EduNinja

[Maximum number: 7]

(a)

Antonio travels 100 km at an average speed of $x \mathrm{~km} / \mathrm{h}$ .

He then travels a further 150 km at an average speed of (x+10) km / h.
The time taken for the whole journey is 4 hours 20 minutes.

[ 7 ]

(i)

Show that $13x^2-620x-3000=0$ .

[ 4 ]

$\frac{100}{x}+\frac{150}{x+10}=4\frac13$ oe or $150=\left(\frac{13}{3}-\frac{100}{x}\right)(x+10)$ $\frac{100(x+10)+150x}{x(x+10)}$ or better
$300x+3000+450x=13x^2+130x$ oe or better
Allow correct multiples of $13x^2-620x-3000=0$

(ii)

Solve $13x^2-620x-3000=0$ to find the speed Antonio travels for the first 100 km of the journey.
You must show all your working and give your answer correct to 1 decimal place.

[ 3 ]

$\frac{620\pm\sqrt{(-620)^2-4(13)(-3000)}}{2(13)}$
or equivalent quadratic formula
M1 for $(-620)^2-4\times13\times(-3000)$ oe
x=52.1 to 52.2 final answer
Reject negative speed

[Maximum number: 3]

18 Solve.
$\frac{3y}{2y-1}=\frac34$ y=

$-\frac12$ oe

B2 for 12y=6y-3 or better.
M1 for $4\times3y=3(2y-1)$ .

[Maximum number: 4]

The line y=x+1 intersects the curve $y=x^{2}+x-3$ at two points.
Find the coordinates of the two points.

Figure for Question 3 — CAIE IGCSE Mathematics Extended

[4]
22 x is inversely proportional to the square root of w. When w=16, x=3.

Find x in terms of w.

x=

(2, 3) and (-2, -1)

4

B3 for x=2 and x=-2

or B2 for $x^{2}-4[=0]$ or better

or for (2,3) or (-2,-1)

or M1 for $x+1=x^{2}+x-3$ oe

22

$\frac{12}{\sqrt{w}}$ oe final answer

2

M1 for $x=\frac{k}{\sqrt{w}}$ oe

CAIE IGCSE Mathematics Extended E2.5 Equations Topic Practice

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

Question 3