CAIE IGCSE Mathematics Core Algebra and Graphs Question Bank

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]

Miguel works in an office.

White paper costs w cents per sheet and pink paper costs p cents per sheet.
Miguel uses 56 sheets of white paper and 21 sheets of pink paper.
Write down an expression, in terms of w and p, for the total cost, in cents, of the paper he uses.
cents

[Maximum number: 10]

(a)

Simplify 3 c-5 d-c+2 d.

[ 2 ]

(b)

Solve the equation 12x-7=23.

x= ___

[ 2 ]

x=2.5
M1 for 12x=23+7 or $x-\frac{7}{12}=\frac{23}{12}$ .

(c)

Multiply out.

9(3-x)

[ 1 ]

(d)

Alphonse is x years old and Beatrice is y years old.

Three times Alphonse's age is equal to 5 times Beatrice's age.
Twice Beatrice's age is 4 years more than Alphonse's age.

[ 5 ]

(i)

Use this information to write down two equations in x and y.

[ 2 ]

(ii)

Find the age of Alphonse and the age of Beatrice.

Alphonse ___ years old
Beatrice ___ years old

[ 3 ]

$\begin{aligned} x&=20\\ y&=12 \end{aligned}$
M1 for correctly eliminating one variable.
B1 for one correct.

[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: 5]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Core

[ 2 ]

(i)

The graph shows the cost, $ c, of travelling a distance, $d \mathrm{~km}$ , with Saanvi's Taxis.

[ 1 ]

(i)

Write down the cost of a 4 km journey.
$

[ 1 ]

(ii)

Krishna's Taxis cost $ 5 to hire plus $ 2 for each kilometre travelled.

[ 1 ]

(i)

Show that the cost of a 4 km journey with Krishna's Taxis is $ 13.

[ 1 ]

$2 \times 4+5$

1

(ii)

Mrs Singh wants to hire a taxi. She says that Saanvi's Taxis are always cheaper than Krishna's Taxis.

Is Mrs Singh correct?
Give a reason for your answer. Use your graph to help you. because

(b)

A minibus can be hired from Dhruv's Minibuses.

The cost is $ h per hour plus $ p per passenger.

[ 3 ]

(i)

When the minibus is hired for 3 hours with 10 passengers the cost is $ 61.

Complete the equation.

3 h+10 p=\ldots \ldots \ldots \ldots \ldots \ldots \ldots .

[ 1 ]

(ii)

When the minibus is hired for 5 hours with 8 passengers the cost is $ 80.

Write this information as an equation. =

[ 2 ]

(iii)

Solve your two simultaneous equations to find h and p. You must show all your working.

\begin{aligned} & h=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \\ & p=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \end{aligned}

[Maximum number: 13]

(a)

P=3 a+5
Find the value of P when a=2.

P=

[ 1 ]

(b)

Solve these equations.

[ 4 ]

(i)

7 x=-42

x=

[ 1 ]

(ii)

9(8 x-7)=72

x=

[ 3 ]

(c)

5^8 x 5^k=5^-24

Find the value of k.

k=

[ 1 ]

(d)

Solve the simultaneous equations.
$\begin{aligned}-6x-y&=13\\8x+y&=-51\end{aligned}$ $x=\quad y=$

(e)

n is an integer where n>-3 and $n\leqslant1$ .
Write down all the possible values of n.

[ 2 ]

(f)

A boy walks for 35 minutes at x metres per minute.

He then runs for t minutes at 160 metres per minute.
Write down an expression, in terms of x and t, for the total distance, in metres, the boy travels.
m
[2]

[ 2 ]

(g)

Figure for Question (g) — CAIE IGCSE Mathematics Core

NOT TO
SCALE

Find an expression for the area of this rectangle.
Give your answer in the form x^2+a x+b.

[ 3 ]

$x^2+3x-10$ final answer
B2 for $x^2+5x-2x-10$ with at least 3 terms correct or B1 for (x+5)(x-2) oe

[Maximum number: 8]

(a)

These are the first four terms of a sequence.

\begin{array}{llll} 8 & 15 & 22 & 29 \end{array}

[ 4 ]

(i)

Write down the next term.

[ 1 ]

(ii)

Write down the term to term rule for continuing this sequence.

[ 1 ]

(iii)

Find an expression for the nth term.

[ 2 ]

7n+1 oe final answer
B1 for 7n+j or kn+1, $k\ne0$ , as final answer, or for 7n+1 seen then spoilt.

(b)

Find the next term in each of these sequences.

[ 2 ]

(i)

18, 21, 26, 33, 42, $\ldots$

[ 1 ]

(ii)

$\quad 18, \quad 20, \quad 24, \quad 32, \quad 48, \quad \ldots$

[ 1 ]

(c)

Find the first three terms of the sequence with nth term $n^{2}+5 n$ .

[ 2 ]

All question bank results loaded

Covered syllabus points

2. Algebra and graphs question 1

2. Algebra and graphs question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)

2. Algebra and graphs question 3

Question (a)

Question (b)

2. Algebra and graphs question 4

Question (a)

Question (i)

Question (i)

Question (ii)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question (iii)

2. Algebra and graphs question 5

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (d)

Question (e)

Question (f)

Question (g)

2. Algebra and graphs question 6

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (b)

Question (i)

Question (ii)

Question (c)