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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
Complete the table of values for
y
=
x
2
−
2
y = x^2 - 2
y
=
x
2
−
2
.
x
x
x
−
2
-2
−
2
−
1
-1
−
1
0
0
0
1
1
1
2
2
2
y
y
y
−
1
-1
−
1
−
2
-2
−
2
2
2
2
Give the missing values of
y
y
y
for
x
=
−
2
x = -2
x
=
−
2
and
x
=
1
x = 1
x
=
1
.
●
●●●●
Level 1
2 marks
Start
→
Mark as done
The graph of
y
=
x
2
−
4
y = x^2 - 4
y
=
x
2
−
4
is drawn. Write down the coordinates of the point where the graph crosses the
y
y
y
-axis, and the values of
x
x
x
where it crosses the
x
x
x
-axis.
●●
●●●
Level 2
2 marks
Start
→
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
→
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.
●●●●
●
Level 4
2 marks
Start
→
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.
●●●●
●
Level 4
4 marks
Start
→
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
Start
→
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.
●●●●
●
Level 4
4 marks
Start
→
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)
●●●●
●
Level 4
3 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
=
−
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
Which of these equations has a straight-line graph?
\quad
A:
y
=
x
2
y = x^2 \qquad
y
=
x
2
B:
y
=
3
x
−
1
y = 3x - 1 \qquad
y
=
3
x
−
1
C:
y
=
1
x
y = \dfrac{1}{x}
y
=
x
1
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Here is a sketch of a graph.
-3
-2
-1
1
2
3
2
4
6
8
Which of these could be its equation?
\quad
A:
y
=
x
2
y = x^2 \qquad
y
=
x
2
B:
y
=
x
3
y = x^3 \qquad
y
=
x
3
C:
y
=
2
x
y = 2x
y
=
2
x
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Here is a sketch of a graph.
-4
-3
-2
-1
1
2
3
4
-4
-3
-2
-1
1
2
3
4
Which of these could be its equation?
\quad
A:
y
=
x
2
y = x^2 \qquad
y
=
x
2
B:
y
=
1
x
y = \dfrac{1}{x} \qquad
y
=
x
1
C:
y
=
x
+
1
y = x + 1
y
=
x
+
1
●
●●●●
Level 1
1 mark
Start
→
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
→
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.
●●●●
●
Level 4
2 marks
Start
→
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
●●●●
●
Level 4
2 marks
Start
→
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
Start
→
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
.
●●●●
●
Level 4
3 marks
Start
→
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)
●●●●
●
Level 4
3 marks
Start
→
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)
●●●●
●
Level 4
2 marks
Start
→
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
(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
→
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
●●●●
●
Level 4
2 marks
Start
→
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°
●●●●
●
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°
●●●●
●
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
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
→