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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)
Complete the table of values for
y
=
x
2
−
2
x
−
8
y = x^2 - 2x - 8
y
=
x
2
−
2
x
−
8
x
x
x
−
2
-2
−
2
−
1
-1
−
1
0
0
0
1
1
1
2
2
2
3
3
3
4
4
4
y
y
y
0
0
0
−
8
-8
−
8
−
8
-8
−
8
0
0
0
(b)
Write down the coordinates of the turning point of the graph of
y
=
x
2
−
2
x
−
8
y = x^2 - 2x - 8
y
=
x
2
−
2
x
−
8
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows the graph of
y
=
x
2
−
4
x
+
3
y = x^2 - 4x + 3
y
=
x
2
−
4
x
+
3
-1
1
2
3
4
5
-2
2
4
6
8
x
y
(a)
Write down the roots of
x
2
−
4
x
+
3
=
0
x^2 - 4x + 3 = 0
x
2
−
4
x
+
3
=
0
(b)
Write down the coordinates of the turning point of the graph.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
The diagram shows the graph of
y
=
x
2
+
2
x
−
3
y = x^2 + 2x - 3
y
=
x
2
+
2
x
−
3
-5
-4
-3
-2
-1
1
2
3
-4
-2
2
4
6
x
y
(a)
Write down the roots of
x
2
+
2
x
−
3
=
0
x^2 + 2x - 3 = 0
x
2
+
2
x
−
3
=
0
(b)
Write down the coordinates of the point where the graph crosses the
y
y
y
-axis.
(c)
Write down the equation of the graph's line of symmetry.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A curve has equation
y
=
4
−
x
2
y = 4 - x^2
y
=
4
−
x
2
(a)
State whether the curve is
∪
\cup
∪
-shaped or
∩
\cap
∩
-shaped. Give a reason for your answer.
(b)
Write down the coordinates of the curve's maximum point.
(c)
Write down the roots of
4
−
x
2
=
0
4 - x^2 = 0
4
−
x
2
=
0
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
Write
x
2
−
6
x
+
2
x^2 - 6x + 2
x
2
−
6
x
+
2
in the form
(
x
−
a
)
2
−
b
(x - a)^2 - b
(
x
−
a
)
2
−
b
(2 marks)
(b)
Hence write down the coordinates of the turning point of the graph of
y
=
x
2
−
6
x
+
2
y = x^2 - 6x + 2
y
=
x
2
−
6
x
+
2
(1 mark)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The curve
y
=
(
x
−
2
)
(
x
+
4
)
y = (x - 2)(x + 4)
y
=
(
x
−
2
)
(
x
+
4
)
is to be sketched.
(a)
Write down the coordinates of the points where the curve crosses the
x
x
x
-axis. [1]
(b)
Write down the coordinates of the point where the curve crosses the
y
y
y
-axis. [1]
(c)
Work out the coordinates of the turning point of the curve. [2]
●●●
●●
Level 3
4 marks
Start
→
Mark as done
(a)
Solve
2
x
2
+
7
x
−
4
=
0
2x^2 + 7x - 4 = 0
2
x
2
+
7
x
−
4
=
0
[3]
(b)
Write down the
x
x
x
-coordinate of the turning point of the graph of
y
=
2
x
2
+
7
x
−
4
y = 2x^2 + 7x - 4
y
=
2
x
2
+
7
x
−
4
. [1]
●●●
●●
Level 3
4 marks
Start
→
Mark as done
(a)
Complete the table of values for
y
=
x
2
+
3
x
−
1
y = x^2 + 3x - 1
y
=
x
2
+
3
x
−
1
x
x
x
−
4
-4
−
4
−
3
-3
−
3
−
2
-2
−
2
−
1
-1
−
1
0
0
0
1
1
1
y
y
y
3
3
3
−
1
-1
−
1
3
3
3
(2 marks)
(b)
On the grid, draw the graph of
y
=
x
2
+
3
x
−
1
y = x^2 + 3x - 1
y
=
x
2
+
3
x
−
1
for values of
x
x
x
from
−
4
-4
−
4
to
1
1
1
-4
-3
-2
-1
1
-4
-3
-2
-1
1
2
3
4
x
y
(2 marks)
(c)
Write down the coordinates of the turning point of the graph of
y
=
x
2
+
3
x
−
1
y = x^2 + 3x - 1
y
=
x
2
+
3
x
−
1
(1 mark)
●●●
●●
Level 3
5 marks
Start
→
Cubic, reciprocal and exponential graphs
17 questions
Lesson
Not started
Mark as done
Here are four graphs,
A
,
B
,
C
and
D
.
