igureMaths
Log in
Start free
←
Inequalities
Get dealt questions instead
→
Browse Inequalities
42 questions at your level
Difficulty
All
Level 1
Level 2
Level 3
Level 4
Level 5
Linear inequalities
16 questions
Lesson
Not started
Mark as done
(a)
Solve the inequality
7
−
2
x
>
1
7 - 2x > 1
7
−
2
x
>
1
(b)
Write down the largest integer that satisfies
7
−
2
x
>
1
7 - 2x > 1
7
−
2
x
>
1
●●●●
●
Level 4
3 marks
Start
→
Mark as done
(a)
Solve the inequality
3
<
2
x
+
1
≤
9
3 < 2x + 1 \le 9
3
<
2
x
+
1
≤
9
(b)
x
x
x
is an integer. Write down all the values of
x
x
x
that satisfy
3
<
2
x
+
1
≤
9
3 < 2x + 1 \le 9
3
<
2
x
+
1
≤
9
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A van-hire company charges a fixed fee of £40 plus £22 per day.
Amy can spend
at most
£150.
Work out the greatest number of whole days Amy can hire the van for.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve the inequality
5
−
3
x
≤
−
7
5 - 3x \le -7
5
−
3
x
≤
−
7
●●●●
●
Level 4
2 marks
Start
→
Mark as done
(a)
Solve the inequality
−
5
≤
3
x
+
1
<
10
-5 \le 3x + 1 < 10
−
5
≤
3
x
+
1
<
10
(b)
x
x
x
is an integer. Write down all the values of
x
x
x
that satisfy
−
5
≤
3
x
+
1
<
10
-5 \le 3x + 1 < 10
−
5
≤
3
x
+
1
<
10
●●●●
●
Level 4
3 marks
Start
→
Quadratic inequalities
15 questions
Lesson
Not started
Mark as done
Solve the inequality
x
2
≤
16
x^2 \le 16
x
2
≤
16
●●●●
●
Level 4
2 marks
Start
→
Mark as done
n
n
n
is an integer and
n
2
<
30
n^2 < 30
n
2
<
30
(a)
Write down the greatest possible value of
n
n
n
.
(b)
Write down the least possible value of
n
n
n
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Solve the inequality
x
2
<
49
x^2 < 49
x
2
<
49
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Solve
x
2
−
3
x
−
4
≤
0
x^2 - 3x - 4 \le 0
x
2
−
3
x
−
4
≤
0
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Solve
x
2
−
5
x
−
14
>
0
x^2 - 5x - 14 > 0
x
2
−
5
x
−
14
>
0
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Solve
(
2
x
+
7
)
(
4
x
−
3
)
<
0
(2x + 7)(4x - 3) < 0
(
2
x
+
7
)
(
4
x
−
3
)
<
0
(2 marks)
●●●●
●
Level 4
2 marks
Start
→
Inequalities as regions on a graph
11 questions
Lesson
Not started
Mark as done
The diagram shows three straight lines and a region
R
R
R
bounded by them.
-1
1
2
3
4
5
6
-1
1
2
3
4
5
y = x + 1
x + y = 5
y = 1
R
x
y
Diagram NOT accurately drawn
All three boundary lines are included in
R
R
R
.
Write down the three inequalities that define
R
R
R
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The diagram shows the lines
y
=
x
y = x
y
=
x
,
y
=
3
y = 3
y
=
3
and
x
=
2
x = 2
x
=
2
, and a region
R
R
R
bounded by them.
y = x
y = 3
x = 2
R
x
y
Diagram NOT accurately drawn
All three boundary lines are included in
R
R
R
.
Write down the three inequalities that define
R
R
R
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A triangular region is bounded by the three inequalities
y
≥
0
,
y
≤
2
x
,
x
≤
3
y \ge 0, \qquad y \le 2x, \qquad x \le 3
y
≥
0
,
y
≤
2
x
,
x
≤
3
x
y
Work out the coordinates of the three vertices of the region.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The diagram shows the vertical line
x
=
−
1
x = -1
x
=
−
1
(solid), the line
y
=
x
−
2
y = x - 2
y
=
x
−
2
(dashed), and the horizontal line
y
=
4
y = 4
y
=
4
(solid). The region
R
R
R
lies to the right of the vertical line, above the dashed line, and below the horizontal line.
R
x
y
Write down the three inequalities that define the region
R
R
R
.
(A dashed line is not included in the region; a solid line is.)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A region is defined by the three inequalities
x
≥
0
,
y
≥
0
,
x
+
y
<
4
x \ge 0, \qquad y \ge 0, \qquad x + y < 4
x
≥
0
,
y
≥
0
,
x
+
y
<
4
How many points with
integer coordinates
lie in the region?
●●●●
●
Level 4
3 marks
Start
→
Mark as done
(a)
On the grid, show by shading, the region that satisfies all of these inequalities.
y
>
−
1
x
<
2
y
<
2
x
+
1
x
+
y
>
−
3
y > -1 \qquad x < 2 \qquad y < 2x + 1 \qquad x + y > -3
y
>
−
1
x
<
2
y
<
2
x
+
1
x
+
y
>
−
3
Label the region
R
R
R
.
-4
-3
-2
-1
1
2
3
4
5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
(4 marks)
Aisha says,
"One of these four inequalities is not needed.
R
R
R
would be the same without it."
Aisha is correct.
(b)
Which inequality is not needed?
(1 mark)
●●●●
●
Level 4
5 marks
Start
→