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Level 1
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Level 4
Level 5
Solving quadratics by factorising
25 questions
Lesson
Not started
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
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→
The quadratic formula
14 questions
Lesson
Not started
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
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
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