Further Graphs (Cambridge (CIE) IGCSE Maths: Core): Exam Questions

Complete the table of values for $y=1+5x-x^2$

On the grid, draw the graph of $y=1+5x-x^2$ for $-1⩽x⩽5$.

i) On the grid, draw the line $y$ = 3.

[1]

ii) Use your line to solve the equation $1+5x-x^2=3$

$x$= .................... or$x$= .................... [2]

The line $L$ is shown on the grid.
Find the equation of the line in the form $y=mx+c$.

$y$ = .............................................. 

i) Complete the table of values for $y=x^2+2x+4$.

[2]

ii) On the grid opposite, draw the graph of $y=x^2+2x+4$ for $–2⩽x⩽3.$

[4]

For $–2⩽x⩽3,$ write down the $x$-coordinate of the point of intersection of the line $L$ with the curve$y=x^2+2x+4.$

$x=$...............................

Complete the table of values for $y=5+2x-x^2$.

On the grid, draw the graph of $y=5+2x-x^2$ for $-2⩽x⩽4$.

i) On the grid, draw the line of symmetry.

[1]

ii) Write down the equation of the line of symmetry.

[1]

Use your graph to find the solutions of the equation $5+2x-x^2=4.$

$x=$ ....................... or $x=$ ..................... 

i) On the grid, draw a line from $(-1,2)\mathrm{to}(1,6).$

[1]

ii) Find the equation of this line in the form $y=mx+c.$

$y=$ ............................ [3]

i) Complete the table of values for $y=x\left(3-x\right)$.

[3]

ii) On the grid, draw the graph of $y=x\left(3-x\right)$ for $-4⩽x⩽4.$

[4]

iii) Write down the co-ordinates of the highest point of the graph for $-4⩽x⩽4.$

[1]

i) Complete the table of values for $y=x^2-x-5.$

[3]

ii) On the grid, draw the graph of $y=x^2-x-5\mathrm{for}-3⩽x\mathit{⩽}4.$

[4]

iii) Write down the co-ordinates of the lowest point on the graph.

[1]

iv)
a) On the grid, draw the line of symmetry of the graph.

[1]

b) Write down the equation of this line.

[1]

Complete the table of values for $y=\frac{15}{x}$

On the grid, draw the graph of $y=\frac{15}{x}$ for $-5⩽x⩽-1$ and $1⩽x⩽5$.

On the grid, draw the line $y$ = 6.

Use your graph to solve $\frac{15}{x}=6$.

$x=$.............................

Complete the table of values for $y=7+2x-x^2$

On the grid, draw the graph of $y=7+2x-x^2$ for $-2⩽x⩽4.$

Write down the equation of the line of symmetry of the graph.

Use your graph to solve the equation $7+2x-x^2=0$

$x$ = .................... or $x$ = .................... 

Complete the table of values for $y=-x^2+x+5$

On the grid, draw the graph of $y=-x^2+x+5$ for $-3⩽x⩽4$.

Write down the coordinates of the highest point of the graph.

Write down the equation of the line of symmetry of the graph.

i) On the grid, draw the line $y=x$ for $-3⩽x⩽4$

[1]

ii) Write down the values of $x$ where the line $y=x$ crosses the curve $y=-x^2+x+5$

$x$ = ...................... and $x$ = ...................... [2]

Complete the table of values for $y=\frac{8}{x}$.

On the grid, draw the graph of $y=\frac{8}{x}$for $-5⩽x⩽-1$ and $1⩽x⩽5.$

[4]

i) Complete the table of values for $y=\frac{12}{x},x\ne 0.$

[3]

ii) On the grid, draw the graph of $y=\frac{12}{x}$ for $-6⩽x⩽-1$ and $1⩽x⩽6$.

[4]

iii) On the grid, draw the line $y=8$.

[1]

iv) Use your graph to solve $\frac{12}{x}=8$.

$x$ = .............................................. [1]