Lesotho General Certificate of Secondary Education: Mathematics: Paper 2

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Examinations Council of Lesotho
Lesotho General Certificate of Secondary Education
Mathematics
Paper 2 (Extended)

1 hour 30 minutes
Marks: 70

Read These Instructions First
(1.) Write your name, centre number and candidate number in the relevant spaces provided at the top of this page.
(2.) Write in dark blue or black pen.
(3.) You may use an HB pencil for any diagrams or graphs.
(4.) Do not use staples, paper clips, glue or correction fluid.
(5.) Answer all questions.
(6.) ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.
(7.) If working is needed for any question, it must be shown below that question.
(8.) The number of marks is given in brackets [ ] at the end of each question or part question.

(1.) Arithmetic Expressions: Evaluate.

$ (a.)\;\; 0.71 - 1.2 \\[3ex] (b.)\;\; 2\dfrac{4}{7} \div \dfrac{9}{14} \\[5ex] $

$ (a.) \\[3ex] 0.71 - 1.2 \\[3ex] = 0.71 - 1.20 \\[3ex] = -1.20 + 0.71 \\[3ex] = -(1.20 - 0.71) \\[3ex] = -0.49 \\[5ex] (b.) \\[3ex] 2\dfrac{4}{7} \div \dfrac{9}{14} \\[5ex] = \dfrac{18}{7} \times \dfrac{14}{9} \\[5ex] = \dfrac{2 \times 2}{1 \times 1} \\[5ex] = 4 $

(2.) Exponents: Work out.

$ \left(\dfrac{1 \times 10^2}{9}\right)^{-\dfrac{3}{2}} \\[5ex] $

$ \left(\dfrac{1 \times 10^2}{9}\right)^{-\dfrac{3}{2}} \\[5ex] = \left(\dfrac{1 \times 100}{9}\right)^{-\dfrac{3}{2}} \\[5ex] = \dfrac{1}{\left(\dfrac{100}{9}\right)^{\dfrac{3}{2}}} \quad\text{(Law 6 Exp)} \\[7ex] ................................................... \\[3ex] \left(\dfrac{100}{9}\right)^{\dfrac{3}{2}} \\[7ex] = \left(\sqrt{\dfrac{100}{9}}\right)^3 \quad\text{(Law 7 Exp)} \\[5ex] = \left(\dfrac{10}{3}\right)^3 \\[5ex] = \dfrac{10^3}{3^3} \quad\text{(Law 5 Exp)} \\[5ex] = \dfrac{1000}{27} \\[5ex] ................................................... \\[3ex] = 1 \div \dfrac{1000}{27} \\[5ex] = 1 \times \dfrac{27}{1000} \\[5ex] = \dfrac{27}{1000} $

(3.) Arithmetic Expressions: By writing each number correct to 1 significant figure, estimate.

$ 2.511 \times \sqrt{8.71} + 7.822 \\[3ex] $

For rounding rules to significant digits:
If the deciding digit is greater than or equal to 5 (at least 5), round up by adding 1 to the target digit, then discard the remaining digits.
If the deciding digit is less than 5, keep the target digit and discard the remaining digits.

$ 2.511 \times \sqrt{8.71} + 7.822 \\[3ex] \text{For } 2.511 \\[3ex] \text{target digit} = \text{1st significant digit} = 2 \\[3ex] \text{deciding digit} = \text{2nd significant digit} = 5 \\[3ex] 5 \ge 5 \\[3ex] 2 + 1 = 3 \\[3ex] 2.511 \approx 3 \quad\text{(to 1 significant figure)} \\[5ex] \text{For } 8.71 \\[3ex] \text{target digit} = \text{1st significant digit} = 8 \\[3ex] \text{deciding digit} = \text{2nd significant digit} = 7 \\[3ex] 7 \ge 5 \\[3ex] 8 + 1 = 9 \\[3ex] 8.71 \approx 9 \quad\text{(to 1 significant figure)} \\[5ex] \text{For } 7.822 \\[3ex] \text{target digit} = \text{1st significant digit} = 7 \\[3ex] \text{deciding digit} = \text{2nd significant digit} = 8 \\[3ex] 8 \ge 5 \\[3ex] 7 + 1 = 8 \\[3ex] 7.822 \approx 8 \quad\text{(to 1 significant figure)} \\[5ex] \implies \\[3ex] 3 \times \sqrt{9} + 8 \\[3ex] \underline{\text{BPEMDAS}} \\[3ex] = 3 \times 3 + 8 \\[3ex] = 9 + 8 \\[3ex] = 17 $

Lesotho General Certificate of Secondary Education: Mathematics: Paper 2

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Examinations Council of Lesotho Lesotho General Certificate of Secondary Education Mathematics Paper 2 (Extended)

Examinations Council of Lesotho
Lesotho General Certificate of Secondary Education
Mathematics
Paper 2 (Extended)