Further Graphs (Cambridge International IGCSE Mathematics): Exam Questions

Complete the table of values for $y=x^{2}-4x-3$

Extract:

Complete the table of values for y = x squared minus 4 x minus 3

| x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 | | y | | 2 | -3 | -6 | | -6 | -3 | 2 |

On the grid, draw the graph of $y=x^{2}-4x-3$ for negative 2 less-than or slanted equal to x less-than or slanted equal to 5.

Extract:

On the grid, draw the graph of y = x squared minus 4 x minus 3 for negative 2 less-than or slanted equal to x less-than or slanted equal to 5.

Use your graph to solve the equation $x^{2}-4x-3=0.$

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

Complete the table of values for $y=x^{2}-3x-6$

Extract:

| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | y | 12 | | -2 | | | | | -2 | | 12 |

On the grid, draw the graph of $y=x^{2}-3x-6$ for -3 less-than or slanted equal to x less-than or slanted equal to 6.

Extract:

y equals x squared minus 3 x minus 6

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

Extract:

Complete the table of values for y = x^2 - 3x - 6 On the grid, draw the graph of y = x^2 - 3x - 6 for -3 ≤ x ≤ 6.

Use your graph to solve the equation $x^{2}-3x-6=0$

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

Complete the table of values for $y=x^{2}-5x+3$.

Extract:

| x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | y | | | -1 | -3 | -3 | -1 | 3 | |

On the grid, draw the graph of $y=x^{2}-5x+3$ for negative 1 less-than or slanted equal to x less-than or slanted equal to 6.

Extract:

On the grid, draw the graph of y equals x squared minus 5 x plus 3 for negative 1 less-than or slanted equal to x less-than or slanted equal to 6.

Use your graph to solve the equation $x^{2}-5x+3=0$

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

i) Complete the table of values for $y=x^{2}-2x$

ii) On the grid, draw the graph of $y=x^{2}-2x$ for negative 2 less-than or slanted equal to x less-than or slanted equal to 4.

i) Complete the table of values for $y=x^{2}-10x.$

ii) On the grid, draw the graph of $y=x^{2}-10x\mathrm{for}-6\leq x\leq15.$

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

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

Extract:

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

| x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | | y | | 1 | 5 | | 7 | | 1 |

On the grid, draw the graph of $y=1+5x-x^{2}$ for negative 1 less-than or slanted equal to x less-than or slanted equal to 5.

Extract:

y equals 1 plus 5 x minus x squared On the grid, draw the graph of y equals 1 plus 5 x minus x squared for negative 1 less-than or slanted equal to x less-than or slanted equal to 5.

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

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 $y=x^{2}+2x+4$.

ii) On the grid opposite, draw the graph of $y=x^{2}+2x+4$ for $- 2 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 3.$

Extract:

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

y = ..............................................

y = x^2 + 2x + 4

For $- 2 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 3 ,$ 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 $y=5+2x-x^{2}$.

Extract:

| x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | | y | | 2 | 5 | 6 | | | -3 |

On the grid, draw the graph of $y=5+2x-x^{2}$ for negative 2 less-than or slanted equal to x less-than or slanted equal to 4.

Extract:

y equals 5 plus 2 x minus x squared

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

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

Extract:

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

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 $(-1,2)\mathrm{to}(1,6).$

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

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

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

ii) On the grid, draw the graph of $y = x ( 3 - x )$ for negative 4 less-than or slanted equal to x less-than or slanted equal to 4.

iii) Write down the co-ordinates of the highest point of the graph for negative 4 less-than or slanted equal to x less-than or slanted equal to 4.

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

ii) On the grid, draw the graph of $y = x ^{2} - x - 5 \text{for} - 3 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 4.$

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

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

b) Write down the equation of this line.

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

Extract:

| x | -5 | -3 | -2 | -1 | | 1 | 2 | 3 | 5 | | y | | | | -15 | | 15 | | | |

On the grid, draw the graph of $y=\frac{15}{x}$ for negative 5 less-than or slanted equal to x less-than or slanted equal to negative 1 and 1 less-than or slanted equal to x less-than or slanted equal to 5.

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

Extract:

On the grid, draw the graph of y = 15 over x for negative 5 ≤ x ≤ negative 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 $y=7+2x-x^{2}$

Extract:

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

| x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | | y | -1 | | | 8 | 7 | | -1 |

On the grid, draw the graph of $y=7+2x-x^{2}$ for negative 2 less-than or slanted equal to x less-than or slanted equal to 4.

Extract:

y equals 7 plus 2 x minus x squared

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 $y=-x^{2}+x+5$

Extract:

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

| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | | y | | -1 | 3 | | | 3 | | |

On the grid, draw the graph of $y=-x^{2}+x+5$ for negative 3 less-than or slanted equal to x less-than or slanted equal to 4.

Extract:

y equals negative x squared plus x plus 5

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

Extract:

y equals negative x squared plus x plus 5

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

Extract:

Complete the table of values for y equals negative x squared plus x plus 5

i) On the grid, draw the line $y=x$ for negative 3 less-than or slanted equal to x less-than or slanted equal to 4

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 $y=\frac{8}{x}$.

Extract:

| x | -5 | -4 | -3 | -2 | -1 | | 1 | 2 | 3 | 4 | 5 | | y | | -2 | -2.7 | -4 | -8 | | 8 | 4 | 2.7 | | |

On the grid, draw the graph of $y=\frac{8}{x}$for negative 5 less-than or slanted equal to x less-than or slanted equal to negative 1 and 1 less-than or slanted equal to x less-than or slanted equal to 5.

i) Complete the table of values for $y=\frac{12}{x},x\neq0.$

ii) On the grid, draw the graph of $y=\frac{12}{x}$ for negative 6 less-than or slanted equal to x less-than or slanted equal to negative 1 and 1 less-than or slanted equal to x less-than or slanted equal to 6.

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

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

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