PAST QUESTIONS 2013

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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.

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Question 1

1. Fifty students in a class took an examination in French and Mathematics. If 14 of them passed French only, 23 passed in both French and Mathematics and 5 of them failed in both subjects, find

   \(\hspace{0.5cm} i)\) the number of students who passed in French,

   \(\hspace{0.5cm} ii)\) the probability of selecting a student who passed in Mathematics.

2. Solve the inequality \(2x - 1\frac{1}{2} \leq 5x - 6\)

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Question 2

1. Convert \(444_{five}\) to a base two numeral.

2. A man had three GH₵50.00, seven GH₵20.00 and five GH₵10.00 notes in his pocket. If he bought a bicycle for GH₵150.00 and two mobile phones at GH₵80.00 each, how many GH₵20.00 and GH₵10.00 notes did he have left?

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Question 3

1. Using a ruler and a pair of compasses only,

   \(\hspace{0.5cm} i)\) construct a triangle \(XYZ\) with length \(XY = 7\) cm, length \(YZ = 5\) cm and angle \(XYZ = 45^\circ\).

   \(\hspace{0.5cm} ii)\) Measure and write down the length of \(XZ\).

2. Given that the circumference of a circle is 44 cm, find

   \(\hspace{0.5cm} i)\) the radius of the circle.

   \(\hspace{0.5cm} ii)\) the area of the circle.

   \(\hspace{0.5cm}\) [Take \(\pi = \frac{22}{7}\)]

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Question 4

The table shows the distribution of marks of students in a class test.

1. Using a graph sheet, draw a bar chart for the distribution.

2. Calculate the mean mark of the distribution correct to the nearest whole number.

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Question 5

1. Simplify \(6(3\frac{5}{6} - 1\frac{1}{4})\)

2. Copy and complete the magic square so that the sum of numbers in each row or column or diagonal is 18.

   

3. Find the sum of all the factors of 24.

4. Given that \(\mathbf{m} = \begin{pmatrix}3 \\ -1\end{pmatrix}\), \(\mathbf{n} = \begin{pmatrix}-1 \\ 2\end{pmatrix}\) and \(\mathbf{r} = \begin{pmatrix}18 \\ -6\end{pmatrix}\). Find \(\mathbf{m} + \mathbf{n} + \mathbf{r}\)

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Question 6

1. Copy and complete the table for the relation \(y = 2x + 5\)

   

2. \(i)\) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes \(Ox\) and \(Oy\) on a graph sheet.

   \(\hspace{0.5cm} ii)\) Mark the \(x\)-axis from \(-6\) to 10 and the \(y\)-axis from \(-6\) 14.

   \(\hspace{0.5cm} iii)\) Using the table, plot all the points of the relation \(y = 2x + 5\) on the graph.

   \(\hspace{0.5cm} iv)\) Draw a straight line through the points.

3. Use the graph to find

   \(\hspace{0.5cm} i)\) \(y\) when \(x = 1.6\),

   \(\hspace{0.5cm} ii)\) \(x\) when \(y = 10\).

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