) n ( A′ ∪ B′ )

16)

Calculate the value of x.
Give your answer correct to 1 decimal place.

17) Simplify fully \[\frac{4x² - 25}{6x² + 13x - 5}\]

18 (a) Differentiate with respect to x
(i) 8x²

(ii) \[\frac{2}{x}\]

(b) The curve with equation y = 8x² + \[\frac{2}{x}\] has one turning point.
Find the coordinates of this turning point.
Show your working clearly.

19) The diagram shows a rectangular playground of width x metres and length 3x metres.



The playground is extended, by adding 10 metres to its width and 20 metres to its
length, to form a larger rectangular playground.
The area of the larger rectangular playground is double the area of the original
playground.
(a) Show that 3x² - 50x - 200 = 0

(b) Calculate the area of the original playground.

20) The diagram shows a parallelogram, PQRS.
M is the midpoint of PS.
PM = a        PQ = b

(a) Find, in terms of a and/or b,
(i) PS

(ii) PR

(iii) MQ

N is the point on MQ such that MN = 1\[\frac{1}{3}\]MQ
(b) Use a vector method to prove that PNR is a straight line.

21) The diagram shows a pyramid with a horizontal rectangular base PQRS.
PQ = 16 cm.
QR = 10 cm.
M is the midpoint of the line PR.
The vertex, T, is vertically above M.
MT = 15cm.



Calculate the size of the angle between TP and the base PQRS.
Give your answer correct to 1 decimal place.