Eswatini General Certificate of Secondary Education: Mathematics: Paper 1

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Examinations Council of Eswatini
Eswatini General Certificate of Secondary Education
Mathematics
Paper 1 Short-Answer Questions (Core)

Time: 1 hour

Read These Instructions First
(1.) Write your centre number, candidate number and name in the spaces provided.
(2.) Write in dark blue or black pen.
(3.) You may use a soft pencil for any diagrams, graphs or rough working.
(4.) Do not use staples, paper clips, highlighters, glue or correction fluid.
(5.) Do not write on the bar code.
(6.) Answer all questions.
(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.
(9.) If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures.
Give answers in degrees to one decimal place.
For π, use either your calculator value or 3.142.
(10.) The total of the marks for this paper is 60.

(1.) Fractions, Decimals, and Percents: (a.) Write $\dfrac{132}{64}$ as a

(i.) mixed number,
(ii.) percentage.

(b.) Work out $3.157^2$ correct to 2 decimal places.

$ (a.)(i.) \\[3ex] \dfrac{132}{64} \\[5ex] = \dfrac{132 \div 4}{64 \div 4} \\[5ex] = \dfrac{33}{16} \\[5ex] = 2\dfrac{1}{16} \\[5ex] (ii.) \\[3ex] \dfrac{132}{64} \\[5ex] = \dfrac{132}{64} \times 100\% \\[5ex] = 206.25\% \\[5ex] (b.) \\[3ex] 3.157^2 \\[3ex] = 9.966649 \\[3ex] \approx 9.97 \quad\text{(to 2 decimal places)} $

(2.) Factors and Multiples: (a.) Find the highest common factor of 72 and 48.

Ratios: (b.) Simplify the ratios
(i.) 72 : 48
(ii.) 7 m : 42 cm

(c.) The length and width of a rectangle are in the ratio, length : width = 3 : 2.
The width of the rectangle is 8 cm.
Find the length of the rectangle.

The colors besides red indicate the common factors that should be counted only one time.
They are the only ones to be included in the calculation of the HCF.

$ (a.) \\[3ex] \underline{\text{Prime Factorization Method}} \\[3ex] \text{Numbers} = 72, 48 \\[3ex] 72 = \color{black}{2} \times \color{black}{2} \times \color{black}{2} \times 3 \times \color{darkblue}{3} \\[3ex] 48 = \color{black}{2} \times \color{black}{2} \times \color{black}{2} \times 2 \times \color{darkblue}{3} \\[5ex] HCF = \color{black}{2} \times \color{black}{2} \times \color{black}{2} \times \color{darkblue}{3} \\[3ex] HCF = 24 \\[5ex] (b.) (i.) \\[3ex] 72 : 48 \\[3ex] = \dfrac{72}{24} : \dfrac{48}{24} \\[5ex] = 3 : 2 \\[5ex] (ii.) \\[3ex] 7 m : 42 cm \\[3ex] ............................................... \\[3ex] 7m \;\;to\;\; cm \\[3ex] \text{Set up units:} \\[3ex] m \times \dfrac{...cm}{...m} \\[5ex] \text{Set up measurements and units:} \\[3ex] 7m \times \dfrac{1\;cm}{10^{-2}\;m} \\[5ex] = 7m \times \dfrac{1\;cm}{0.01\;m} \\[5ex] = 7 \times 1000g \\[3ex] = 700cm \\[3ex] ............................................... \\[3ex] = \dfrac{700cm}{42cm} \\[5ex] = \dfrac{700 \div 7}{42 \div 7} \\[5ex] = \dfrac{100 \div 2}{6 \div 2} \\[5ex] = \dfrac{50}{3} \\[5ex] = 50 : 3 \\[5ex] (c.) \\[3ex] \text{width} = 8cm \\[3ex] \text{length : width} = 3 : 2 \\[3ex] \text{length : 8} = 3 : 2 \\[3ex] \dfrac{\text{length}}{8} = \dfrac{3}{2} \\[5ex] \text{length} = 8 \times \dfrac{3}{2} \\[5ex] = 4 \times 3 \\[3ex] = 12cm $

Eswatini General Certificate of Secondary Education: Mathematics: Paper 1

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Examinations Council of Eswatini Eswatini General Certificate of Secondary Education Mathematics Paper 1 Short-Answer Questions (Core)

Examinations Council of Eswatini
Eswatini General Certificate of Secondary Education
Mathematics
Paper 1 Short-Answer Questions (Core)