💥 Q 08 Prep 2 Question Bank T1

a) Write each of the following sets as an interval and represent it on the number line:

1. A = \{X : X ∈ ℝ, 1 < X ≤ 3\}, is \( \sqrt{2} \) ∈ A?

A = ]1, 3]

∵ \( \sqrt{2} = 1.4 \)

∴ yes \( \sqrt{2} \in A \)

2. B = \{X : X ∈ ℝ, -2 < X < 2\}, is \( \sqrt[3]{-9} \) ∈ B?

B = ]-2, 2[

∵ \( \sqrt[3]{-9} \approx -2.08 \)

∴ no \( \sqrt[3]{-9} \notin B \)

3. \{X : X ∈ ℝ, X ≥ -2\}

[-2, ∞[

4. \{X : X ∈ ℝ, X < 1\}

]-∞, 1[

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💥 Q 07 Prep 2 Question Bank T1

a) Find the solution set for each of the following equations in Q and R:

1. \( \frac{3}{4}x^2 = \frac{9}{2} \)

∵ \( \frac{3}{4}x^2 = \frac{9}{2} \)

∴ \( x^2 = \frac{9}{2} \times \frac{4}{3} = 6 \)

∴ \( x = \pm \sqrt{6} \)

∴ The solution set in \( \mathbb{Q} = \left\{ -\sqrt{6}, \sqrt{6} \right\} \)

∴ The solution set in \( \mathbb{R} = \left\{ -\sqrt{6}, \sqrt{6} \right\} \)

2. \( 2(x^2 - 1) = -10 \)

∵ \( 2(x^2 - 1) = -10 \)

∴ \( x^2 - 1 = -10 \div 2 = -5 \)

∴ \( x^2 = -5 + 1 = -4 \)

∴ \( x = \pm \sqrt{-4} \)

∴ The solution set in \( \mathbb{Q} = \emptyset \)

∴ The solution set in \( \mathbb{R} = \emptyset \)

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💥 Q 06 Prep 2 Question Bank T1

a) Find the solution set for each of the following equations in \( \mathbb{Q} \):

1. \( 2x^2 - 3 = 9 \)

∵ \( 2x^2 - 3 = 9 \)

∴ \( 2x^2 = 9 + 3 = 12 \)

∴ \( x^2 = 12 ÷ 2 = 6 \)

∴ \( x = \pm \sqrt{6} \)

∴ The solution set = \( \left\{ -\sqrt{6}, \sqrt{6} \right\} \)

2. \( 6x^2 - 3 = 4x^2 + 7 \)

∵ \( 6x^2 - 3 = 4x^2 + 7 \)

∴ \( 6x^2 - 4x^2 = 7 + 3 \)

∴ \( 2x^2 = 10 \)

∴ \( x^2 = 10 ÷ 2 = 5 \)

∴ \( x = \pm \sqrt{5} \)

∴ The solution set = \( \left\{ -\sqrt{5}, \sqrt{5} \right\} \)

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💥 Q 05 Prep 2 Question Bank T1

a) Find the solution set for each of the following equations in \( \mathbb{R} \):

4. \( 3x^2 - 1 = -13 \)

∵ \( 3x^2 - 1 = -13 \)

∴ \( 3x^2 = -13 + 1 = -12 \)

∴ \( x^2 = -12 ÷ 3 = -4 \)

∴ \( x = \pm \sqrt{-4} \notin \mathbb{R} \)

∴ The solution set = \( \emptyset \)

5. \( 5x^3 - 1 = 4x^3 + 8 \)

∵ \( 5x^3 - 1 = 4x^3 + 8 \)

∴ \( 5x^3 - 4x^3 = 8 + 1 \)

∴ \( x^3 = 9 \)

∴ \( x = \sqrt[3]{9} \)

∴ The solution set = \( \{\sqrt[3]{9}\} \)

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💥 Q 04 Prep 2 Question Bank T1

a) Find the solution set for each of the following equations in \( \mathbb{R} \):

1. \( x^3 - 11 = 5 \)

∵ \( x^3 - 11 = 5 \)

∴ \( x^3 = 5 + 11 = 16 \) ∴ \( x = \sqrt[3]{16} \)

∴ The solution set = \( \left\{ \sqrt[3]{16} \right\} \)

2. \( 2x^3 + 13 = 67 \)

∵ \( 2x^3 + 13 = 67 \)

∴ \( 2x^3 = 67 - 13 = 54 \)

∴ \( x^3 = 54 ÷ 2 = 27 \) ∴ \( x = \sqrt[3]{27} = 3 \)

∴ The solution set = \( \left\{ 3 \right\} \)

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💥 Q 03 Prep 2 Question Bank T1

Mathematics Questions

a) Put the appropriate symbol \( \in \) or \( \notin \) in the empty box:

1	\(\overline{0.36}\)	□	\( \mathbb{Q'} \)
2	\( \sqrt{5} \)	□	\( \mathbb{Q} \)
3	\( |-4| \)	□	\( \mathbb{Z} \)
4	\( \sqrt[3]{3\frac{3}{8}} \)	□	\( \mathbb{Q} \)
5	\( \sqrt[3]{3} \)	□	\( \mathbb{Q} \)
6	\( \sqrt{-1} \)	□	\( \mathbb{R} \)

1	\(\overline{0.36}\)	\( \notin \)	\( \mathbb{Q}' \)
2	\( \sqrt{5} \)	\( \notin \)	\( \mathbb{Q} \)
3	\( |-4| \)	\( \in \)	\( \mathbb{Z} \)
4	\( \sqrt[3]{3\frac{3}{8}} \)	\( \in \)	\( \mathbb{Q} \)
5	\( \sqrt[3]{3} \)	\( \notin \)	\( \mathbb{Q} \)
6	\( \sqrt{-1} \)	\( \notin \)	\( \mathbb{R} \)

😊 TRUE: The correct answers are shown in the table above.

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💥 Q 02 Prep 2 Question Bank T1

Mathematics Questions

a) If \( x \in \mathbb{Z} \), \( x < \sqrt{29} < x + 1 \), what is the value of \( x \)?

(a) 4

(b) 5

(c) 6

(d) 7

😊 TRUE: The correct answer is (b) 5. Since \( \sqrt{25} = 5 \) and \( \sqrt{36} = 6 \), we have \( 5 < \sqrt{29} < 6 \), so \( x = 5 \).

😞 FALSE: Please try again.

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b) Estimating \( \sqrt[3]{25} \) to the closest integer is ……….

(a) 2

(b) 3

(c) 5

(d) 12.5

😊 TRUE: The correct answer is (c) 5. Since \( 2^3 = 8 \) and \( 3^3 = 27 \), \( \sqrt[3]{25} \) is closer to 3 than to 2.

😞 FALSE: Please try again.

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c) Which of the following numbers is an irrational number that lies between 2 and 3?

(a) \( 2.5 \)

(b) \( \sqrt[4]{10} \)

(c) \( \sqrt[3]{6.25} \)

(d) \( \sqrt[3]{\frac{9}{9}} \)

😊 TRUE: The correct answer is (b) \( \sqrt[4]{10} \). Since \( 2^4 = 16 \) and \( \sqrt[4]{10} \) is approximately 1.78, which is between 2 and 3.

😞 FALSE: Please try again.

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