INSTRUCTION AND INFORMATION 1. Answer All the questions 2. Read ALL questions carefully 3 Number the answers according to the numbering system used in this question paper 4. Clearly show AlL calculations, diagram, graphs etc. 5. Round off the answers to TWO decimal places, unless otherwise stated 6. Use \( \pi=3.14 \) 7. Write neatly and legibly QUESTION 1 1.1 Caleulate the following without using a calculator. Show ALL steps used in calculating the answer. Leave the answer as a mixed fraction. No marks will be awarded for the final answer only. HINT:BODMAS \( 1.1 .14 \frac{3}{4}+1 \frac{1}{12}-2 \frac{5}{6}=3+\frac{1}{12}-\frac{5}{3} \) \[ =\frac{17}{12} \] \( 1.1 .22^{3}+\frac{3}{\sqrt[3]{5^{2}+2}} \) \[ 2^{3}+\frac{3}{\sqrt[3]{5^{2}+2}}=8+\frac{3}{3} \] 1.2 Rearrange the following fractions in ascending order: \[ \begin{array}{l} \text { Rearrange the following fractions in ascending order: } \\ 1 \frac{1}{3} ; \frac{2}{5} ; \frac{3}{5} ; 2 \frac{2}{5} ; 7 ; 8 \%=8 \% \frac{2}{5} ; \frac{3}{5}, 1 \frac{1}{3}, 7 \frac{2}{5}, 7 \end{array} \] 1.3 A train departed on Tuesday at 7:25 and arrived at its destination on Friday at 23:47 of the same week. How long did the journey take? Write the answer in days, hours and minutes. (3) 1.4 If the ratio of chocolates to ice-cream cones in a box is \( 5: 8 \) and the number of chocolates is 30. Find the number of ice cream \( \frac{8}{5}=\frac{30}{1 e c} \) cicam cone \( =\frac{5}{8}(3) \) 1.5 Venetia Mining company shares decreased by \( 7 \% \) from the previous week's price of \( \begin{aligned} & \frac{30 \times 8}{5(3)} \\ = & 48\end{aligned} \) 1.6 Lufuno 's salary after a \( 8,5 \% \) increase is R16 205. Calculate Lufuno's original salary. Show ALL steps that are used to determine the answer. (3) 1.7 Convert \( 24^{\circ} \mathrm{C} \) in Paris. What will the temperature be if converted to \( { }^{\circ} \mathrm{F} \). (2) You may use the formula: \( \left({ }^{\circ} \mathrm{C} \times 1,8\right)+32^{\circ} \) 1.8 Write 3 p.m. in 24 -hour notation (2)

Let's solve each question step by step, following the instructions provided. ### QUESTION 1 #### 1.1 Calculate the following without using a calculator. Show ALL steps used in calculating the answer. Leave the answer as a mixed fraction. **1.1.1** \[ 1.14 \frac{3}{4} + 1 \frac{1}{12} - 2 \frac{5}{6} \] First, convert the mixed numbers to improper fractions: - \( 1.14 = 1 + 0.14 = 1 + \frac{14}{100} = \frac{100 + 14}{100} = \frac{114}{100} = \frac{57}{50} \) - \( \frac{3}{4} = \frac{3}{4} \) - \( 1 \frac{1}{12} = 1 + \frac{1}{12} = \frac{12 + 1}{12} = \frac{13}{12} \) - \( 2 \frac{5}{6} = 2 + \frac{5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \) Now, we can rewrite the expression: \[ \frac{57}{50} + \frac{13}{12} - \frac{17}{6} \] Next, we need a common denominator. The least common multiple of \( 50, 12, \) and \( 6 \) is \( 300 \). Convert each fraction: - \( \frac{57}{50} = \frac{57 \times 6}{50 \times 6} = \frac{342}{300} \) - \( \frac{13}{12} = \frac{13 \times 25}{12 \times 25} = \frac{325}{300} \) - \( \frac{17}{6} = \frac{17 \times 50}{6 \times 50} = \frac{850}{300} \) Now substitute back into the expression: \[ \frac{342}{300} + \frac{325}{300} - \frac{850}{300} = \frac{342 + 325 - 850}{300} = \frac{-183}{300} \] This can be simplified: \[ \frac{-61}{100} \] So, the final answer is: \[ -0.61 \] **1.1.2** \[ 2^{3} + \frac{3}{\sqrt[3]{5^{2}+2}} \] Calculate \( 2^{3} \): \[ 2^{3} = 8 \] Now calculate \( \sqrt[3]{5^{2}+2} \): \[ 5^{2} = 25 \implies 5^{2} + 2 = 27 \implies \sqrt[3]{27} = 3 \] Now substitute back: \[ 8 + \frac{3}{3} = 8 + 1 = 9 \] #### 1.2 Rearrange the following fractions in ascending order: \[ 1 \frac{1}{3}, \frac{2}{5}, \frac{3}{5}, 2 \frac{2}{5}, 7, 8 \% = 8 \frac{2}{5} \] Convert mixed numbers to improper fractions: - \( 1 \frac{1}{3} = \frac{4}{3} \) - \( 2 \frac{2}{5} = \frac{12}{5} \) - \( 8 \% = 0.08 \) Now convert all to decimals for easier comparison: - \( \frac{4}{3} \approx 1.33 \) - \( \frac{2}{5} = 0.4 \) - \( \frac{3}{5} = 0.6 \) - \( \frac{12}{5} = 2.4 \) - \( 7 = 7.0 \) - \( 0.08 = 0.08 \) Now arrange in ascending order: \[ 0.08, \frac{2}{5}, \frac{3}{5}, 1 \frac{1}{3}, 2 \frac{2}{5}, 7 \] #### 1.3 A train departed on Tuesday at 7:25 and arrived at its destination on Friday at 23:47 of the same week. How long did the journey take? Calculate the total time from Tuesday to Friday: - From Tuesday 7:25 to Wednesday 7:25 = 24 hours - From Wednesday 7:25 to Thursday 7:25 = 24 hours - From Thursday 7:25 to Friday 7:25 = 24 hours - From Friday 7:25 to Friday 23:47 = 16 hours and 22 minutes Total time: \[ 24 + 24 + 24 + 16 \text{ hours} = 88 \text{ hours} \] \[ 88 \text{ hours} + 22 \text{ minutes} \] Convert hours to days: \[ 88 \text{ hours} = 3 \text{ days} + 16 \text{ hours} \] So, the total journey time is: \[ 3 \text{ days}, 16 \text{ hours}, 22 \text{ minutes} \] #### 1.4 If the ratio of chocolates to ice-cream cones in a box is \( 5: 8 \) and the number of chocolates is 30. Find the number of ice cream cones. Let \( c \) be the number of ice-cream cones. The ratio gives us: \[ \frac{5}{8} = \frac{30}{c} \] Cross-multiply: \[ 5c = 240 \implies c = \frac{240}{5} = 48 \] So, the number of ice-cream cones is: \[ 48 \] #### 1.5 Venetia Mining company shares decreased by \( 7 \% \) from the previous week's price of \( \frac{30 \times 8}{5(3)} \). Calculate the previous week's price: \[ \frac{30 \times 8}{5(3)} = \frac{240}{15} = 16 \] Now calculate the decrease: \[ 7\% \text{ of } 16 = 0.07 \times 16 = 1.12 \] So, the new price is: \[ 16 - 1.12 = 14.88 \] #### 1.6 Lufuno's salary after an \( 8.5\% \) increase is R16,205. Calculate Lufuno's original salary. Let \( x \) be the original salary. The equation is: \[ x + 0.085x = 16205 \im