Question 1
Consider the following inequalities.
1(a):
Which value for x will satisfy the following inequality?
6>x\geq -5ANSWER: Multiple Choice (Type 1)
A: x=-10
B: x=-1
C: x=6
D: x=10
Answer: B
Workings:
-1 is the only value that falls between 6 & -5
Marks = 1
1(b):
Which inequality is satisfied by x=3?
ANSWER: Multiple Choice (Type 1)
A: x≤-3
B: x>-2
C: 3>x>-9
D: x>3
Answer: B
Workings:
x>-2 is the only inequality that is true for x=3.
Marks = 1
1(c):
Which inequality is equivalent to the following?
6x -3<2x+9ANSWER: Multiple Choice (Type 1)
A: x<\dfrac{6}{8}
B: x>3
C: x<3
D: x>\dfrac{6}{8}
Answer: C
Workings:
4x < 12\\ x < 3Marks = 1
Question 2
Consider the following inequalities.
2(a):
Give the inequality described on the number line below.
ANSWER: Multiple Choice (Type 1)
A: x< -6
B: x\leq -5
C: x\geq -5
D: x> -5
Answer: C
Workings:
All values above and including -5 are included in the number line.
Marks = 2
2(b):
Give the inequality described on the number line below.
ANSWER: Multiple Choice (Type 1)
A: x>7
B: x<7
C: x\leq 7
D: x<8
Answer: B
Workings:
All numbers less than but NOT including 7 are included in the number line.
Marks = 2
2(c):
Give the inequality described on the number line below.
ANSWER: Multiple Choice (Type 1)
A: x\leq -1
B: x\leq 0
C: x< -1
D: x> -1
Answer: A
Workings:
All numbers less than and including -1 are included in the number line.
Marks = 2
Question 3
Consider the following inequalities.
3(a):
Give the inequality described on the number line below.
ANSWER: Multiple Choice (Type 1)
A: -6< x< 6
B: -6\leq x\leq 8
C: -6< x< 8
D: -6\leq x\leq 6
Answer: D
Workings:
All numbers between and including -6 and 6 are included on the number line.
Marks = 2
3(b):
Give the inequality described on the number line below.
ANSWER: Multiple Choice (Type 1)
A: -1\leq x<7
B: -1< x<7
C: -1\leq x\leq 7
D: -1< x\leq 7
Answer: A
Workings:
All numbers above and including -1 and less than but not including 7 are included on the number line.
Marks = 2
3(c):
Give the inequality described on the number line below.
ANSWER: Multiple Choice (Type 1)
A: -4\leq x\leq 4
B: -4<x<4
C: -4<x\leq 4
D: -4\leq x<4
Answer: B
Workings:
All numbers between but not including -4 and 4 are included on the number line.
Marks = 2
Question 4
Consider the following inequalities.
4(a):
Which number line describes the following inequality:
x<4ANSWER: Multiple Choice (Type 1)
A:
B:
C:
D:
Answer: A
Workings:
The correct number line is pointing infinitely left and has a white circle at point 4 as we have a < symbol so 4 is not included.
Marks = 2
4(b):
Which number line describes the following inequality:
x\geq -1ANSWER: Multiple Choice (Type 1)
A:
B:
C:
D:
Answer: D
Workings:
Because we have a \geq symbol following x, the arrow should be pointing infinitely right and start with a solid circle on the -1 mark.
Marks = 2
4(c):
Which number line describes the following inequality:
-2\leq x\leq 8ANSWER: Multiple Choice (Type 1)
A:
B:
C:
D:
Answer: C
Workings:
There are two \leq symbols, so a number line between -2 and 8 with a solid circle at each end is required.
Marks = 2
Question 5
Which number line displays the following inequality:
-0.7 < x \leq -0.1ANSWER: Multiple Choice (Type 1)
A:
B:
C:
D:
Answer: D
Workings:
There is a \lt symbol followed by a \leq symbol, so a line between -0.7 and -0.1 is required with an empty circle at the left hand end and a solid circle at the right hand end. A suitable scale that covers both -0.7 and -0.1 is required. An increment of 0.1 is recommended for this question.
Marks = 2
Question 6
In order to be profitable, a bus company requires a certain number of passengers for each tour; however, the bus can only hold so many seated passengers.
6(a):
Write an inequality for a bus, b, if the company requires more than 6 passengers to be profitable but can only hold 54 passengers.
ANSWER: Multiple Choice Answer
A: 6 \leq b \leq 54
B: 6 < b \leq 54
C: 6 < b < 54
D: 6 \leq b < 54
Answer: B
Workings:
Because there must be more than 6 people we have b>6.
Because the maximum number of people is 54 we have b\leq 54.
Combing these gives the final inequality: 6 < b \leq 54.
Marks = 3
6(b):
Which number line displays the inequality?
ANSWER: Multiple Choice (Type 1)
A:
B:
C:
D:
Answer: B
Workings:
Because there is both a < symbol and a \leq symbol there should be a line between points 6 and 54 with an empty circle on the left hand end and a solid circle on the right hand end.
Marks = 2