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53 questions at your level
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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
(a)
Factorise
y
2
−
81
y^2 - 81
y
2
−
81
(b)
Solve
x
2
=
7
x
x^2 = 7x
x
2
=
7
x
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Level 4
4 marks
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→
Mark as done
Solve
2
x
2
+
7
x
−
15
=
0
2x^2 + 7x - 15 = 0
2
x
2
+
7
x
−
15
=
0
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Level 4
3 marks
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→
Mark as done
Solve
x
(
x
+
2
)
=
24
x(x + 2) = 24
x
(
x
+
2
)
=
24
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Level 4
3 marks
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→
Mark as done
Solve
3
x
2
−
10
x
+
8
=
0
3x^2 - 10x + 8 = 0
3
x
2
−
10
x
+
8
=
0
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Level 4
3 marks
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→
Mark as done
Solve
x
2
=
5
x
+
36
x^2 = 5x + 36
x
2
=
5
x
+
36
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Level 4
3 marks
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→
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)
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Level 4
4 marks
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→
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)
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Level 4
3 marks
Start
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The quadratic formula
14 questions
Lesson
Not started
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.
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●
Level 4
3 marks
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→
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.
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●
Level 4
2 marks
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→
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.
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●
Level 4
3 marks
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→
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)
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Level 4
4 marks
Start
→
Completing the square
14 questions
Lesson
Not started
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)
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●
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]
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●
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)
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●
Level 4
3 marks
Start
→