Mathematics Grade 9 Page 2 Of 6 Vhembe East /I QUESTION 1 Four options are provided as possible answers to the following questions. correct option and write only the letter ( $$ A-D $$ ) next to the question numbe 1.11. D 1.1. Which of the following is a rational number? A $$ \pi $$ B $$ \sqrt{-1} $$ C $$ 1,2 \dot{3} $$ D $$ \sqrt{10} $$ 1.2. What is the LCM of 60 and 80 if their prime factors are $$ \begin{array}{l} 60=2 \times 2 \times 3 \times 5 \ 80=2 \times 2 \times 2 \times 2 \times 5 ? \end{array} $$ A $$ \quad 2 \times 2 \times 5 $$ B $$ \quad 2 \times 2 \times 3 $$ C $$ \quad 2 \times 2 \times 2 \times 2 \times 3 \times 5 $$ D $$ \quad 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5 $$ 1.3. Calculate: $$ -5-(-8)= $$ A -13 B $$ \quad-3 $$ C 13 D 3 1.4. Calculate: $$ 6+6 \div 2-6 \times(-2)= $$ A 21 B $$ \quad 18 $$ C 12 D 0 1.5. Calculate: $$ -(-3)^{2} \times-3= $$

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1.1. The options are:  
  $$ A: \pi $$ (irrational)  
  $$ B: \sqrt{-1} $$ (imaginary)  
  $$ C: 1.2\overline{3} $$ (a repeating decimal, hence rational)  
  $$ D: \sqrt{10} $$ (irrational)

Answer: **C**

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1.2. Prime factorizations:  
  $$ 60 = 2 \times 2 \times 3 \times 5 $$  
  $$ 80 = 2 \times 2 \times 2 \times 2 \times 5 $$

To get the LCM, take the highest powers of each prime:  
  For $$2$$: $$2^4$$ (from 80)  
  For $$3$$: $$3^1$$ (from 60)  
  For $$5$$: $$5^1$$ (from both)

Thus,  
$$
\text{LCM} = 2^4 \times 3 \times 5 = 16 \times 15 = 240.
$$

Option matching:  
  $$ C: 2 \times 2 \times 2 \times 2 \times 3 \times 5 $$.

Answer: **C**

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1.3. Calculate:  
$$
-5 - (-8) = -5 + 8 = 3.
$$

The option with $$3$$ is $$ D $$.

Answer: **D**

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1.4. Calculate using order of operations (PEMDAS/BODMAS):  
  Division: $$6 \div 2 = 3$$  
  Multiplication: $$6 \times (-2) = -12$$

Now substitute back:  
$$
6 + 3 - (-12) = 6 + 3 + 12 = 21.
$$

The option with $$21$$ is $$ A $$.

Answer: **A**

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1.5. Calculate:  
$$
-(-3)^2 \times -3
$$

Step 1: Compute the exponent. Note that the exponent applies only to $$-3$$ inside the parentheses:  
$$
(-3)^2 = 9.
$$

Step 2: Apply the preceding negative sign:  
$$
-(-3)^2 = -9.
$$

Step 3: Multiply by $$-3$$:  
$$
-9 \times (-3) = 27.
$$

Answer: $$27$$
1.1. **C** 1.2. **C** 1.3. **D** 1.4. **A** 1.5. **27**

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