igureMaths
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Graphs of functions
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45 questions at your level
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Level 5
Quadratic graphs
17 questions
Lesson
Not started
Mark as done
The diagram shows the graph of
y
=
x
2
−
2
x
−
8
y = x^2 - 2x - 8
y
=
x
2
−
2
x
−
8
and the line
y
=
−
3
y = -3
y
=
−
3
-4
-2
2
4
6
-10
-5
5
x
y
Use the diagram to estimate the solutions of the equation
x
2
−
2
x
−
8
=
−
3
x^2 - 2x - 8 = -3
x
2
−
2
x
−
8
=
−
3
●●●●●
Level 5
2 marks
Start
→
Mark as done
The diagram shows the graph of
y
=
x
2
−
2
x
−
8
y = x^2 - 2x - 8
y
=
x
2
−
2
x
−
8
and the line
y
=
x
y = x
y
=
x
-4
-2
2
4
6
-10
-5
5
x
y
Use the graph to estimate the solutions of the equation
x
2
−
2
x
−
8
=
x
x^2 - 2x - 8 = x
x
2
−
2
x
−
8
=
x
Give each answer correct to 1 decimal place.
●●●●●
Level 5
3 marks
Start
→
Cubic, reciprocal and exponential graphs
17 questions
Lesson
Not started
Mark as done
The curve
y
=
x
3
−
4
x
y = x^3 - 4x
y
=
x
3
−
4
x
crosses the
x
x
x
-axis at three points.
Find the
x
x
x
-coordinate of each of the three points.
●●●●●
Level 5
3 marks
Start
→
Mark as done
A curve has ALL three of these properties:
it passes through
(
0
,
1
)
(0, 1)
(
0
,
1
)
y
y
y
is positive for every value of
x
x
x
as
x
x
x
becomes more negative,
y
y
y
gets closer and closer to
0
0
0
Which of the following could be its equation? Explain why each of the others is impossible.
y
=
x
2
+
1
y
=
2
x
y
=
1
x
y
=
x
3
+
1
y = x^2 + 1 \qquad y = 2^x \qquad y = \dfrac{1}{x} \qquad y = x^3 + 1
y
=
x
2
+
1
y
=
2
x
y
=
x
1
y
=
x
3
+
1
●●●●●
Level 5
3 marks
Start
→
Trigonometric graphs
11 questions
Lesson
Not started
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
You are given that
sin
30
°
=
0.5
\sin 30° = 0.5
sin
30°
=
0.5
(a)
Find the other solution of
sin
x
=
0.5
\sin x = 0.5
sin
x
=
0.5
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
(b)
Write down the smallest solution of
sin
x
=
−
0.5
\sin x = -0.5
sin
x
=
−
0.5
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
●●●●●
Level 5
3 marks
Start
→
Mark as done
The diagram shows the graph of
y
=
cos
x
y = \cos x
y
=
cos
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
You are given that
cos
60
°
=
0.5
\cos 60° = 0.5
cos
60°
=
0.5
Find the other solution of
cos
x
=
0.5
\cos x = 0.5
cos
x
=
0.5
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
●●●●●
Level 5
2 marks
Start
→
Mark as done
The diagram shows the graph of
y
=
cos
x
y = \cos x
y
=
cos
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
cos
40
°
=
0.766
\cos 40° = 0.766
cos
40°
=
0.766
, correct to 3 decimal places.
(a)
Use the graph to write down another solution of
cos
x
=
0.766
\cos x = 0.766
cos
x
=
0.766
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
(b)
Use the graph to solve
cos
x
=
−
0.766
\cos x = -0.766
cos
x
=
−
0.766
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
●●●●●
Level 5
3 marks
Start
→
Mark as done
The diagram shows the graph of
y
=
2
sin
x
y = 2\sin x
y
=
2
sin
x
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
50
100
150
200
250
300
350
-2
-1
1
2
x°
y
(a)
Write down the maximum and minimum values of
y
=
2
sin
x
y = 2\sin x
y
=
2
sin
x
(b)
Solve
2
sin
x
=
1
2\sin x = 1
2
sin
x
=
1
for
0
°
≤
x
≤
360
°
0° \le x \le 360°
0°
≤
x
≤
360°
●●●●●
Level 5
4 marks
Start
→
Mark as done
(a)
Sketch the graph of
y
=
sin
x
°
y = \sin x°
y
=
sin
x
°
for
0
≤
x
≤
360
0 \le x \le 360
0
≤
x
≤
360
90
180
270
360
O
x
y
(2 marks)
(b)
Solve the equation
2
sin
x
°
=
−
3
2\sin x° = -\sqrt{3}
2
sin
x
°
=
−
3
for
0
≤
x
≤
360
0 \le x \le 360
0
≤
x
≤
360
(2 marks)
●●●●●
Level 5
4 marks
Start
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