Chapter 12: Inequalities Paper 1
This test paper contains 20 questions. Answer ALL ALL the questions. The diagrams accompanying the questions are not drawn to scale unless mentioned. You are allowed to use a scientific calculator that t hat cannot be programmed. is a negative integer. integer. The possible values for for x ≥ −6 are – 5, − 4, − 3, − 2, − 1 A – 5, − 4, − 3, − 2, − 1, 0 B C – 6, − 5, − 4, − 3, − 2, − 1 – 6, − 5, − 4, − 3, − 2, − 1, 0 D
1
x
is a positive integer y is an odd number y
2
The values for y ≤ 11 are A 9, 7, 5, 3, 1 11, 9, 7, 3, 1 B 11, 9, 7, 5, 3, 1 C D 11, 9, 7, 5, 3, 2, 1 p ≤ 15 ?
3
p is a prime number, which of the following set of integers satisfies If p A 11, 7, 5, 3, 2 13, 11, 9, 7, 5, 3 B 13, 11, 7, 5, 3, 2 C D 13, 11, 7, 5, 3, 2, 1
4
Which of the following number lines represents the inequality x < − 5? A
−8 −7 −6 −5 −4 −3 −2 −1
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− 8 − 7 − 6 −5 − 4 − 3 − 2 − 1
C
−8 −7 −6 −5 −4 −3 −2 −1
D
5
−8 −7 −6 −5 −4 −3 −2 −1 2 x + 7 > 19 3 Given that , find the smallest possible integer for x. 16 A B 17 18 C 19 D
6
Given the inequality 3 x > 7, find the smallest possible integer for x. 2 A 3 B – 2 C D −3
7
Solve 3 x − 2 ≥ x + 8.
8
A
x ≥ −5
B
x ≤ 5
C
x ≥
D
x ≤ −5
Solve 3( x + 5) ≤ 2(5 − x) .
A
9
5
x ≤ −1
5
B
x ≤
C
x ≤ −5
D
x ≤ 1
If x is an integer, find the values of x that satisfy the inequalities 3( x − 2) > 9 and 2 x − 9 < 5 .
A B C D
4 5 6 7
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10
The values 7, 8 and 9 are the values of x that satisfy which pairs of inequalities given below? x ≥ 7 and x < 10. A
C
7 and x > 7 and
x ≤ 10 .
D
x ≥
7 and
x ≤ 10 .
B
11
x >
x < 10.
4 x + 3 > 15 and 3 x + 1 < 19 are two inequalities where x is an integer. Find the solution for both inequalities. 4, 5 A 4, 5, 6 B 3, 4, 5 C 3, 4, 5, 6 D
2 12
x is an integer in the linear inequalities 3
x + 5 > 3
−
and
1 3
x + 4 >1
.
Solve them to find x.
13
14
A
3< x<9
B
−3<
x<9
C
−9 <
x<3
D
−9 <
x < −3
If
−5 ≤
2 x − 3 < 3 , therefore
A
−1 ≤
x<3
B
−2≤
x<3
C
−2≤
x<4
D
−
4 < x < −2
1 y Given that 1 < x < 10 , where x is an even number, and <
< 10
, where y is a
x
prime number, what is the largest value of y ?
8
A
3
7 B
2 9
C D
2 4
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15
If 3 x + 2 > 14 , where x is an odd number, and find the smallest value for 2 7 A 8 B C 9 10 D
x − y
16
17
18
−
2< y
<
2 , where y is an integer,
.
Solve 7 < 3t − 2 < 16 .
A
−6 <
t < −3
B
3 < t < 5
C
3 < t < 6
D
9 < t < 18
Which of the following is formed when –3 is added to both sides of the inequality −4 >
x+5?
A
−7 >
x+2
B
−7 >
x−9
C
7 > x−2
D
7 > x+2
Solve the simultaneous linear inequalities given below. x − 3 < 11 and 5 x − 3 > 17
A
2 < x < 12
B
4
C
4 < x < 14
D
5 < x < 15
19
Which of the following is a possible solution for 4 < 3 x − 8 < 7 ? 3.0 A B 3.5 4.0 C 4.5 D
20
Which of the following is a solution for the simultaneous linear equations
1 5 x − 3 ≤ 2 and 2
A
−1 <
x≤9
B
−9 <
x ≤1
C
−9 <
x≤5
(5 − x) < 7 ?
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D
5< x≤9
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Paper 2 This test paper contains 10 questions. Answer ALL the questions. The diagrams accompanying the questions are not drawn to scale unless mentioned. You are not allowed to use a calculator.
1
Diagram 1 is a number line.
− 11 − 10 − 9 − 8 − 7 − 6 − 5 − 4 DIAGRAM 1
Use the number line to represent the inequality
y ≤ −6.
2
Given the inequality 5 x < 9. Find the largest possible integer for x.
3
Solve 7 x − 3 ≥ 2(3 + 4 x).
4
Diagram 2 is a number line.
−3
4 DIAGRAM 2
Write the inequality that is represented by the number line.
5≤
2x + 3 3
≤
9.
5
Solve
6
Solve 2 ≤ 7 + 5 x ≤ 22 .
x
7
Solve 8 < 4 + 3 < 11.
28
− 2 x <
16
8
Given that 3
3 , where x is an integer, determine the smallest value of x.
9
Find the largest integer of x that satisfies the inequality 5 x – 7 < 23.
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2
10
Solve 5
x + 3 <
7 5
x.
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