Using Calculators for Graphs & Equations (Cambridge International IGCSE Maths): Exam Questions

Complete the mapping diagram for the function $\mathrm{f} ( x ) = 3 x - 5$.

Complete the mapping diagram.

On the diagram, sketch the graph of $y=x^{3}-4x$ for $-2\leq x\leq2$.

On the diagram, sketch the graph of $y=0.25x^{4}$ for $-2\leq x\leq2$.

On the diagram, sketch the graph of $y = 2 - ( x - 1 )^{2}$ for $-1\leq x\leq3$

You are not required to find any axes intercepts.

Complete the mapping diagram for $\mathrm{f} ( x ) = \frac{3 ( x + 4 )}{2}$.

On the diagram, sketch the graph of $y=x^{3}-12x$ for $-4\leq x\leq4$

Extract:

y equals x cubed minus 12 x

Find the coordinates of the points where the curve crosses the $x$-axis.

Give your answers to 2 decimal places, where relevant.

Extract:

y equals x cubed minus 12 x

Find the coordinates of the local maximum.

Extract:

y equals x cubed minus 12 x

Find the coordinates of the local minimum.

On the diagram, sketch the graph of $y=x^{3}$ for $-2\leq x\leq2$

On the same diagram as part (a), sketch the graph of $y=2-x$ for $-2\leq x\leq2$

Find the coordinates of the point of intersection of $y=x^{3}$ and $y=2-x$.

Extract:

Find the coordinates of the point of intersection of y = x^3 and y = 2 - x.

Solve the equation

$x^{3}=2-x$

The diagram shows the graph of $y = \mathrm{f} ( x )$ where $\mathrm{f} ( x ) = - 2 x^{2} + 5 x + 6$ for $-2\leq x\leq4.$

Use your calculator to find the zeros of $\mathrm{f} ( x )$ .

Extract:

f(x) = -2x^2 + 5x + 6 for -2 ≤ x ≤ 4.

Use your calculator to find the co-ordinates of the local maximum.

(....................... , .......................)

Extract:

Use your calculator to find the co-ordinates of the local maximum.

Write down the equation of the line of symmetry.

Find all three solutions to the equation

$x^{3}-4x=x^{2}-4$

Show your working on the axes below.

The diagram shows a sketch of the graph of $y=0.1x^{3}+0.25x^{2}-2x-1$ for $-7\leq x\leq5.$

Two points, $P$ and $Q,$ are also marked.

Draw the graph of $y=0.1x^{3}+0.25x^{2}-2x-1$ on your calculator and use it to answer the following questions.

Find the coordinates of point $P$ and point$Q$.

$P=$ ( ...................... , ......................)

$Q=$ ( ...................... , ......................)

Extract:

The diagram shows a sketch of the graph of y = 0.1 x^3 + 0.25 x^2 - 2 x - 1 for -7 ≤ x ≤ 5. Draw the graph of y = 0.1 x^3 + 0.25 x^2 - 2 x - 1 on your calculator and use it to answer the following questions.

Find the coordinates of

(i) the local maximum point

( ...................... , ......................) [2]

(ii) the local minimum point.

( ...................... , ......................) [2]

Extract:

y equals 0.1 x cubed plus 0.25 x squared minus 2 x minus 1

The line $y=a$ intercepts the graph of $y=0.1x^{3}+0.25x^{2}-2x-1$ at 3 points.

Complete the range of values for $a$.

.................. $<a<$..................

On the diagram, sketch the graph of $y=x^{3}-5x+3$ for $-3\leq x\leq3.$

On the diagram, sketch the graph of $y=\frac{2}{x^{2}}$ for values of $x$ from $-3$ to $3.$

Find the $x$-coordinate of each point of intersection of $y=x^{3}-5x+3$ and $y=\frac{2}{x^{2}}.$