Mathematics Grade 9 March Test 75 marks 13/hour Question-1 1 Calculate the following without the use of a calculator. Show all steps! $$ 1.1 \quad 18-10+4-6 $$ $$ 1.2-24-(-18) $$ (2) $$ 1.38 \times(-3)+(-6) $$ $$ 1.4 \quad-4^{2}+(-4)^{3} $$ 15 $$ 1.5 \sqrt{169}-\sqrt[3]{-0,064} $$ $$ 1.6 \sqrt{1 \frac{9}{16}} \times 1 \frac{2}{3}+9,3 $$ [15] Question 2 2.1 Simplify the following and give your answers as positive exponents. 2.1.1 $$ -4\left(x^{3}\right)^{0} $$ 2.1.2 $$ \left(-4 x^{3}\right)^{0} $$ 2.1.3 $$ \quad 3^{-1} a^{2} b^{-5} $$ 2.1.4 $$ \left(-2 y^{2}\right)(-2 y)^{-2} $$ $$ 2.1 .3-{ }^{2}-8 $$ $$ 2.1 .5 \frac{x^{4} y^{3}}{x^{5} y^{3}} $$ 2.2 Calculate the following without the use of a calculator. Show all your work. (3) $$ 4^{-2} \times 6^{2} \times 3^{-2} $$

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### Question 1

#### 1.1 Calculate $$ 18 - 10 + 4 - 6 $$

1. Start with $$ 18 - 10 $$:
   $$
   18 - 10 = 8
   $$
2. Now add $$ 4 $$:
   $$
   8 + 4 = 12
   $$
3. Finally, subtract $$ 6 $$:
   $$
   12 - 6 = 6
   $$

**Answer:** $$ 6 $$

---

#### 1.2 Calculate $$ -24 - (-18) $$

1. Rewrite the expression:
   $$
   -24 + 18
   $$
2. Now perform the addition:
   $$
   -24 + 18 = -6
   $$

**Answer:** $$ -6 $$

---

#### 1.3 Calculate $$ 3 \times (-3) + (-6) $$

1. Start with $$ 3 \times (-3) $$:
   $$
   3 \times (-3) = -9
   $$
2. Now add $$ -6 $$:
   $$
   -9 + (-6) = -15
   $$

**Answer:** $$ -15 $$

---

#### 1.4 Calculate $$ -4^{2} + (-4)^{3} $$

1. Calculate $$ -4^{2} $$:
   $$
   -4^{2} = -16
   $$
2. Calculate $$ (-4)^{3} $$:
   $$
   (-4)^{3} = -64
   $$
3. Now add the two results:
   $$
   -16 + (-64) = -80
   $$

**Answer:** $$ -80 $$

---

#### 1.5 Calculate $$ \sqrt{169} - \sqrt[3]{-0.064} $$

1. Calculate $$ \sqrt{169} $$:
   $$
   \sqrt{169} = 13
   $$
2. Calculate $$ \sqrt[3]{-0.064} $$:
   $$
   \sqrt[3]{-0.064} = -0.4
   $$
3. Now perform the subtraction:
   $$
   13 - (-0.4) = 13 + 0.4 = 13.4
   $$

**Answer:** $$ 13.4 $$

---

#### 1.6 Calculate $$ \sqrt{1 \frac{9}{16}} \times 1 \frac{2}{3} + 9.3 $$

1. Convert $$ 1 \frac{9}{16} $$ to an improper fraction:
   $$
   1 \frac{9}{16} = \frac{16 + 9}{16} = \frac{25}{16}
   $$
2. Calculate $$ \sqrt{\frac{25}{16}} $$:
   $$
   \sqrt{\frac{25}{16}} = \frac{5}{4}
   $$
3. Convert $$ 1 \frac{2}{3} $$ to an improper fraction:
   $$
   1 \frac{2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
   $$
4. Now multiply:
   $$
   \frac{5}{4} \times \frac{5}{3} = \frac{25}{12}
   $$
5. Convert $$ 9.3 $$ to a fraction:
   $$
   9.3 = \frac{93}{10}
   $$
6. Now add $$ \frac{25}{12} + \frac{93}{10} $$:
   - Find a common denominator (60):
   $$
   \frac{25}{12} = \frac{25 \times 5}{12 \times 5} = \frac{125}{60}
   $$
   $$
   \frac{93}{10} = \frac{93 \times 6}{10 \times 6} = \frac{558}{60}
   $$
   - Now add:
   $$
   \frac{125}{60} + \frac{558}{60} = \frac{683}{60}
   $$

