CAIE IGCSE Mathematics Extended E2.10 Graph…tions

Covered syllabus points

E2.10.1 Draw and interpret function graphs E2.10.2 Solve equations graphically E2.10.3 Exponential growth and decay graphs

[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 $y=x^{3}-2 x+3$ .
Where appropriate, values of y are given correct to 2 decimal places.

Table for Question 2 — CAIE IGCSE Mathematics Extended

(a)

Draw the graph of $y=x^{3}-2 x+3$ for $-2 \leqslant x \leqslant 2$ .

Figure for Question (a) — CAIE IGCSE Mathematics Extended

[ 4 ]

(b)

By drawing a suitable straight line on the grid, solve the equation $x^3-2.5x+1=0$ .

x= or x= or x=

[ 4 ]

y=2+0.5 x ruled
M1 for [y=] 2+0.5 x oe soi

e.g. $x^{3}-2 x+3=2+0.5 x$

or y=k+0.5 x ruled

or y=k x+2 ruled, but not y=2

-1.85 to -1.7,0.4 to 0.5,
1.25 to 1.4
A1 for two correct values dep on M2
If M0 or M1 scored, SC1 for three correct values

[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: 4]

The table shows some values for $y=x^{3}-2 x+3$ .
Where appropriate, values of y are given correct to 2 decimal places.

Table for Question 4 — CAIE IGCSE Mathematics Extended

Draw the graph of $y=x^{3}-2 x+3$ for $-2 \leqslant x \leqslant 2$ .

Figure for Question 4 — CAIE IGCSE Mathematics Extended

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

Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question 3

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 4