igureMaths
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Graphs of functions
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45 questions at your level
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Level 1
Level 2
Level 3
Level 4
Level 5
Quadratic graphs
17 questions
Lesson
Not started
Mark as done
A parabola crosses the
x
x
x
-axis at
x
=
−
1
x = -1
x
=
−
1
and
x
=
5
x = 5
x
=
5
.
Find the equation of its line of symmetry.
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Level 4
2 marks
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→
Mark as done
A curve has equation
y
=
(
x
−
2
)
(
x
+
4
)
y = (x - 2)(x + 4)
y
=
(
x
−
2
)
(
x
+
4
)
(a)
Write down the roots of
(
x
−
2
)
(
x
+
4
)
=
0
(x - 2)(x + 4) = 0
(
x
−
2
)
(
x
+
4
)
=
0
(b)
Write down the coordinates of the point where the curve crosses the
y
y
y
-axis.
(c)
Find the coordinates of the turning point of the curve.
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●
Level 4
4 marks
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→
Mark as done
A parabola has line of symmetry
x
=
3
x = 3
x
=
3
, and one of its roots is
x
=
−
1
x = -1
x
=
−
1
.
(a)
Find the other root.
(b)
Write down the
x
x
x
-coordinate of the parabola's turning point.
●●●●
●
Level 4
3 marks
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→
Mark as done
A curve has equation
y
=
x
2
−
6
x
+
5
y = x^2 - 6x + 5
y
=
x
2
−
6
x
+
5
(a)
Factorise
x
2
−
6
x
+
5
x^2 - 6x + 5
x
2
−
6
x
+
5
(b)
Hence write down the roots of
x
2
−
6
x
+
5
=
0
x^2 - 6x + 5 = 0
x
2
−
6
x
+
5
=
0
(c)
Work out the coordinates of the curve's turning point.
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Level 4
4 marks
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→
Mark as done
The curve
C
C
C
has equation
y
=
4
x
2
−
20
x
+
9
y = 4x^2 - 20x + 9
y
=
4
x
2
−
20
x
+
9
Find the coordinates of the turning point on
C
C
C
.
(3 marks)
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●
Level 4
3 marks
Start
→
Cubic, reciprocal and exponential graphs
17 questions
Lesson
Not started
Mark as done
(a)
Write down the coordinates of the point where the graph of
y
=
2
x
y = 2^x
y
=
2
x
crosses the
y
y
y
-axis.
(b)
Explain why the graph of
y
=
2
x
y = 2^x
y
=
2
x
never touches the
x
x
x
-axis.
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●
Level 4
2 marks
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→
Mark as done
(a)
Explain why the graph of
y
=
1
x
y = \dfrac{1}{x}
y
=
x
1
has no point where
x
=
0
x = 0
x
=
0
(b)
Write down the coordinates of the point on the graph of
y
=
1
x
y = \dfrac{1}{x}
y
=
x
1
where
x
=
1
2
x = \dfrac{1}{2}
x
=
2
1
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Level 4
2 marks
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→
Mark as done
y
=
3
x
y = 3^x
y
=
3
x
(a)
Work out the value of
y
y
y
when
x
=
4
x = 4
x
=
4
(b)
Work out the value of
x
x
x
when
y
=
1
3
y = \dfrac{1}{3}
y
=
3
1
●●●●
●
Level 4
2 marks
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→
Mark as done
y
=
5
x
y = 5^x
y
=
5
x
(a)
Work out the value of
y
y
y
when
x
=
3
x = 3
x
=
3
(b)
Work out the value of
x
x
x
when
y
=
1
25
y = \dfrac{1}{25}
y
=
25
1
(c)
Explain why
y
y
y
can never equal
0
0
0
.
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●
Level 4
3 marks
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→
Mark as done
The curve
y
=
x
3
−
3
x
2
y = x^3 - 3x^2
y
=
x
3
−
3
x
2
crosses or touches the
x
x
x
-axis at two points.
Find the
x
x
x
-coordinate of each of these points.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Here are some graphs.
A
x
y
B
x
y
C
x
y
D
x
y
E
x
y
F
x
y
G
x
y
H
x
y
Each equation in the table is the equation of one of the graphs.
Complete the table.
Equation
Letter of graph
y
=
2
x
−
1
y = 2x - 1
y
=
2
x
−
1
y
=
−
3
x
y = -\dfrac{3}{x}
y
=
−
x
3
y
=
0.5
x
y = 0.5^x
y
=
0.
5
x
y
=
x
3
−
4
x
y = x^3 - 4x
y
=
x
3
−
4
x
(3 marks)
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●
Level 4
3 marks
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→
Mark as done
Here is a sketch of part of the graph of
y
=
k
x
y = k^x
y
=
k
x
where
k
k
k
is a positive constant.
(−2, 0.36)
O
x
y
The graph passes through the point with coordinates
(
−
2
,
0.36
)
(-2, 0.36)
(
−
2
,
0.36
)
Find the value of
k
k
k
.
(2 marks)
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●
Level 4
2 marks
Start
→
Trigonometric graphs
11 questions
Lesson
Not started
Mark as done
(a)
Explain why the equation
sin
x
=
1.2
\sin x = 1.2
sin
x
=
1.2
has
no
solutions.
(b)
Write down the maximum value of
3
sin
x
3\sin x
3
sin
x
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●
Level 4
2 marks
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→
Mark as done
The diagram shows the graph of
y
=
tan
x
y = \tan x
y
=
tan
x
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
50
100
150
200
250
300
350
-4
-3
-2
-1
1
2
3
4
x°
y
tan
45
°
=
1
\tan 45° = 1
tan
45°
=
1
(a)
Use the graph to write down another solution of
tan
x
=
1
\tan x = 1
tan
x
=
1
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
(b)
Explain why
tan
x
\tan x
tan
x
has no value at
x
=
90
°
x = 90°
x
=
90°
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●
Level 4
3 marks
Start
→
Mark as done
The diagram shows the graph of
y
=
sin
x
y = \sin x
y
=
sin
x
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
50
100
150
200
250
300
350
-1.5
-1
-0.5
0.5
1
1.5
x°
y
sin
30
°
=
0.5
\sin 30° = 0.5
sin
30°
=
0.5
Use the graph to solve
sin
x
=
−
0.5
\sin x = -0.5
sin
x
=
−
0.5
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
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●
Level 4
3 marks
Start
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