IGCSE Edexcel Paper 3H January 2015 Quiz

1) Change £50 to yen. 
1 euro = 120 yen
£1 = 1.2 euros.

2) (a) Work out the value of \[\frac{451.4}{14.1 + 10.3}\]

(b) Work out the value of √7.8² - 7.2²

3) (a) Factorise 14x – 35

(b) Expand and simplify 3(2c – 5) – 2(c – 4)

(c) Simplify (4e³)²

(d) Expand and simplify (a + 5)(2a – 1)

4) The diagram shows a shape with one line of symmetry.



Work out the area of the shape.

5) A jar contains coloured beads.
Ajit takes at random a bead from the jar.
The probability that the bead is yellow is 0.08
The probability that the bead is pink is 0.1
The probability that the bead is blue is 0.25
(a) (i) Find the probability that the bead is yellow or blue.

(ii) Find the probability that the bead is neither yellow nor pink.

Ajit replaces the first bead in the jar.
He then takes at random a second bead from the jar.
(b) Find the probability that the first bead is yellow and the second bead is blue

A second jar contains 100 coloured beads.
20 of these beads are brown.
Ajit takes at random a bead from the jar.
He records the colour of the bead and then returns the bead to the jar.
He does this 60 times.
(c) Work out an estimate for the number of times Ajit records a brown bead.

6) Solve 4(5y – 1) = 3(6y + 7)
Show clear algebraic working.

7) Eloy’s height was 125 cm when his age was 7 years.
His height was 153 cm when his age was 12 years.
(a) Work out the percentage increase in Eloy’s height between the ages of 7 and 12 years.

Eloy’s height at the age of 12 years was 85% of his height at the age of 20 years.
(b) Work out Eloy’s height when his age was 20 years.

8)

ABC is a triangle.
The point D lies on AC.
Angle BDC = 90º
BD = 10 cm, AB = 15 cm and DC = 12.5 cm.
(a) Calculate the length of AD.
Give your answer correct to 3 significant figures.

(b) Calculate the size of angle BCD.
Give your answer correct to 1 decimal place

9 (a) Find the sum of the interior angles of a polygon with 7 sides.

The diagram shows a regular polygon with 7 sides.
(b) Work out the value of x.
Give your answer correct to 1 decimal place.

10) (a) Find the gradient of the line with equation 3y – 2x = 6

(b) Find an equation of the line with gradient –3 that passes through the point (2, 5).

11)

(a) Find the highest common factor (HCF) of 3780 and 3240
Give your answer as a product of prime factors.

(b) Find the lowest common multiple (LCM) of 3780 and 3240
Give your answer as a product of prime factors.

12) Solve the simultaneous equations
5y – 4x = 8
y + x = 7
Show clear algebraic working.

13) The cumulative frequency graph gives information about the intelligence quotients (IQ)
of a random sample of 100 adults.

(a) Use the cumulative frequency graph to find an estimate for the number of adults in
the sample who have an IQ between 85 and 115

(b) Find an estimate for the upper quartile of the IQ of adults in the sample.

14)

P, Q, R and S are points on a circle, centre O.
QS is a diameter of the circle.
QS and PR intersect at the point T.
OS = 5 cm, QT = 3 cm and TR = 6 cm.
Work out the length of PT.

15)

Zane buys mineral water in large bottles and in small bottles.
The large bottles are mathematically similar to the small bottles.
Large bottles have a height of 32 cm and a volume of 2000 cm3
Small bottles have a volume of 500 cm³
Work out the height of a small bottle.
Give your answer correct to 3 significant figures.

16) Gemma has 9 counters.
Each counter has a number on it.

Gemma puts the 9 counters into a bag.
She takes at random a counter from the bag and does not replace the counter.
She then takes at random a second counter from the bag.
(a) Work out the probability that the number on each counter is an even number.

(b) Work out the probability that the number on the first counter added to the number on
the second counter gives an odd number.

17) P is directly proportional to q³
P = 270 when q = 7.5
(a) Find a formula for P in terms of q

(b) Work out the positive value of q when P = q

18) y = x³– 4x² + 4x + 3
(a) Find \[\frac{dy}{dx}\]

The diagram shows a sketch of the curve with equation y = x³– 4x²+ 4x + 3
The point P is a turning point on the curve.
(b) Work out the coordinates of P.
Show clear algebraic working

(c) Write down the range of values of x for which the curve has a negative gradient.

19)

The Venn diagram shows all of the elements in sets A, B and E.
(a) Write down the elements in A′

(b) Find n(A ∩ B)´

(c) Find the elements in (A ∩ B) ∪ (A ∪ B)´

A ∩ C = Ø
B ∪ C = {5, 6, 7, 8, 9}
n(C) = 3
(d) Write down the elements in C

20) f:x → 2x² + 1      g:x → \[\frac{2x}{x - 1}\] where x ≠ 1
(a) Express the composite function gf in the form gf:x →...
Give your answer as simply as possible.

(b) Express the inverse function \[g^{-1}\] in the form \[g^{-1}\]:x →...

21)

A solid cone has a height of 15 cm.
The volume of the cone is 320π cm³
Work out the curved surface area of the cone.
Give your answer correct to 3 significant figures.

22)

The diagram shows a triangle ABC.
AB = (2x + 1) cm, AC = (2x – 1) cm and BC = 2√7 cm.
Angle BAC = 60º
Work out the value of x.
Show clear algebraic working.