Edexcel IGCSE Math A 2 algebra equations and formulae

Use this Algebra question-bank hub to move from notation and formulae into equations, quadratics, graphs, inequalities and proportion skills.

Covered syllabus points

2.1 Use of symbols 2.2 Algebraic manipulation 2.3 Expressions and formulae 2.4 Linear equations 2.5 Proportion 2.6 Simultaneous linear equations 2.7 Quadratic equations 2.8 Inequalities

[Maximum number: 8]

(a)

Solve 5(4-x)=7-3 x
Show clear algebraic working.

[ 3 ]

(b)

Factorise fully $16 m^{3} g^{3}+24 m^{2} g^{5}$

[ 2 ]

$8m^2g^3(2m+3g^2)$

Marking guidance:
- M1 for any correct partial factorisation with at least 2 factors, one of which must be a letter, or the correct common factor with no more than 1 error inside the bracket
- A1 for $8m^2g^3(2m+3g^2)$

(c)

Factorise $y^{2}-2 y-48$

[ 2 ]

(y-8)(y+6)

Marking guidance:
- M1 for $(y\pm6)(y\pm8)$
- A1 for (y-8)(y+6)

(d)

Hence, solve $y^{2}-2 y-48=0$

[ 1 ]

[Maximum number: 4]

18 y is inversely proportional to $x^{3}$

y=4 \text { when } x=3

Work out the value of x when y=864

Since y is inversely proportional to $x^3$ ,

y=\frac{k}{x^3}

4=\frac{k}{3^3} \quad\Rightarrow\quad k=4\times3^3=108

864=\frac{108}{x^3} \quad\Rightarrow\quad x^3=\frac{108}{864}=\frac18

Final answer:

x=0.5

M1 for a correct inverse-proportion formula with a constant k.
M1 for substituting x=3 and y=4.
M1 for a method to find $x^3$ .
A1 for 0.5 oe.

[Maximum number: 3]

Solve the simultaneous equations

$\begin{aligned} 3x+5y&=8\\ 4x+y&=-3.5 \end{aligned}$

Show clear algebraic working.

$\begin{aligned} x&=\\ y&= \end{aligned}$

$\begin{aligned} 3x+5y&=8\\ 20x+5y&=-17.5 \end{aligned}$

Subtract:
-17x=-25.5x=-1.5

Substitute:
y=2.5

Final answer:
$x=-1.5,\qquad y=2.5$

Working required.

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Covered syllabus points

2 Equations, formulae and identities question 1

Question (a)

Question (b)

Question (c)

Question (d)

2 Equations, formulae and identities question 2

2 Equations, formulae and identities question 3