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Level 1
Level 2
Level 3
Level 4
Level 5
Solving quadratics by factorising
25 questions
Lesson
Not started
Mark as done
Solve
(
x
−
3
)
(
x
+
2
)
=
0
(x - 3)(x + 2) = 0
(
x
−
3
)
(
x
+
2
)
=
0
●
●●●●
Level 1
1 mark
Start
→
Mark as done
The correct factorisation of
x
2
−
9
x^2 - 9
x
2
−
9
is
Circle your answer.
A
(
x
−
3
)
2
(x - 3)^2
(
x
−
3
)
2
B
(
x
+
3
)
2
(x + 3)^2
(
x
+
3
)
2
C
(
x
−
3
)
(
x
+
3
)
(x - 3)(x + 3)
(
x
−
3
)
(
x
+
3
)
D
x
(
x
−
9
)
x(x - 9)
x
(
x
−
9
)
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Solve
x
2
+
5
x
+
6
=
0
x^2 + 5x + 6 = 0
x
2
+
5
x
+
6
=
0
●●
●●●
Level 2
2 marks
Start
→
Mark as done
Solve
x
2
−
4
x
=
0
x^2 - 4x = 0
x
2
−
4
x
=
0
●●
●●●
Level 2
2 marks
Start
→
Mark as done
(a)
Expand and simplify
(
2
x
+
3
)
(
x
−
4
)
(2x + 3)(x - 4)
(
2
x
+
3
)
(
x
−
4
)
[2]
(b)
Factorise
4
x
2
−
25
4x^2 - 25
4
x
2
−
25
[1]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
(a)
Factorise
x
2
+
3
x
−
28
x^2 + 3x - 28
x
2
+
3
x
−
28
(b)
Hence solve
x
2
+
3
x
−
28
=
0
x^2 + 3x - 28 = 0
x
2
+
3
x
−
28
=
0
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
Factorise
x
2
−
9
x
+
20
x^2 - 9x + 20
x
2
−
9
x
+
20
(b)
Hence solve
x
2
−
9
x
+
20
=
0
x^2 - 9x + 20 = 0
x
2
−
9
x
+
20
=
0
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Solve
x
2
−
49
=
0
x^2 - 49 = 0
x
2
−
49
=
0
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Solve
x
2
+
3
x
−
10
=
0
x^2 + 3x - 10 = 0
x
2
+
3
x
−
10
=
0
(3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Solve
x
2
−
5
x
−
24
=
0
x^2 - 5x - 24 = 0
x
2
−
5
x
−
24
=
0
(3 marks)
●●●
●●
Level 3
3 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)
Factorise
y
2
−
81
y^2 - 81
y
2
−
81
(b)
Solve
x
2
=
7
x
x^2 = 7x
x
2
=
7
x
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Solve
2
x
2
+
7
x
−
15
=
0
2x^2 + 7x - 15 = 0
2
x
2
+
7
x
−
15
=
0
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
x
(
x
+
2
)
=
24
x(x + 2) = 24
x
(
x
+
2
)
=
24
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
3
x
2
−
10
x
+
8
=
0
3x^2 - 10x + 8 = 0
3
x
2
−
10
x
+
8
=
0
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
x
2
=
5
x
+
36
x^2 = 5x + 36
x
2
=
5
x
+
36
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
3
x
+
2
+
4
2
x
−
3
=
1
\dfrac{3}{x + 2} + \dfrac{4}{2x - 3} = 1
x
+
2
3
+
2
x
−
3
4
=
1
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Show that
2
x
2
+
7
x
−
15
4
x
2
−
9
\frac{2x^2 + 7x - 15}{4x^2 - 9}
4
x
2
−
9
2
x
2
+
7
x
−
15
can be written in the form
a
x
+
b
c
x
+
d
\dfrac{ax + b}{cx + d}
c
x
+
d
a
x
+
b
where
a
a
a
,
b
b
b
,
c
c
c
and
d
d
d
are integers.
(3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A rectangle has length
(
x
+
5
)
(x + 5)
(
x
+
5
)
cm and width
(
x
−
2
)
(x - 2)
(
x
−
2
)
cm.
(x + 5) cm
(x − 2) cm
Diagram NOT accurately drawn
The area of the rectangle is 60 cm².
(a)
Show that
x
2
+
3
x
−
70
=
0
x^2 + 3x - 70 = 0
x
2
+
3
x
−
70
=
0
(b)
Find the length and the width of the rectangle.
