IGCSE Edexcel Paper 3H June 2017 Quiz

1 (a) Factorise 10a + 25

(b) Factorise 7w² - 4w

(c) Expand p²(p - 5)

(d) Expand and simplify (x - 3)(x + 7)

G = f³ - 7f
(e) Work out the value of G when f = 2

2)

(a) On the grid, enlarge shape P with scale factor 2 and centre (7, 3)
Label the new shape Q.

(b) On the grid, rotate shape P through 90° anticlockwise about the point (7, 3)
Label the new shape R.

3) Here is a list of ingredients needed to make apple and blackberry crumble for 4 people.



Rufus wants to make apple and blackberry crumble for 10 people.
(a) Work out the amount of apples he needs.

Roland makes apple and blackberry crumble for a group of people.
He uses 920 grams of blackberries.
(b) Work out the number of people in the group.

4) The table shows information about the lengths, in cm, of 40 leaves.



(a) Write down the modal class.

(b) Work out an estimate for the mean length of the 40 leaves.
Give your answer correct to 1 decimal place.

5) (a) Use your calculator to work out the value of \[\frac{7.3 + 2.1}{6.4}\] + 2.2²
Give your answer as a decimal.
Write down all the figures on your calculator display.

(b) Give your answer to part (a) correct to 3 significant figures.

6) On the grid, draw the graph of y = 2x + 4 for values of x from -3 to 3

7)

Calculate the length of AC.
Give your answer correct to 3 significant figures.

8) In 2014, Donald's weekly pay was $640
In 2015, Donald's weekly pay was $668.80
(a) Work out the percentage increase in Donald's pay between 2014 and 2015

In 2015, Donald's weekly pay was 95% of his weekly pay in 2016
(b) Work out Donald's weekly pay in 2016

9) Use ruler and compasses to construct the bisector of angle PQR.
You must show all your construction lines.

10) Solve the simultaneous equations
2x + 7y = 31
5x - 3y = 16
Show clear algebraic working.

11) The table gives information about the ages of all the 90 adults in a supermarket.

One of these 90 adults is picked at random.
(a) Find the probability that this adult's age is more than 50 years

(b) Complete the cumulative frequency table for these 90 adults.

(c) On the grid, draw a cumulative frequency graph for your table.

All of these adults with an age greater than 65 years receive a discount on their shopping bill.
(d) Use your graph to find an estimate for the number of these adults who receive a discount

12) (a) Write 0.000451 in standard form.

(b) Work out 7 8 10\[\frac{7.8 x \[10^{5}\]}{2.4 x \[10^{-4}\]}\]
Give your answer in standard form.

13) Here are two mathematically similar cups, A and B.


A has height 12 cm and base diameter 9 cm.
B has height 8 cm and base diameter d cm.
(a) Work out the value of d.

The volume of B is 160 millilitres.
(b) Work out the volume of A.

14) (a) Simplify \[(√x)^{8}\]

(b) Solve \[\frac{6 + 4y}{3}\] = 5 - 2y
Show clear algebraic working.

(c) Make g the subject of g - 1 = gh + 3h

15) P is directly proportional to r³
P = 343 when r = 3.5
Find a formula for P in terms of r.

16) (5√2 - e)(3√2 + e) = f√2 - 6
Given that e and f are positive integers,
find the value of e and the value of f.

17)

PQS is a triangle.
X is the midpoint of QS and Y is the midpoint of PS.
R is the point of intersection of PX and QY.
V is a point so that VQXS is a straight line.
PQ = a
PS = b
(a) Find, in terms of a and b,
(i) QS

(ii) QY

(iii) PXl

P has coordinates (3, 1) and PR = \[\frac{2}{3}\] PX

(b) Work out the coordinates of V.

18 A and B are two sets.
n(E ) = 50
n(A∩ B) = 4
n(A) = 5
n(B) = 9
(a) Complete the Venn diagram to show the numbers of elements.

(b) Find
(i) n(A ∩ B')

(ii) n(A ∪ B')

19) f(x) = \[\frac{4}{x- 3}\]
g(x) = \[\frac{x - 2}{x}\]
(a) Express the inverse function \[f^{-1}\] in the form \[f^{-1}\](x) = ...

(b) Solve fg(a) = 1
Show clear algebraic working.

20) A bag contains 12 marbles.
6 of the marbles are red, 4 of the marbles are blue and 2 of the marbles are green.
Raj takes at random 3 marbles from the bag.
Find the probability that exactly 2 of these marbles are blue.

21) The diagram shows a triangular prism with a horizontal base ABCD.



M is the midpoint of AD.
The vertex V is vertically above M.
DC = 18 cm, BC = 10 cm, MV = 7 cm.
Calculate the size of the angle between VC and the plane ABCD.
Give your answer correct to 3 significant figures.

22) Simplify fully \[\frac{3}{2x + 12}\] - \[\frac{x - 15}{x² - 2x - 48}\]
Show clear algebraic working.