CAIE IGCSE Mathematics Core 2 Algebra and Graphs Questions

Practise algebraic manipulation, equations, inequalities, sequences, functions and coordinate or practical graphs across CAIE IGCSE Mathematics.

Covered syllabus points

C2.1 Introduction to algebra C2.2 Algebraic manipulation C2.4 Indices II C2.5 Equations C2.6 Inequalities C2.7 Sequences C2.9 Graphs in practical situations C2.10 Graphs of functions C2.11 Sketching curves

[Maximum number: 2]

A bar of chocolate costs $ 3 and a bag of sweets costs $ 5.
Write down an expression for the total cost, in dollars, of x bars of chocolate and y bags of sweets.
$

[Maximum number: 2]

Simplify 4 m+7 k-m+3 k.

[Maximum number: 2]

Simplify.

(a)

$y^{3} \div y^{5}$

[ 1 ]

$y^{-2}$ or $\frac1{y^2}$ final answer

(b)

$7 x^{0}$

[ 1 ]

[Maximum number: 11]

(a)

Simplify.
5a+3b+2a-4b

[ 2 ]

(b)

P=8x+3y
Find the value of x when P=21 and y=-5.
x=

[ 2 ]

4.5
M1 for $21=8x+3\times(-5)$ oe or better

(c)

Multiply out and simplify.
(x-3)(x+5)

[ 2 ]

$x^2+2x-15$ final answer
B1 for three correct terms from $x^2-3x+5x-15$

(d)

Nasser has x marbles.

Selina has 15 more marbles than Nasser.
Hanif has 3 times as many marbles as Selina.
In total they have 150 marbles.
Find the value of x.

[ 5 ]

18
B1 for x+15 or $3\times\text{their }(x+15)$ oe
M1 for $x+\text{their }(x+15)+\text{their }3(x+15)=150$ or better
M1 for 5x+60=150 or better, or their linear equation simplified to ax+b=150
M1 for solving their ax+b=c to $x=\frac{150-b}{a}$

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Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (b)

Question 4

Question (a)

Question (b)

Question (c)

Question (d)