13 original questions, 49 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
The curve y = x2 - 6x + 8 crosses the x-axis at x = 2 and at x = 4.
Write down the solutions of x2 - 6x + 8 = 0
Write down the x-coordinate of the turning point of the curve.
2 marks
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a) x = 2 and x = 4b) x = 3
2
Here is a table of values for y = x2 + x − 2
x
−3
−2
−1
0
1
2
y
4
−2
4
Complete the table.
On the grid, draw the graph of y = x2 + x − 2 for values of x from −3 to 2
4 marks
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a) 0, -2, 0b) smooth U-shaped curve through (-3, 4), (-2, 0), (-1, -2), (0, -2), (1, 0), (2, 4)
3
The diagram shows the graph of y = x2 - 2x - 3
Write down the coordinates of the point where the graph crosses the y-axis.
Write down the solutions of x2 - 2x - 3 = 0
Write down the coordinates of the turning point of the graph.
3 marks
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a) (0, -3)b) x = -1 and x = 3c) (1, -4)
4
The graph of y = x2 − 4x + 1 is drawn on the grid.
Write down the equation of the line of symmetry of the graph.
Write down the coordinates of the turning point.
Use the graph to estimate the solutions of x2 − 4x + 1 = 0
Use the graph to estimate the solutions of x2 − 4x + 1 = 2
4 marks
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a) x = 2b) (2, -3)c) x ≈ 0.3 and x ≈ 3.7d) x ≈ -0.2 and x ≈ 4.2
5
The diagram shows five sketch graphs, labelled A, B, C, D and E.
Match each equation below to the letter of its graph.
y = -x2
y = x3
y = 5x
3 marks
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a) Cb) Dc) E
6
Here is a table of values for y = 6x
x
0.5
1
2
3
4
6
y
6
2
Complete the table.
On the grid, draw the graph of y = 6x for values of x from 0.5 to 6
Explain why the graph never meets the y-axis.
4 marks
Show answer
a) 12, 3, 1.5, 1b) smooth curve through (0.5, 12), (1, 6), (2, 3), (3, 2), (4, 1.5), (6, 1)c) on the y-axis x = 0, and 6 ÷ 0 cannot be worked out
7
Here is a table of values for y = x3 − 4x + 1
x
−2
−1
0
1
2
y
1
1
Complete the table.
On the grid, draw the graph of y = x3 − 4x + 1 for values of x from −2 to 2
4 marks
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a) 4, -2, 1b) smooth curve through (-2, 1), (-1, 4), (0, 1), (1, -2), (2, 1)
8
Kwame throws a ball straight up into the air. Its height, h metres, after t seconds is given by h = 20t − 5t2
The graph of h against t is drawn on the grid.
Write down the greatest height of the ball, and the time when it reaches this height.
Use the graph to find the two times when the ball is 15 m high.
How long is the ball in the air?
4 marks
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a) 20 m, after 2 secondsb) 1 second and 3 secondsc) 4 seconds
9
The graph of y = x3 − 6x2 + 9x is drawn on the grid.
Use the graph to write down the solutions of x3 − 6x2 + 9x = 0
Use the graph to estimate the three solutions of x3 − 6x2 + 9x = 2
4 marks
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a) x = 0 and x = 3b) x ≈ 0.3, x = 2 and x ≈ 3.7
10
On the grid, draw the graph of x2 + y2 = 16
Write down the radius of the circle x2 + y2 = 49
Does the point (2, 3) lie inside, on or outside the circle x2 + y2 = 16? Show how you decide.
4 marks
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a) circle with centre (0, 0) and radius 4b) 7c) inside, because 22 + 32 = 13, which is less than 16
11
On the axes, sketch the graph of y = 6x for negative and positive values of x
Write down the coordinates of any points where the graph crosses the coordinate axes.
4 marks
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a) reciprocal curve with one branch in the first quadrant and one branch in the third quadrant, approaching but never touching the axesb) There are no such points - the graph never crosses the axes
Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.
12
The graph of y = x2 − 3x is drawn on the grid.
Use the graph to solve x2 − 3x = 0
By drawing a suitable straight line on the grid, estimate the solutions of x2 − 4x − 1 = 0
5 marks
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a) x = 0 and x = 3b) draw y = x + 1; x ≈ -0.2 and x ≈ 4.2
13
On the grid, draw the graph of x2 + y2 = 25
On the same grid, draw the line y = x + 1
Write down the coordinates of the points where the line meets the circle.
4 marks
Show answer
a) circle with centre (0, 0) and radius 5b) straight line through (0, 1), (3, 4) and (-4, -3)c) (3, 4) and (-4, -3)
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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.