Edexcel IGCSE Maths exam readiness check

Question 1

Amira and Bilal share some money in the ratio $5 : 3$.

Amira gives Bilal AED 60, and they then have equal amounts.

Work out how much money they shared altogether.

Accepted Answer

Let one part be $x$. Amira has $5x$, Bilal has $3x$; the difference is $2x$.

After the transfer they are equal, so the transfer of 60 must close a gap of $120$: $2x = 120$, giving $x = 60$.

Total $= 8x = 8 	imes 60 = 	extbf{AED } 480$.

(Check: $300$ and $180$; after the transfer both hold $240$.)

Question 2

Make $r$ the subject of $T = 2\pi\sqrt{\dfrac{r}{g}}$.

Accepted Answer

$\dfrac{T}{2\pi} = \sqrt{\dfrac{r}{g}}$

Square both sides: $\dfrac{T^{2}}{4\pi^{2}} = \dfrac{r}{g}$

Multiply by $g$: $r = \dfrac{gT^{2}}{4\pi^{2}}$.

Question 3

In triangle $ABC$, $AB = 9.4$ cm, angle $BAC = 52°$ and angle $ABC = 71°$.

Work out the area of triangle $ABC$, correct to 3 significant figures.

Accepted Answer

$\angle ACB = 180 - 52 - 71 = 57°$.

Sine rule: $AC = \dfrac{9.4 \sin 71°}{\sin 57°} = 10.594...$ cm.

Area $= 	frac12 	imes AB 	imes AC 	imes \sin(\angle BAC) = 	frac12 	imes 9.4 	imes 10.594 	imes \sin 52°$

$= 39.2$ cm² (3 s.f.).

Question 4

Simplify fully $\dfrac{2x^{2} + 5x - 3}{x^{2} - 9}$.

Accepted Answer

$2x^{2} + 5x - 3 = (2x - 1)(x + 3)$

$x^{2} - 9 = (x - 3)(x + 3)$

$\dfrac{(2x - 1)(x + 3)}{(x - 3)(x + 3)} = \dfrac{2x - 1}{x - 3}$.

Question 5

A car travels $d = 148$ m, measured to the nearest metre, in $t = 9.2$ s, measured to the nearest tenth of a second.

Calculate the upper bound for the average speed of the car. Give your answer to 3 significant figures, and explain which bounds you used.

Accepted Answer

Distance: $147.5 \le d < 148.5$, so the upper bound is $148.5$ m.

Time: $9.15 \le t < 9.25$, so the lower bound is $9.15$ s.

Maximum speed $= \dfrac{148.5}{9.15} = 16.229... = 	extbf{16.2 m/s}$ (3 s.f.).

Edexcel IGCSE Maths — free exam readiness check