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]

Simplify.

(a)

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

[ 1 ]

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

(b)

$7 x^{0}$

[ 1 ]

[Maximum number: 4]

(a)

A boat sails from A to B.
The travel graph shows this journey.

Figure for Question (a) — CAIE IGCSE Mathematics Core

[ 4 ]

(i)

Write down the time that the boat leaves A.

[ 1 ]

(ii)

Work out how long, in minutes, it takes the boat to sail from A to B.
min [1]

[ 1 ]

(iii)

The boat stays at B for 20 minutes.

The boat then sails to C at a constant speed of $8 \mathrm{~km} / \mathrm{h}$ .
Complete the travel graph.

[ 2 ]

Ruled lines from
(1100,6) to (1120,6)
and (1120,6) to (1250,18)

2

B1 for each line
If 0 scored, SC1 for
(their1120, 6) to
(their $1120+1 \frac{1}{2} h, 18$ )

[Maximum number: 9]

Figure for Question 3 — CAIE IGCSE Mathematics Core

(a)

Table for Question (a) — CAIE IGCSE Mathematics Core

Complete the table of values for $y=x^2-3x-3$ .

[ 2 ]

(b)

On the grid, draw the graph of $y=x^2-3x-3$ for $-2\leqslant x\leqslant5$ .

[ 4 ]

(c)

On the grid, draw the line of symmetry of the graph of $y=x^{2}-3 x-3$ .

[ 1 ]

(d)

Write down the equation of the line of symmetry.

[ 1 ]

(e)

Write down the coordinates of the point where line L intersects the graph of $y=x^{2}-3 x-3$ for x>0.
(, )

[ 1 ]

[Maximum number: 5]

(a)

Factorise completely.
$15x^3y-3x$

[ 2 ]

$3x(5x^2y-1)$ final answer
B1 for $3(5x^3y-x)$ or $x(15x^2y-3)$ , or correct answer spoilt

(b)

Make n the subject of the formula V=3n+t.
n=

[ 2 ]

$\frac{V-t}{3}$ oe final answer
M1 for V-t=3n or $\frac V3=n+\frac t3$

(c)

$\frac{7^{15}}{7^x}=7^9$
Find the value of x.
x=

[ 1 ]

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 3

Question (a)

Question (b)

Question (c)

Question (d)

Question (e)

Question 4

Question (a)

Question (b)

Question (c)