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42 questions at your level
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Level 5
Linear inequalities
16 questions
Lesson
Not started
Mark as done
A rectangle has width
w
w
w
cm and length
(
w
+
7
)
(w + 7)
(
w
+
7
)
cm.
The perimeter of the rectangle must be
less than
46
46
46
cm.
(a)
Show that
w
<
8
w < 8
w
<
8
(b)
The width is a whole number of centimetres. Write down the largest possible width.
●●●●●
Level 5
4 marks
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→
Quadratic inequalities
15 questions
Lesson
Not started
Mark as done
Solve the inequality
x
2
−
3
x
−
10
>
0
x^2 - 3x - 10 > 0
x
2
−
3
x
−
10
>
0
●●●●●
Level 5
3 marks
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→
Mark as done
Solve the inequality
x
2
+
x
−
12
<
0
x^2 + x - 12 < 0
x
2
+
x
−
12
<
0
●●●●●
Level 5
3 marks
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→
Mark as done
Solve the inequality
x
2
>
3
x
x^2 > 3x
x
2
>
3
x
●●●●●
Level 5
3 marks
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→
Mark as done
Solve the inequality
x
2
−
5
x
+
6
≥
0
x^2 - 5x + 6 \ge 0
x
2
−
5
x
+
6
≥
0
●●●●●
Level 5
3 marks
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→
Mark as done
Solve the inequality
x
2
+
4
x
−
21
≤
0
x^2 + 4x - 21 \le 0
x
2
+
4
x
−
21
≤
0
●●●●●
Level 5
3 marks
Start
→
Mark as done
(a)
Solve the inequality
x
2
−
2
x
−
8
>
0
x^2 - 2x - 8 > 0
x
2
−
2
x
−
8
>
0
(b)
Write down the smallest
positive integer
that satisfies
x
2
−
2
x
−
8
>
0
x^2 - 2x - 8 > 0
x
2
−
2
x
−
8
>
0
●●●●●
Level 5
4 marks
Start
→
Mark as done
n
n
n
is an integer that satisfies
both
of the inequalities
n
2
<
40
and
2
n
+
3
>
8
n^2 < 40 \qquad \text{and} \qquad 2n + 3 > 8
n
2
<
40
and
2
n
+
3
>
8
Write down all the possible values of
n
n
n
.
●●●●●
Level 5
3 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
→
Inequalities as regions on a graph
11 questions
Lesson
Not started
Mark as done
A region is defined by the three inequalities
x
≥
1
,
y
≤
x
+
1
,
x
+
y
<
8
x \ge 1, \qquad y \le x + 1, \qquad x + y < 8
x
≥
1
,
y
≤
x
+
1
,
x
+
y
<
8
The point
(
a
,
3
)
(a, 3)
(
a
,
3
)
lies in the region, where
a
a
a
is an integer.
Find all the possible values of
a
a
a
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
A region is defined by the three inequalities
y
≥
1
,
y
<
2
x
+
1
,
x
+
y
≤
7
y \ge 1, \qquad y < 2x + 1, \qquad x + y \le 7
y
≥
1
,
y
<
2
x
+
1
,
x
+
y
≤
7
The point
(
2
,
b
)
(2, b)
(
2
,
b
)
, where
b
b
b
is an
integer
, lies in the region.
Write down all the possible values of
b
b
b
.
●●●●●
Level 5
3 marks
Start
→