Igcse Edexcel Specimen 2h quiz

Q.no1 (a) Simplify
                           3e⁷f × 4e²f

(b) Simplify fully (27a¹²)²/³

(c) Solve the inequality 2q ≥ 31 – 3q

–2 ≤ n < 3
n is an integer
(d) Write down all the possible values of n

Q.no 2  The diagram shows a circle and a trapezium.

The height of the trapezium is h cm.
The area of the circle is equal to the area of the trapezium.
Work out the value of h.
Give your answer correct to 1 decimal place.

Q.no 3 In a bag there are only red bricks, blue bricks, green bricks and orange bricks.
The number of green bricks in the bag is the same as the number of orange bricks.
Jiao takes at random a brick from the bag.
The table gives the probability that Jiao takes a red brick and the probability that he takes
a blue brick.


(a) Work out the probability that Jiao takes an orange brick.

Jiao puts the brick back into the bag.
There are 91 red bricks in the bag.
Jiao is going to build a tower using all the red bricks and all the blue bricks but no
other bricks.
The tower will be in the shape of a cuboid.
There will be 4 bricks in each layer of the tower.
(b) Work out how many layers the tower will have.

Q.no 4 Here are the first five terms of a number sequence.
7 11 15 19 23
(a) Find an expression, in terms of n, for the nth term of this sequence.

The nth term of a different number sequence is given by 80 – 2n
(b) Write down the first 3 terms of this sequence.

Yuen says there are no numbers that are in both of the sequences.
Yuen is correct.
(c) Explain why.

Q.no5 Aayush invests 18 000 rupees for 3 years at a rate of 4% per year compound interest.
Work out the total amount of interest Aayush has received by the end of 3 years.
Give your answer correct to the nearest rupee.

Q.no6

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

Q.no 7

A and C are points on a circle, centre O.
AB and CB are tangents to the circle.
Angle ABC = 52°
Work out the size of angle x.
Give a reason for each stage of your working.

Q.no8  Ahmed, Behnaz and Carmen each have some money.
Ahmed has 20% more money than Behnaz.
Carmen has \[\frac{7}{8}\] of the amount of money that Behnaz has.
Carmen has 31.50 euros.
Work out how much money Ahmed has.

Q.no 9 The frequency table shows information about the ages of 60 people on a train. 

(a) Complete the cumulative frequency table.

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

(c) Use your graph to find an estimate for the interquartile range of the ages of the 60 people.

(d) Use your graph to find an estimate for how many of the 60 people are more than
48 years of age.

Q.no 10 The diagram shows two congruent regular pentagons drawn inside a regular octagon. 


One side of each pentagon lies along a side of the octagon.
AB is a side of the octagon.
AC is a side of one of the pentagons.
BC is a side of the other pentagon.
Work out the size of angle y.
Show your working clearly.

Q.no 11 Solve 
\[\frac{3x - 2}{5}\] - \[\frac{3-4x}{2}\] =2
Show clear algebraic working.

Q.no 12 y = x³– 6x²– 15x
(a) Find \[\frac{dy}{dx}\]

The curve with equation y = x³– 6x²– 15x has two stationary points.
(b) Work out the coordinates of these two stationary points.

Q.no 13 In a school, students must study at least one language from German, French and Spanish.
There are 30 students in a class of this school.
Of these students
7 study all three of the languages
10 study both German and French
12 study both Spanish and German
9 study both French and Spanish
16 study Spanish
18 study German
Work out the total number of the students in the class who study French.
You may use the Venn diagram to help with your calculations.

14 (a) Use algebra to show that 0.324 = \[\frac{107}{330}\]

(b) Rationalise the denominator of\[\frac{4}{7-√5}\] 
Show each stage of your working.
Give your answer in the form a + b √5 where a and b are fractions in their simplest forms.

Q.no15 Sophie takes an examination.
If she fails the examination, she will resit.
The probability that Sophie passes the examination on her first attempt is 0.7
If she fails the examination on any attempt, the probability she passes on the next
attempt is 0.9
Work out the probability that Sophie takes at most 2 attempts to pass the examination.

Q.no 16 The diagram shows part of a sketch of the curve y = sin x°

(a) Write down the coordinates of
(i) the point P

(ii) the point Q

(b) Sketch the graph of y = tan x for 0° ≤ x ≤ 360°
Show the coordinates of any points of intersection with the coordinate axes.

Q.no17 A solid metal cube has sides of length 125mm, correct to 3 significant figures.
The cube is melted down and the metal used to make solid spheres.
The volume of each sphere is to be 140cm³, correct to the nearest 10cm³
Work out the greatest number of spheres that could be made from the metal.
Show your working clearly

Q.no 18 The diagram shows part of the curve with equation y=f(x)

The coordinates of the minimum point on this curve are (3, –4)
(a) Write down the coordinates of the minimum point on the curve with equation
(i) y = f(x – 4)

(ii) y = 3f(x)

(iii) y = f(\[\frac{1}{2}\]x)

The curve with equation y = f(x) is translated to give curve C.
C has a minimum at the point with coordinates (3, 5)
The equation of C is y = f(x) + k
(b) Write down the value of k

19 The diagram shows triangle ABD

N is the midpoint of BC.
C is the midpoint of AD.
M is the point on AB such that AM:MB = 3 :1

(b) State, giving reasons, two different geometric facts relating MN and BD.

Q.no20 A cone has a volume of 562.5π cm3
The radius of the base of the cone is equal to twice the height of the cone.
Work out the curved surface area of the cone.
Give your answer correct to 3 significant figures.

Q.no 21 Write \[\frac{5}{4x² - 25}\] - (2x + 3) ÷\[\frac{4x² + 16x + 15}{7}\]  as a single fraction in its simplest form. Show clear algebraic working.

Q.no 22 The 3rd term of an arithmetic series, A, is 19
The sum of the first 10 terms of A is 290
Find the 10th term of A.