GPTSICRADE I MATHEMATICS ASSIGNMENT QUESTION 1 11 Given $$ \sqrt{9+25} ; \pi-4 ; \sqrt[3]{-27} ; \frac{10}{2} ; \frac{2}{3} ; \sqrt{-27} $$ From the list given above, write down. 1.1.1 A natural number. (1) 1.12 A negative irrational number. 1.1.3 A non-real number. (1) (1) 1.2 Between which two consecutive integers does $$ \sqrt{138} $$ lie? (3) [6] QUESTION 2 2.1 Rewrite 92 and 146 as products of their prime factors. (2) 22 Use the prime factorization of 92 and 146 to find the following (2) 2.2.1 HCF 2.22 LCM 23 Use prime factors to determine whether 18 is a factor of 252 (4) 24 Divide 240 g in the ratio $$ 5: 3: 4 $$. (3) 25 Brooklyn earns R35 540 per month. She splits her earnings into the ratio 2.6 (3) and saves the smaller amount. How much of her eamings does she spend? 2.6 A municipality has budgeted R80 000 for putting up new street name boards. (3) The street name boards cost R134 each. How many new street name boards can be put up, and how much money will be left in the budget? 2.7 The price of petrol increased from R12,58 per lifre to R13.28 per litre. (2) Determine the percentage increase in price. 2.8 If Luke can consistently run 80 m in 16 s : 28.1 How long will it take him to run 400 m ? (2) 2.8.2 How far can Luke run in 1 minute and 4 seconds? 2.82 How far can Luke run in 1 minute and 4 car can travel 10 km on every litre of petrol. How much petrol will I need to 29 cill (2) (2) drive 400 km ?

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### QUESTION 1

**1.1 Given the list:**
- $$ \sqrt{9+25} $$
- $$ \pi-4 $$
- $$ \sqrt[3]{-27} $$
- $$ \frac{10}{2} $$
- $$ \frac{2}{3} $$
- $$ \sqrt{-27} $$

**1.1.1 A natural number:**
- $$ \frac{10}{2} = 5 $$ is a natural number.

**1.1.2 A negative irrational number:**
- $$ \pi - 4 $$ is a negative irrational number since $$ \pi $$ is approximately 3.14, making $$ \pi - 4 $$ approximately -0.86.

**1.1.3 A non-real number:**
- $$ \sqrt{-27} $$ is a non-real number because it involves the square root of a negative number.

**1.2 Between which two consecutive integers does $$ \sqrt{138} $$ lie?**
- First, we calculate $$ \sqrt{138} $$:
  - $$ 11^2 = 121 $$
  - $$ 12^2 = 144 $$
- Therefore, $$ \sqrt{138} $$ lies between 11 and 12.

### QUESTION 2

**2.1 Rewrite 92 and 146 as products of their prime factors:**
- $$ 92 = 2^2 \times 23 $$
- $$ 146 = 2 \times 73 $$

**2.2.1 HCF of 92 and 146:**
- The common prime factor is $$ 2 $$.
- Therefore, $$ \text{HCF} = 2 $$.

**2.2.2 LCM of 92 and 146:**
- The LCM can be calculated using the formula:
  $$
  \text{LCM} = \frac{a \times b}{\text{HCF}}
  $$
  where $$ a = 92 $$ and $$ b = 146 $$.
- Thus,
  $$
  \text{LCM} = \frac{92 \times 146}{2} = 6724
  $$

**2.3 Use prime factors to determine whether 18 is a factor of 252:**
- Prime factorization of 18: $$ 2 \times 3^2 $$
- Prime factorization of 252: $$ 2^2 \times 3^2 \times 7 $$
- Since all prime factors of 18 are present in 252, 18 is a factor of 252.

**2.4 Divide 240 g in the ratio $$ 5:3:4 $$:**
- Total parts = $$ 5 + 3 + 4 = 12 $$
- Each part = $$ \frac{240}{12} = 20 $$
- Therefore:
  - First part: $$ 5 \times 20 = 100 $$ g
  - Second part: $$ 3 \times 20 = 60 $$ g
  - Third part: $$ 4 \times 20 = 80 $$ g

**2.5 Brooklyn earns R35,540 per month. She splits her earnings into the ratio 2:6 and saves the smaller amount. How much of her earnings does she spend?**
- Total parts = $$ 2 + 6 = 8 $$
- Each part = $$ \frac{35,540}{8} = 4,442.50 $$
- Smaller amount (savings) = $$ 2 \times 4,442.50 = 8,885 $$
- Amount spent = $$ 35,540 - 8,885 = 26,655 $$

**2.6 A municipality has budgeted R80,000 for putting up new street name boards. The street name boards cost R134 each. How many new street name boards can be put up, and how much money will be left in the budget?**
- Number of boards = $$ \frac{80,000}{134} \approx 597 $$ (whole number)
- Total cost = $$ 597 \times 134 = 79,998 $$
- Money left = $$ 80,000 - 79,998 = 2 $$

**2.7 The price of petrol increased from R12.58 per litre to R13.28 per litre. Determine the percentage increase in price.**
- Increase = $$ 13.28 - 12.58 = 0.70 $$
- Percentage increase = $$ \frac{0.70}{12.58} \times 100 \approx 5.57\% $$

**2.8 If Luke can consistently run 80 m in 16 s:**
- **2.8.1 How long will it take him to run 400 m?**
  - Speed = $$ \frac{80}{16} = 5 $$ m/s
  - Time = $$ \frac{400}{5} = 80 $$ s

- **2.8.2 How far can Luke run in 1 minute and 4 seconds?**
  - 1 minute and 4 seconds = 64 seconds
  - Distance = Speed × Time = $$ 5 \times 64 = 320 $$ m

- **2.8.3 A car can travel 10 km on every litre of petrol. How much petrol will I need to drive 400 km?**
  - Petrol needed = $$ \frac{400}{10} = 40 $$ litres

This concludes the detailed solution to the assignment questions. If you have any further questions or need clarification on any part, feel free to ask!
**Simplified Answers:** 1. **Natural Number:** 5 2. **Negative Irrational Number:** $$ \pi - 4 $$ 3. **Non-Real Number:** $$ \sqrt{-27} $$ 4. **Range of $$ \sqrt{138} $$:** Between 11 and 12 **Question 2:** 1. **Prime Factors:** - 92: $$ 2^2 \times 23 $$ - 146: $$ 2 \times 73 $$ 2. **HCF:** 2 3. **LCM:** 6724 4. **18 is a factor of 252:** Yes 5. **Division in Ratio 5:3:4:** 100 g, 60 g, 80 g 6. **Brooklyn's Spending:** R26,655 7. **Street Name Boards:** - Number of Boards: 597 - Money Left: R2 8. **Petrol Price Increase:** Approximately 5.57% 9. **Luke's Running Times:** - 400 m: 80 seconds - 1 minute and 4 seconds: 320 meters - 400 km: 40 liters of petrol **Note:** All calculations are based on the given data and standard mathematical principles.

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