1.1 Calculate the following without using a calculator. 1.1.1 Calculate $180 + 20 \times (-5)$. Step 1: Use the order of operations (multiplication before addition). Step 2: Calculate $20 \times (-5) = -100$. Step 3: Add $180 + (-100) = 80$. Answer: $80$. 1.1.2 Calculate $\frac{1}{2} (3.5 + 6.5) + \frac{1}{10} (3)$. Step 1: Add inside the parentheses: $3.5 + 6.5 = 10$. Step 2: Calculate $\frac{1}{2} \times 10 = 5$. Step 3: Calculate $\frac{1}{10} \times 3 = 0.3$. Step 4: Add $5 + 0.3 = 5.3$. Answer: $5.3$. 1.1.3 Calculate $\sqrt{16} + 3^3$. Step 1: Calculate $\sqrt{16} = 4$. Step 2: Calculate $3^3 = 27$. Step 3: Add $4 + 27 = 31$. Answer: $31$. 1.2 Rearrange the times from early morning to late at night: 13:15; 2:30 pm; 4:15 am; 01:15. Step 1: Convert all times to 24-hour format. - 13:15 is 13:15. - 2:30 pm is 14:30. - 4:15 am is 04:15. - 01:15 is 01:15. Step 2: Order from earliest to latest: 01:15, 04:15, 13:15, 14:30. Answer: 01:15; 4:15 am; 13:15; 2:30 pm. 1.3 Calculate total amount paid including 11% tip on R279. Step 1: Calculate tip: $11\%$ of $279 = 0.11 \times 279 = 30.69$. Step 2: Total amount = $279 + 30.69 = 309.69$. Answer: $309.69$. 1.4 Bleach powder and peroxide ratio 1:3, total mixture 175 ml. Step 1: Total parts = $1 + 3 = 4$. Step 2: Amount of peroxide = $\frac{3}{4} \times 175 = 131.25$ ml. Answer: $131.25$ ml. 1.5 Map scale 1:50 000, map distance 4 cm. Step 1: Actual distance in cm = $4 \times 50,000 = 200,000$ cm. Step 2: Convert to km: $\frac{200,000}{100,000} = 2$ km. Answer: $2$ km. 1.6 Convert 132 minutes to hours and minutes. Step 1: $132 \div 60 = 2$ hours remainder $12$ minutes. Answer: 2 hours 12 minutes. 1.7 Sipho earns 25.75 per hour, wants to buy bicycle for 1750. Step 1: Hours needed = $\frac{1750}{25.75} \approx 67.96$. Step 2: Full hours = $68$ hours. Answer: $68$ hours. 1.8 Spanners cost 255 after 15% discount. Step 1: Let original price be $P$. Step 2: $P - 0.15P = 255 \Rightarrow 0.85P = 255$. Step 3: $P = \frac{255}{0.85} = 300$. Answer: $300$. 1.9 Petrol consumption: 394 km with 33.5 L. Step 1: Consumption = $\frac{394}{33.5} \approx 11.76$ km/L. Step 2: Round to 1 decimal place: $11.8$ km/L. Answer: $11.8$ km/L. 1.10 Length of wooden block from 3 cm to 10 cm on ruler. Step 1: Length = $10 - 3 = 7$ cm. Answer: $7$ cm. 2.1 Match terms: 2.1.1 Cube - D 2.1.2 Area - A 2.1.3 Scale - E 2.1.4 Co-ordinates - B 2.2 Boardroom table questions: 2.2.1 Length CE = length EF = 7 m (rectangle length). Answer: $7$ m. 2.2.2 Circumference of semicircle CDE: Formula: $\pi r + 2r$ for semicircle perimeter including diameter. Step 1: $\pi r = 3.14 \times 1.5 = 4.71$ m. Step 2: Diameter $= 2 \times 1.5 = 3$ m. Step 3: Circumference = $4.71 + 3 = 7.71$ m. Answer: $7.71$ m. 2.2.3 Length of wood tape to trim entire edge: Step 1: Perimeter = rectangle sides + semicircle arcs. Step 2: Rectangle sides: $2 \times 7 = 14$ m (length sides), plus $2 \times 3 = 6$ m (width sides including semicircle diameters). Step 3: Total perimeter = $14 + 6 = 20$ m. Step 4: Add semicircle arcs: $2 \times (\pi r / 2) = 2 \times 4.71 = 9.42$ m. Step 5: Total tape length = $14 + 9.42 = 23.42$ m. Answer: $23.42$ m. 2.2.4 Rolls needed: Step 1: Rolls = $\lceil \frac{23.42}{10} \rceil = 3$ rolls. Answer: $3$ rolls. 2.2.5 Total surface area: Step 1: Area rectangle = $7 \times 3 = 21$ m$^2$. Step 2: Area semicircles = $2 \times \frac{1}{2} \pi r^2 = \pi r^2 = 3.14 \times 1.5^2 = 7.07$ m$^2$. Step 3: Total area = $21 + 7.07 = 28.07$ m$^2$. Answer: $28.07$ m$^2$. 2.2.6 Chairs accommodated: Step 1: Table length in mm = $7 \times 1000 = 7000$ mm. Step 2: Chairs = $\frac{7000}{1500} = 4.66$. Step 3: Only full chairs fit, so 4 chairs. Answer: $4$ chairs. 