●●●●●
Level 5
5 marks
Start
→
Mark as done
Solve
12
x
−
x
=
4
\dfrac{12}{x} - x = 4
x
12
−
x
=
4
, where
x
≠
0
x \neq 0
x
=
0
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
Find the set of possible values of
x
x
x
for which
9
x
2
−
49
<
0
9x^2 - 49 < 0
9
x
2
−
49
<
0
\qquad and \qquad
15
−
7
x
−
2
x
2
>
0
15 - 7x - 2x^2 > 0
15
−
7
x
−
2
x
2
>
0
You must show all your working.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
Find the set of possible values of
x
x
x
for which
x
2
+
2
x
>
24
x^2 + 2x > 24
x
2
+
2
x
>
24
\qquad and \qquad
2
x
2
<
7
x
+
30
2x^2 < 7x + 30
2
x
2
<
7
x
+
30
You must show all your working.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
Solve algebraically the simultaneous equations
2
x
2
+
3
y
2
=
35
2x^2 + 3y^2 = 35
2
x
2
+
3
y
2
=
35
2
x
−
y
=
7
2x - y = 7
2
x
−
y
=
7
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
A solid cuboid is
15
15
15
cm long.
Its volume is
180
180
180
cm³ and its total surface area is
234
234
234
cm²
The height of the cuboid is less than its width.
Work out the height of the cuboid.
You must show all your working.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
x
−
3
x - 3
x
−
3
,
x
+
1
x + 1
x
+
1
and
4
x
−
2
4x - 2
4
x
−
2
are three consecutive terms of an arithmetic sequence.
(a)
Find the value of
x
x
x
.
(2 marks)
y
−
3
y - 3
y
−
3
,
y
+
1
y + 1
y
+
1
and
4
y
−
2
4y - 2
4
y
−
2
are three consecutive terms of a geometric sequence.
(b)
Find the possible values of
y
y
y
.
(5 marks)
●●●●●
Level 5
7 marks
Start
→
The quadratic formula
14 questions
Lesson
Not started
Mark as done
Solve
x
2
+
4
x
−
9
=
0
x^2 + 4x - 9 = 0
x
2
+
4
x
−
9
=
0
Give your answers correct to 2 decimal places.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Solve
x
2
−
6
x
+
2
=
0
x^2 - 6x + 2 = 0
x
2
−
6
x
+
2
=
0
Give your answers correct to 2 decimal places.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Solve
2
x
2
−
7
x
+
4
=
0
2x^2 - 7x + 4 = 0
2
x
2
−
7
x
+
4
=
0
Give your solutions correct to 2 decimal places. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Solve
3
x
2
+
5
x
−
4
=
0
3x^2 + 5x - 4 = 0
3
x
2
+
5
x
−
4
=
0
Give your solutions correct to 2 decimal places. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
Solve
3
x
2
+
4
x
−
5
=
0
3x^2 + 4x - 5 = 0
3
x
2
+
4
x
−
5
=
0
. Give your solutions correct to 3 decimal places. [3]
(b)
Write down the coordinates of the point where the graph of
y
=
3
x
2
+
4
x
−
5
y = 3x^2 + 4x - 5
y
=
3
x
2
+
4
x
−
5
crosses the
y
y
y
-axis. [1]
●●●
●●
Level 3
4 marks
Start
→
Mark as done
Solve
3
x
2
−
8
x
+
2
=
0
3x^2 - 8x + 2 = 0
3
x
2
−
8
x
+
2
=
0
Give your answers correct to 3 significant figures.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
2
x
2
+
5
x
−
4
=
0
2x^2 + 5x - 4 = 0
2
x
2
+
5
x
−
4
=
0
Give your answers in surd form.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Amir tries to solve
x
2
+
3
x
+
5
=
0
x^2 + 3x + 5 = 0
x
2
+
3
x
+
5
=
0
using the quadratic formula, but his calculator shows an error.
Explain why the equation has
no
real solutions.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Solve
2
x
2
+
3
x
−
7
=
0
2x^2 + 3x - 7 = 0
2
x
2
+
3
x
−
7
=
0
Give your answers correct to 3 significant figures.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
3
x
2
−
6
x
+
1
=
0
3x^2 - 6x + 1 = 0
3
x
2
−
6
x
+
1
=
0
Give your answers in the form
a
±
b
c
\dfrac{a \pm \sqrt{b}}{c}
c
a
±
b
, simplified as far as possible.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
3
x
+
1
+
2
x
−
2
=
1
\dfrac{3}{x + 1} + \dfrac{2}{x - 2} = 1
x
+
1
3
+
x
−
2
2
=
1
Give your solutions correct to 2 decimal places. (4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Show that the equation
5
x
+
x
=
7
\dfrac{5}{x} + x = 7
x
5
+
x
=
7
can be written as
x
2
−
7
x
+
5
=
0
x^2 - 7x + 5 = 0
x
2
−
7
x
+
5
=
0
, and hence solve it.
Give your answers correct to 2 decimal places.
