On the diagram, sketch the graph ofĀ .
Show the values of the intersections with the axes.Ā
Expand and simplify.
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On the diagram, sketch the graph ofĀ .
Show the values of the intersections with the axes.Ā
Expand and simplify.
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The diagram shows the graph ofĀ forĀ .
By drawing a suitable straight line on the grid, solve forĀ .
................................................
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The table shows some values for .
-1 | -0.5 | 0 | 0.5 | 1 | 1.5 | 2 | |
-3 | 1.75 | Ā | Ā | Ā | 0.75 | 3 |
Complete the table.
Draw the graph of Ā forĀ .
Ā ........................ or Ā ........................ or Ā ........................ [3]
[1]
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,Ā
Ā
Complete the table forĀ .
0.5 | 1 | 2 | 3 | 4 | 5 | 6 | |
-7.9 | -3.8 | Ā | 0.9 | Ā | 5.5 | 8.3 |
The graph of forĀ is drawn on the grid.
On the same grid, draw the graph ofĀ forĀ .
By drawing a suitable tangent, estimate the gradient of the graph ofĀ at the
point (ā4, 5).
,Ā
Ā
Complete the table forĀ .
Ā
-4 | -3 | -2 | -1 | Ā | 1 | 2 | 3 | 4 | |
-2.3 | Ā | -4.5 | -9 | Ā | 9 | 4.5 | Ā | 2.3 |
On the same grid, draw the graph ofĀ Ā forĀ Ā Ā andĀ Ā .
Ā = ................................................. [1]
[1]
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Ā | Ā |
Ā | Ā |
On the grid, draw the graphs ofĀ andĀ Ā forĀ .
Use your graphs to solve the equations.
............................................... [1]
[1]
Complete the statement.
This straight line is a .................................. to the graph of
at the point ( ....... , ....... ).
[2]
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On the diagram, sketch the graph of .
Label the values where the graph meets the -axis and the -axis.
Ā
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Sketch the graph of the function.
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The diagrams A, B, C, D, E and F are six graphs of different functions.
Complete the table to identify the correct graph for each function.
One has been done for you.Ā
Function | ||||
Diagram | E | Ā | Ā | Ā |
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Complete the table.
-10 | -8 | -5 | -2 | -1.6 | Ā | 1.6 | 2 | 5 | 8 | 10 | |
-12 | -10.5 | -9 | -12 | -14.1 | Ā | 14.1 | 12 | Ā | Ā | 12 |
On the grid, draw the graph ofĀ for andĀ .
Using your graph, solve the equation .
= ..................Ā Ā orĀ Ā = .................
is a prime number and has no solutions.
Find the possible values of .
The gradient of the graph ofĀ at the pointis .
Write down the coordinates of the other point on the graph of where the gradient is .
Ā (....................... , .......................)
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The table shows some values forĀ
-3.5 | -3 | -2.5 | -2 | -1.5 | -1 | -0.5 | 0 | 0.5 | 1 | 1.5 | |
-4.1 | Ā | 5.1 | 6 | 5.4 | 4 | 2.6 | Ā | 2.9 | Ā | 12.1 |
Complete the table.
On the grid, draw the graph ofĀ forĀ
Use your graph to solve the equationĀ forĀ
Ā
= ....................................................
By drawing a suitable straight line, solve the equationĀ forĀ
Ā
= ....................................................
ForĀ the equationĀ has three solutions andĀ is an integer.
Write down a possible value of .
Ā
= ....................................................
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The table shows some values ofĀ Ā .
-3 | -2.5 | -2 | -1.5 | -1 | 0 | 1 | 1.5 | 2 | 2.5 | 3 | |
-19 | -9.1 | Ā | 0.1 | 1 | -1 | -3 | -2.1 | 1 | 7.1 | Ā |
Ā
Complete the table of values.
Draw the graph ofĀ Ā Ā forĀ Ā .
A straight line through (0, ā17) is a tangent to the graph ofĀ Ā .
[1]
(................ , ................) [1]
Ā = ................................................ [3]
By drawing a suitable straight line on the grid, solve the equationĀ Ā .
Ā
= ................... orĀ = ................... orĀ = ...................
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The diagram shows a circle centre .
is a point on the circumference of the circle.
Find the equation of the tangent at .
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