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PAST QUESTIONS 2005
Time yourself to improve on your speed. You are to use not more than 60 minutes for this section.
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Try the questions first, using not more than 15 minutes for each question, and watch the accompanying videos to see how the questions are solved.
Question 1
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A boy has enough money to buy 14 pencils at ₵450.00 each. How many erasers costing ₵300.00 each can he buy with the same amount of money?
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A circle has a circumference of 44 cm. Calculate its radius if \(\pi = \frac{22}{7}\)
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Simplify \((2\frac{1}{4} - 1\frac{5}{8}) \div 3\frac{7}{16}\)
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If \(\frac{5(n + 6)}{n} = 1\), find \(n\)
Solution
Solution
Circumference \(= 44\) cm
\(\pi = \frac{22}{7}\)
Circumference of a circle \(= 2\pi r\)
Substituting the given values:
\(\Rightarrow 44 = 2 \times \frac{22}{7} \times r\)
\(\Rightarrow 44 = \frac{44}{7} \times r\)
\(\Rightarrow 44 \times 7 = \frac{44}{7} r \times 7\)
\(\Rightarrow 44 \times 7 = 44 r\)
Dividing both sides by the coefficient
\(\Rightarrow \frac{44 \times 7}{44} = \frac{44 r}{44}\)
\(\Rightarrow r = 7 \)
\(\therefore \) the radius is 7 cm.
Solution
Solution
Question 2
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Copy and complete the table below for the relation; \(x + y = 180\)
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\((i)\) Using a scale of 2 cm to 20 units on both axes, draw two perpendicular axes \(Ox\) and \(Oy\).
\((ii)\) Mark both axes from 0 to 180.
\((iii)\) Plot all the seven points. Use a ruler to join the points.
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Using your graph, find
\((i)\) \(y\) when \(x = 100\);
\((ii)\) \(x\) when \(y = 70\).
Solution
Question 3
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There are 30 boys in a sporting club. 20 of them play hockey and 15 play volleyball. Each boy plays at least one of the two games.
\((i)\) Illustrate the information on a Venn diagram.
\((ii)\) How many boys play volleyball only?
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Factorise \(xy + 3x + 6y + 18\)
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Multiply \((3 + x)\) by \((5 - 2x)\)
Solution
Solution
Solution
Question 4
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Find
\((i)\) the interest for the 2 years;
\((ii)\) how much she paid in all to the bank after the 2 years.
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She used the ₵2,000,000.00 to purchase a fridge and sold it at a profit of 45%. Find the selling price of the fridge.
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If she used the amount raised from the sale of the fridge to pay for the bank loan and interest, find how much money is left.
A woman borrowed ₵2,000,000.00 from a bank at a rate of 15% per annum simple interest for 2 years.
Solution
Question 5
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Using a pair of compasses and a ruler only, construct
\((i)\) triangle \(ABC\) with \(|AB| = 10\) cm, angle \(ABC = 30^\circ\) and angle \(CAB = 60^\circ\);
\((ii)\) a perpendicular from the point C to meet the line \(AB\) at \(P\).
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\((i)\) Extend line \(CP\) to the point \(D\) such that \(|BC| = |BD|\).
\((ii)\) Join \(A\) to \(D\) and \(B\) to \(D\)
\((iii)\) Measure \(|AC|\) and \(|AD|\)
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What type of quadrilateral is \(ADBC\)?
Solution
Question 6
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Construct a frequency distribution table for the data.
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What is the modal mark?
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Calculate the mean mark.
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How many pupils scored more than 6 marks?
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What is the probability that a student chosen at random obtained 2 marks?
The following marks were obtained by pupils in a test.
\(\hspace{0.5cm}\)6 \(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 2 \(\hspace{0.5cm}\) 8
\(\hspace{0.5cm}\)6 \(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 10
\(\hspace{0.5cm}\)8 \(\hspace{0.5cm}\) 9 \(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 6 \(\hspace{0.5cm}\) 10
\(\hspace{0.5cm}\)2 \(\hspace{0.5cm}\) 2 \(\hspace{0.5cm}\) 6 \(\hspace{0.5cm}\) 6 \(\hspace{0.5cm}\) 6
Solution
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