●●●●●
Level 5
4 marks
Start
→
Mark as done
(a)
Show that the equation
x
(
x
+
3
)
=
2
x
+
9
x(x + 3) = 2x + 9
x
(
x
+
3
)
=
2
x
+
9
can be written as
x
2
+
x
−
9
=
0
x^2 + x - 9 = 0
x
2
+
x
−
9
=
0
(b)
Hence solve
x
(
x
+
3
)
=
2
x
+
9
x(x + 3) = 2x + 9
x
(
x
+
3
)
=
2
x
+
9
, giving your answers correct to 2 decimal places.
●●●●●
Level 5
5 marks
Start
→
Mark as done
The equation
k
x
2
+
6
x
+
3
=
0
kx^2 + 6x + 3 = 0
k
x
2
+
6
x
+
3
=
0
, where
k
k
k
is a positive constant, has exactly
one
solution (a repeated root).
Work out the value of
k
k
k
.
●●●●●
Level 5
3 marks
Start
→
Completing the square
14 questions
Lesson
Not started
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
(b)
Write down the minimum value of
x
2
+
6
x
+
2
x^2 + 6x + 2
x
2
+
6
x
+
2
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
Write
x
2
+
4
x
+
9
x^2 + 4x + 9
x
2
+
4
x
+
9
in the form
(
x
+
a
)
2
+
b
(x + a)^2 + b
(
x
+
a
)
2
+
b
(b)
Write down the minimum value of
x
2
+
4
x
+
9
x^2 + 4x + 9
x
2
+
4
x
+
9
●●●
●●
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
(a)
Write
x
2
−
8
x
+
3
x^2 - 8x + 3
x
2
−
8
x
+
3
in the form
(
x
−
a
)
2
−
b
(x - a)^2 - b
(
x
−
a
)
2
−
b
(b)
Hence write down the coordinates of the turning point of the graph of
y
=
x
2
−
8
x
+
3
y = x^2 - 8x + 3
y
=
x
2
−
8
x
+
3
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
x
2
+
10
x
+
18
=
0
x^2 + 10x + 18 = 0
x
2
+
10
x
+
18
=
0
by completing the square.
Give your answers in surd form.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
(a)
Write
x
2
−
10
x
+
18
x^2 - 10x + 18
x
2
−
10
x
+
18
in the form
(
x
−
a
)
2
−
b
(x - a)^2 - b
(
x
−
a
)
2
−
b
(b)
Hence write down the coordinates of the turning point of the graph of
y
=
x
2
−
10
x
+
18
y = x^2 - 10x + 18
y
=
x
2
−
10
x
+
18
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve
x
2
−
6
x
+
4
=
0
x^2 - 6x + 4 = 0
x
2
−
6
x
+
4
=
0
by completing the square.
Give your answers in surd form.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
(a)
Write
x
2
+
8
x
+
3
x^2 + 8x + 3
x
2
+
8
x
+
3
in the form
(
x
+
a
)
2
+
b
(x + a)^2 + b
(
x
+
a
)
2
+
b
, where
a
a
a
and
b
b
b
are integers. (2 marks)
(b)
Hence solve the equation
x
2
+
8
x
+
3
=
0
x^2 + 8x + 3 = 0
x
2
+
8
x
+
3
=
0
Give your answers in surd form. (2 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Solve
x
2
+
6
x
−
5
=
0
x^2 + 6x - 5 = 0
x
2
+
6
x
−
5
=
0
by completing the square.
Give your answers in the form
a
±
b
a \pm \sqrt{b}
a
±
b
, where
a
a
a
and
b
b
b
are integers. [4]
●●●●
●
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
Write
2
x
2
+
12
x
+
5
2x^2 + 12x + 5
2
x
2
+
12
x
+
5
in the form
a
(
x
+
p
)
2
+
q
a(x + p)^2 + q
a
(
x
+
p
)
2
+
q
●●●●●
Level 5
3 marks
Start
→
Mark as done
Show that
x
2
−
4
x
+
9
x^2 - 4x + 9
x
2
−
4
x
+
9
is positive for
all
values of
x
x
x
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Write
3
x
2
−
12
x
+
5
3x^2 - 12x + 5
3
x
2
−
12
x
+
5
in the form
a
(
x
+
p
)
2
+
q
a(x + p)^2 + q
a
(
x
+
p
)
2
+
q
●●●●●
Level 5
3 marks
Start
→
Mark as done
(a)
Write
x
2
+
8
x
+
3
x^2 + 8x + 3
x
2
+
8
x
+
3
in the form
(
x
+
a
)
2
+
b
(x + a)^2 + b
(
x
+
a
)
2
+
b
(b)
Write down the coordinates of the minimum point of the graph of
y
=
x
2
+
8
x
+
3
y = x^2 + 8x + 3
y
=
x
2
+
8
x
+
3
(c)
Explain why the equation
x
2
+
8
x
+
3
=
−
20
x^2 + 8x + 3 = -20
x
2
+
8
x
+
3
=
−
20
has
no
solutions.
●●●●●
Level 5
4 marks
Start
→