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42 questions at your level
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Level 1
Level 2
Level 3
Level 4
Level 5
Linear inequalities
16 questions
Lesson
Not started
Mark as done
Solve the inequality
4
x
−
3
<
17
4x - 3 < 17
4
x
−
3
<
17
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Level 3
2 marks
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→
Mark as done
n
n
n
is an integer and
−
2
<
n
≤
3
-2 < n \le 3
−
2
<
n
≤
3
Write down all the possible values of
n
n
n
.
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Level 3
2 marks
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→
Mark as done
n
n
n
is an integer.
n
n
n
satisfies
both
of the inequalities
−
4
<
n
≤
1
and
n
>
−
2
-4 < n \le 1 \qquad \text{and} \qquad n > -2
−
4
<
n
≤
1
and
n
>
−
2
Write down all the possible values of
n
n
n
.
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Level 3
2 marks
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→
Mark as done
(a)
Solve
−
4
≤
2
x
+
2
<
10
-4 \le 2x + 2 < 10
−
4
≤
2
x
+
2
<
10
(3 marks)
(b)
Write down all the integer values of
x
x
x
that satisfy the inequality in part (a). (1 mark)
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Level 3
4 marks
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→
Mark as done
−
4
<
n
≤
3
-4 < n \le 3
−
4
<
n
≤
3
n
n
n
is an integer.
(a)
Write down the least possible value of
n
n
n
.
(1 mark)
(b)
On the number line below, show the inequality
−
2
≤
y
<
4
-2 \le y < 4
−
2
≤
y
<
4
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
y
(2 marks)
(c)
Solve
3
4
w
+
5
<
17
\dfrac{3}{4}w + 5 < 17
4
3
w
+
5
<
17
(3 marks)
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Level 3
6 marks
Start
→
Inequalities as regions on a graph
11 questions
Lesson
Not started
Mark as done
The diagram shows the line
x
=
2
x = 2
x
=
2
and the line
y
=
1
y = 1
y
=
1
.
y = 1
x = 2
R
x
y
Diagram NOT accurately drawn
The region
R
R
R
is to the right of the line
x
=
2
x = 2
x
=
2
and below the line
y
=
1
y = 1
y
=
1
.
Points on the line
x
=
2
x = 2
x
=
2
are included in
R
R
R
; points on the line
y
=
1
y = 1
y
=
1
are not.
Write down the two inequalities that define
R
R
R
.
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Level 3
2 marks
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Mark as done
A region is defined by the three inequalities
x
≥
0
,
y
<
x
+
1
,
x
+
y
≤
6
x \ge 0, \qquad y < x + 1, \qquad x + y \le 6
x
≥
0
,
y
<
x
+
1
,
x
+
y
≤
6
Here are three points:
A
(
2
,
1
)
B
(
4
,
3
)
C
(
1
,
4
)
\;A(2, 1) \qquad B(4, 3) \qquad C(1, 4)
A
(
2
,
1
)
B
(
4
,
3
)
C
(
1
,
4
)
Which of the points lies in the region? You must show how you decide.
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Level 3
3 marks
Start
→
Mark as done
A region
R
R
R
is defined by the two inequalities
x
<
3
and
y
≥
2
x < 3 \qquad \text{and} \qquad y \ge 2
x
<
3
and
y
≥
2
x
y
(a)
Is the point
(
1
,
4
)
(1, 4)
(
1
,
4
)
in the region
R
R
R
? Give a reason.
(b)
Is the point
(
3
,
2
)
(3, 2)
(
3
,
2
)
in the region
R
R
R
? Give a reason.
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Level 3
3 marks
Start
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