-3
-2
-1
1
2
3
2
4
6
8
A
-2
-1
1
2
-8
-6
-4
-2
2
4
6
8
B
-4
-3
-2
-1
1
2
3
4
-4
-3
-2
-1
1
2
3
4
C
-3
-2
-1
1
2
3
2
4
6
8
D
(a)
Write down the letter of the graph of
y
=
x
3
y = x^3
y
=
x
3
(b)
Write down the letter of the graph of
y
=
1
x
y = \dfrac{1}{x}
y
=
x
1
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Here are four graphs,
A
,
B
,
C
and
D
.
-3
-2
-1
1
2
3
-8
-6
-4
-2
A
-3
-2
-1
1
2
3
2
4
6
8
B
-4
-3
-2
-1
1
2
3
4
-4
-3
-2
-1
1
2
3
4
C
-2
-1
1
2
-4
-2
2
4
D
Write down the letter of the graph that could be
(a)
y
=
−
x
2
y = -x^2
y
=
−
x
2
(b)
y
=
(
1
2
)
x
y = \left(\dfrac{1}{2}\right)^x
y
=
(
2
1
)
x
(c)
y
=
x
3
−
3
x
y = x^3 - 3x
y
=
x
3
−
3
x
●●●
●●
Level 3
3 marks
Start
→
Mark as done
y
=
6
x
y = \dfrac{6}{x}
y
=
x
6
for
x
≠
0
x \neq 0
x
=
0
(a)
Work out the value of
y
y
y
when:
x
=
1
\;x = 1
x
=
1
,
x
=
2
\;x = 2
x
=
2
,
x
=
3
\;x = 3
x
=
3
(b)
Explain why the graph of
y
=
6
x
y = \dfrac{6}{x}
y
=
x
6
never crosses the
y
y
y
-axis.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The velocity–time graph shows the first
40
40
40
seconds of a train's journey.
10
20
30
40
2
4
6
8
10
12
14
Time (s)
Velocity (m/s)
(a)
Work out the acceleration of the train in the first
10
10
10
seconds. [2]
(b)
Work out the total distance travelled in the
40
40
40
seconds. [3]
●●●
●●
Level 3
5 marks
Start
→
Mark as done
(a)
Complete the table of values for
y
=
x
3
−
2
x
+
1
y = x^3 - 2x + 1
y
=
x
3
−
2
x
+
1
x
x
x
−
2
-2
−
2
−
1
-1
−
1
0
0
0
1
1
1
2
2
2
y
y
y
−
3
-3
−
3
1
1
1
(2 marks)
(b)
On the grid, draw the graph of
y
=
x
3
−
2
x
+
1
y = x^3 - 2x + 1
y
=
x
3
−
2
x
+
1
for values of
x
x
x
from
−
2
-2
−
2
to
2
2
2
-2
-1
1
2
-4
-3
-2
-1
1
2
3
4
5
6
x
y
(2 marks)
(c)
Use your graph to find estimates for the solutions of the equation
x
3
−
2
x
+
1
=
2
x^3 - 2x + 1 = 2
x
3
−
2
x
+
1
=
2
(2 marks)
●●●
●●
Level 3
6 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
(a)
Write down the maximum value of
sin
x
\sin x
sin
x
(b)
Write down the three values of
x
x
x
in this range for which
sin
x
=
0
\sin x = 0
sin
x
=
0
●●●
●●
Level 3
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
(a)
Write down the value of
cos
0
°
\cos 0°
cos
0°
(b)
Write down the value of
cos
180
°
\cos 180°
cos
180°
●●●
●●
Level 3
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
(a)
Write down the values of
x
x
x
for which
cos
x
=
0
\cos x = 0
cos
x
=
0
in this interval.
(b)
Write down the value of
cos
360
°
\cos 360°
cos
360°
●●●
●●
Level 3
3 marks
Start
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