**Answer:** $$ \frac{683}{60} $$ or approximately $$ 11.38 $$

---

### Question 2

#### 2.1 Simplify the following and give your answers as positive exponents.

##### 2.1.1 Calculate $$ -4(x^{3})^{0} $$

1. Since $$ (x^{3})^{0} = 1 $$:
   $$
   -4 \times 1 = -4
   $$

**Answer:** $$ -4 $$

---

##### 2.1.2 Calculate $$ (-4 x^{3})^{0} $$

1. Since $$ (-4 x^{3})^{0} = 1 $$:
   $$
   1
   $$

**Answer:** $$ 1 $$

---

##### 2.1.3 Calculate $$ 3^{-1} a^{2} b^{-5} $$

1. Rewrite with positive exponents:
   $$
   \frac{a^{2}}{3 b^{5}}
   $$

**Answer:** $$ \frac{a^{2}}{3 b^{5}} $$

---

##### 2.1.4 Calculate $$ (-2 y^{2})(-2 y)^{-2} $$

1. Calculate $$ (-2 y)^{-2} $$:
   $$
   (-2 y)^{-2} = \frac{1}{(-2 y)^{2}} = \frac{1}{4 y^{2}}
   $$
2. Now multiply:
   $$
   (-2 y^{2}) \times \frac{1}{4 y^{2}} = \frac{-2 y^{2}}{4 y^{2}} = \frac{-2}{4} = -\frac{1}{2}
   $$

**Answer:** $$ -\frac{1}{2} $$

---

##### 2.1.5 Calculate $$ \frac{x^{4} y^{3}}{x^{5} y^{3}} $$

1. Simplify:
   $$
   \frac{x^{4}}{x^{5}} = x^{4-5} = x^{-1}
   $$
   $$
   \frac{y^{3}}{y^{3}} = 1
   $$
2. Therefore:
   $$
   x^{-1} = \frac{1}{x}
   $$

**Answer:** $$ \frac{1}{x} $$

---

#### 2.2 Calculate $$ 4^{-2} \times 6^{2} \times 3^{-2} $$

1. Calculate each term:
   \[
   4^{-2} = \frac{1}{16}, \quad 6^{2} = 36, \quad 
**Question 1:** 1. **1.1** $$ 18 - 10 + 4 - 6 = 6 $$ 2. **1.2** $$ -24 - (-18) = -6 $$ 3. **1.3** $$ 3 \times (-3) + (-6) = -15 $$ 4. **1.4** $$ -4^{2} + (-4)^{3} = -80 $$ 5. **1.5** $$ \sqrt{169} - \sqrt[3]{-0.064} = 13.4 $$ 6. **1.6** $$ \sqrt{1 \frac{9}{16}} \times 1 \frac{2}{3} + 9.3 = \frac{683}{60} \approx 11.38 $$ **Question 2:** 1. **2.1.1** $$ -4(x^{3})^{0} = -4 $$ 2. **2.1.2** $$ (-4 x^{3})^{0} = 1 $$ 3. **2.1.3** $$ 3^{-1} a^{2} b^{-5} = \frac{a^{2}}{3 b^{5}} $$ 4. **2.1.4** $$ (-2 y^{2})(-2 y)^{-2} = -\frac{1}{2} $$ 5. **2.1.5** $$ \frac{x^{4} y^{3}}{x^{5} y^{3}} = \frac{1}{x} $$ 6. **2.2** $$ 4^{-2} \times 6^{2} \times 3^{-2} = \frac{1}{16} \times 36 \times \frac{1}{9} = \frac{36}{144} = \frac{1}{4} $$

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