3.1 Bank questions: 3.1.1 Minimum amount to open account: R40. Answer: 40. 3.1.2 (a) Cheque deposit charge: Free. Answer: 0. 3.1.2 (b) Cash deposit R800: Step 1: Up to 500: R1.05. Step 2: Above 500: R1.25 per 100 or part thereof for R300. Step 3: $\frac{300}{100} = 3$ parts. Step 4: Additional charge = $3 \times 1.25 = 3.75$. Step 5: Total charge = $1.05 + 3.75 = 4.80$. Answer: 4.80. 3.1.3 Withdraw R600: ATM charge: 14.70. Branch charge: 11.50 + $1 \times \lceil \frac{600}{100} \rceil = 11.50 + 6 = 17.50$. Cheaper: ATM. Answer: ATM is cheaper. 3.2 Invoice: 3.2.1 Calculate A and B. A: Quantity of nails. $89 \times A = 445 \Rightarrow A = \frac{445}{89} = 5$. B: Amount for wood tape. $62 \times 55 = 3410$. Answer: A=5, B=3410. 3.2.2 VAT amount C: $C = 0.14 \times 18369 = 2571.66$. Answer: 2571.66. 3.2.3 Total including VAT D: $D = 18369 + 2571.66 = 20940.66$. Answer: 20940.66. 3.3 Salaries: 3.3.1 Ratio 3:2, total 18000. Step 1: Total parts = 3 + 2 = 5. Step 2: Nandi = $\frac{3}{5} \times 18000 = 10800$. Step 3: Sipho = $\frac{2}{5} \times 18000 = 7200$. Answer: Nandi=10800, Sipho=7200. 3.3.2 (a) Sipho new salary 7704 after 7% increase. Step 1: Old salary = $\frac{7704}{1.07} = 7200$. Step 2: Nandi new salary = $10800 \times 1.07 = 11556$. Answer: 11556. 3.3.2 (b) Sipho UIF 1% per annum: $7704 \times 0.01 = 77.04$. Answer: 77.04. 4.1 Line graph questions: 4.1.1 3 artisans produce $1 + 3 \times 3 = 10$ tables. Answer: 10. 4.1.2 To produce 1 table, additional artisans = 0. Answer: 0. 4.1.3 To produce 11 tables: $11 = 1 + 3x \Rightarrow x = \frac{10}{3} \approx 3.33$ artisans. Since artisans must be whole, 4 artisans. Answer: 4. 4.1.4 Relationship is increasing because number of tables increases as artisans increase. Answer: Increasing relationship. 4.1.5 Pattern 1,4,7,10,... has common difference $4-1=3$. Answer: Constant difference pattern with difference 3. 4.1.6 (a) For 7 artisans: $1 + 3 \times 7 = 22$ tables. Answer: 22. (b) For 25 tables: $25 = 1 + 3x \Rightarrow x = 8$ artisans. Answer: 8 artisans. 4.2 Renting table and chairs: 4.2.1 Cost for 3 days: Day 1: 1000 + 1500 = 2500 Day 2: 1000 + 2*1500 = 4000 Day 3: 1000 + 3*1500 = 5500 Answer: 5500. 4.2.2 Formula: Cost = 1000 + 1500 * (number of days). Answer: $C = 1000 + 1500d$. 5.1 Furniture renting and purchasing: 5.1.1 Month purchasing less than renting: January (1 < 3). Answer: January. 5.1.2 Best months: May and June (highest totals). Answer: May and June. 5.1.3 Total renting customers: $3+4+6+3+3+7=26$. Answer: 26. 5.1.4 Mode of purchasing: Purchasing data: 1,4,7,4,7,8 Modes: 4 and 7 (both appear twice). Answer: 4 and 7. 5.1.5 Median renting: Sorted renting: 3,3,3,4,6,7 Median = average of 3rd and 4th values = $\frac{3+4}{2} = 3.5$. Answer: 3.5. 5.1.6 Range purchasing: Max 8, min 1, range = 7. Answer: 7. 5.1.7 Mean renting: Mean = $\frac{26}{6} \approx 4.33$. Answer: 4.33. 5.2 Budget expenditure: 5.2.1 Total budget: $216.7 + 31.6 + 21.1 + 15.8 + 15.3 + 7.4 = 307.9$ billion. Answer: 307.9. 5.2.2 Smallest budget: Technical and Vocational Education and Training (7.4). Answer: Technical and Vocational Education and Training. 5.2.3 Highest budget: Basic Education (216.7). Reasons: It covers the largest number of students and foundational education. Answer: Basic Education; covers most students; foundational importance. 5.2.4 (a) Two DHET departments: University Subsidies, National Student Financial Aid Scheme. Answer: University Subsidies, National Student Financial Aid Scheme. (b) Total DHET budget: $31.6 + 15.3 + 21.1 = 68$ billion. Answer: 68. (c) Percentage DHET budget: $\frac{68}{307.9} \times 100 \approx 22.08\%$. Answer: 22.08%.