Edexcel IGCSE Math B 3.G equations

Practise equation questions by choosing an efficient method, showing algebraic steps and checking whether any substitution changes the variable.

Exam points

Solve equations by factorising, completing the square or using substitutions.
Use a previous factorisation or graph result to find roots or x-intercepts.
Show clear algebraic working when solving transformed quadratic or cubic equations.

[Maximum number: 6]

Here are the functions f, g and h.
$\begin{aligned}f:x&\mapsto 2x-5,\quad x>1,\\g:x&\mapsto 7-\frac{8x}{2x+1},\\h:x&\mapsto 2x^2+4x-5,\quad x>-1.\end{aligned}$

(a)

Find the value of m for which f(m)=0.

[ 2 ]

2m-5=0

Final answer:
m=2.5

M1 for setting f(m)=0. A1 oe, for example $\frac52$ .

(b)

Find the value of x for which f(x)=g(x).
Show your working clearly.

[ 4 ]

(2x-5)(2x+1)=7-8x $4x^2+2x-10x-5=7-8x$ $x^2=3$

Final answer:
x=1.73

M1 for removing the fraction. M1 for multiplying out. M1 for gaining $x^2=3$ .
A1 awrt 1.73 or $\sqrt3$ .

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3.G Equations question 1

Question (a)

Question (b)