EduNinja

[Maximum number: 6]

(a)

The diagram shows the graph of y=f(x) for $-1.5\leqslant x\leqslant5$ .

[ 6 ]

(i)

Find f(2).

[ 1 ]

(ii)

Solve the equation f(x)=0 for $-1.5\leqslant x\leqslant5$ .
x= or x= or x=

[ 3 ]

(iii)

On the grid, draw a line y=mx so that f(x)=mx has exactly one solution for $-1.5\leqslant x\leqslant5$ .

[ 2 ]

[Maximum number: 6]

The straight line y=2 x+1 intersects the curve $y=x^{2}+3 \boldsymbol{x}-4$ at the points A and B.

Find the coordinates of A and B.
Give your answers correct to 2 decimal places.

(-2.79,-4.58) and (1.79,4.58)

B5 for $(-2.791,-4.583\text{ to }-4.582)$ and $(1.791,4.582\text{ to }4.583)$ , or B4 for -2.79 or -2.791 and 1.79 or 1.791.
OR
M1 for $2x+1=x^2+3x-4$ or better.
M2 for $\frac{-1\pm\sqrt{1^2-4(1)(-5)}}{2(1)}$ .
FT their quadratic not $x^2+3x-4$ ;
or M1 for $\frac{-1\pm p}{2(1)}$ or $1^2-4(1)(-5)$ , FT their quadratic not $x^2+3x-4$ .

[Maximum number: 8]

The table shows some values for $y=x^{3}+4 x^{2}-4$ .

Table for Question 3 — CAIE IGCSE Mathematics Extended

(a)

On the grid, draw the graph of $y=x^{3}+4 x^{2}-4$ for $-4.5 \leqslant x \leqslant 1.5$ .

Figure for Question (a) — CAIE IGCSE Mathematics Extended

[ 4 ]

(b)

By drawing a suitable straight line on the grid, solve the equation $x^{3}+4 x^{2}-x-6=0$ .

x=\ldots \ldots \ldots \ldots \ldots \ldots . \text { or } x=\ldots \ldots \ldots \ldots \ldots \ldots . \text { or } x=

[ 4 ]

CAIE IGCSE Mathematics Extended E2.10 Graphs of Functions Topic Practice

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 2

Question 3

Question (a)

Question (b)