Question 1:
Consider the numbers below
\pi \,, \sqrt{144} \,, \sqrt{81} \,, 0 \,, \sqrt{-2} \,, \sqrt{1000}
Question 1(a): [1 mark]
Select the numbers which are rational.
Answer type: Multiple choice type 1
A: \pi
B: \sqrt{144}
C: \sqrt{81}
D: 0
E: \sqrt{-2}
F: \sqrt{1000}
ANSWER: B:\sqrt{144} = 12, C:\sqrt{81} = 9, D: 0
Question 1(b): [1 mark]
Select the numbers which are irrational.
Answer type: Multiple choice type 1
A: \pi
B: \sqrt{144}
C: \sqrt{81}
D: 0
E: \sqrt{-2}
F: \sqrt{1000}
ANSWER: A: \pi, F: \sqrt{1000}
Question 2(a): [1 mark]
\sqrt{m} is an integer.
Given that the value of ? lies between between 29 and 39, write down the value of ?.
Answer type: Simple text answer
ANSWER: 36
Question 2(b): [1 mark]
Which of the following are irrational numbers between 1 and 2?
Answer type: Multiple choice type 1
A: \sqrt{2}
B: \sqrt{3}
C: \sqrt{5.25}
D: \sqrt{4}
ANSWER: A: \sqrt{2}, B: \sqrt{3}
WORKING: \sqrt{4} = 2 , which does not lie between 1 and 2. \sqrt{5.25} > 2
Question 3:
Consider the expressions below.
2\sqrt{4} \,, - \dfrac{2}{5}\,, \sqrt{7} \,, \sqrt{7}
Question 3(a): [1 mark]
Which one of these expressions is an integer?
Answer type: Multiple choice type 1
A: 2\sqrt{4}
B: - \dfrac{2}{5}
C: \sqrt{7}
D: \sqrt{7}
ANSWER: A: 2\sqrt{4}
WORKING: 2\sqrt{4} = \sqrt{4 \times 4} = \sqrt{16} = 4
Question 3(b): [1 mark]
Two of the expressions shown above are multiplied together to produce an integer. Choose which two expressions.
Answer type: Multiple choice type 1
A: 2\sqrt{4}
B: - \dfrac{2}{5}
C: \sqrt{7}
D: \sqrt{7}
ANSWER: C: \sqrt{7}, D: \sqrt{7}
WORKING: \sqrt{7} \times \sqrt{7} = 7
Question 4(a): [1 mark]
Consider the equation below
x^2 + 3y = 10
Which of the following solutions for x and y give a rational solution.
Answer type: Multiple choice type 1
A: x = \pm 3, y = \dfrac{1}{3}
B: x = \pm 2, y = 1
C: x = \pm 2, y = 2
D: x = \pm 1, y = 2
ANSWER: A:x = \pm 1, y = 3, C: x = \pm 2, y = 2
Question 4(b): [1 mark]
The following equation has no integer solutions:
6x + 3y = 5
Which of the following solutions for x and y give a rational solution.
Answer type: Multiple choice type 1
A: x = 1, y = - \dfrac{1}{3}
B: x = 0, y = \dfrac{3}{2}
C: x = 2, y = -\dfrac{1}{4}
D: x = 0, y = \dfrac{5}{3}
ANSWER: A: x = 1, y = - \dfrac{1}{3}, D: x = 0, y = \dfrac{5}{3}
Question 5:
Consider the triangle below. The perimeter of the triangle is 13.6 cm.
Question 5(a): [1 mark]
What is the value of x?
Answer type: simple text answer
ANSWER: 6.1 cm
WORKING: 13.6 - 4.5 - 3 = x = 6.1
Question 5(b): [1 mark]
Is x an integer?
Answer type : Multiple choice type 1
A: Yes
B: No
ANSWER: B: No
Question 5(c): [1 mark]
Is x rational or irrational?
Answer type : Multiple choice type 1
A: Rational
B: Irrational
ANSWER: A: Rational
WORKING: An irrational number is a real number that cannot be written as a simple fraction. x can be written as a fraction, so x is rational.
Question 6(a):
Consider the statements below.
Which of the following are never true?
Answer type: Multiple choice type 2
A: Rational + Irrational = Rational
B: Integer + Rational = Rational
C: Rational × Rational = Integer
D: Irrational × Rational = Rational
E: Irrational + Irrational = Rational
ANSWER: A: Rational + Irrational = Rational
WORKING: Rational + Irrational = Irrational
Question 6(b):
Which of the following are only sometimes true?
Answer type: Multiple choice type 2
A: Rational + Irrational = Rational
B: Integer + Rational = Rational
C: Rational × Rational = Integer
D: Irrational × Rational = Rational
E: Irrational + Irrational = Rational
ANSWER:
D: Irrational × Rational = Rational, E: Irrational + Irrational = Rational
WORKING: D: e.g. \sqrt{2} \, \times\, 0 = 0
E: e.g. \sqrt{2} \, + \, (1 - \sqrt{2}) = 1