PAST QUESTIONS 2011

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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. In a school of 255 students, 80 of them study Arabic only and 125 study French only. Each student studies at least one of the two subject.

   \(\hspace{0.5cm} i)\) Draw a Venn diagram to represent the information.

   \(\hspace{0.5cm} ii)\) How many students study

   \(\hspace{1cm} \alpha)\) both subjects?

   \(\hspace{1cm} \beta)\) French?

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2. Make \(h\) the subject of \(v = \frac{1}{3}\pi r^2h\).

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3. A bookseller bought 80 copies of books at \(GH₵3.50\) per copy. He sold each of them at \(GH₵4.20\). Find

   \(\hspace{0.5cm} i)\) the total cost price;

   \(\hspace{0.5cm} ii)\) his percentage profit.

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Question 2

1. The pie chart below shows the distribution of exercise books to six schools \(A, B, C, D, E\) and \(F\) in a town. School \(D\) was given \(8,000\) exercise books.

   

   \(\hspace{0.5cm} i)\) How many exercise books were given to each of the rest of the schools?

   \(\hspace{0.5cm} ii)\) What is the average number of exercise books given to the schools?

   \(\hspace{0.5cm} iii)\) How many schools had less than the average number of exercise books?

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2. Solve the inequality below and illustrate the answer on the number line.

   \(\hspace{0.5cm}\) \(\frac{1}{3}x + 1 \geq \frac{1}{2}x + \frac{1}{4}(2 - x)\)

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Question 3

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

   \(\hspace{0.5cm} i)\) triangle \(ABC\) such that \(|AB| = 8\) cm, angle \(CBA = 45^\circ\) and angle \(CAB = 60^\circ\).

   \(\hspace{0.5cm} ii)\) the bisector of angle \(ACB\) to meet \(|AB|\) at \(T\).

2. Measure

   \(\hspace{0.5cm} i)\) \(|CT|\);

   \(\hspace{0.5cm} ii)\) angle \(CTB\)

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3. A boy spent \(\frac{3}{8}\) of his money and had Gh₵15.00 left. How much did he have?

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Question 4

1. The perimeter of a rectangular plot of land whose length is \((2x + 5)\) m and width \((x - 5)\) m is 80 m. Find the

   \(\hspace{0.5cm} i)\) value of \(x\);

   \(\hspace{0.5cm} ii)\) area of the plot;

   \(\hspace{0.5cm} iii)\) cost of weeding the plot at Gh₵0.24 per m\(^2\).

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2. Find the value of \(x\) and \(w\) in the diagram below if \(|AB| = |BC|\).

   
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Question 5

1. \(a)\) Given that \(\mathbf{a} = \begin{pmatrix}-3 \\ 3 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix}4 \\ -6 \end{pmatrix}\)

   calculate

   \(\hspace{0.5cm} i)\) \(\mathbf{a} + 2\mathbf{b}\)

   \(\hspace{0.5cm} ii)\) \(\frac{1}{2}(2\mathbf{a} - \mathbf{b})\)

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2. The number of pupils in a primary school is given in the table below:

   

   \(\hspace{0.5cm} i)\) Find the number of pupils in the school.

   \(\hspace{0.5cm} ii)\) What is the mean number of pupils in a class?

   \(\hspace{0.5cm} iii)\) What percentage of pupils are in class six?

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3. Convert \(312_{five}\) to a base ten numeral.

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Question 6

1. Copy and complete the table below for the relation \(y = \frac{x}{20}\), where \(y\) is the cost (in Ghana cedis) and \(x\) is the weight (in grammes) of rice sold in a market.

   

2. \(i)\) On a graph sheet, draw two perpendicular axes \(OX\) and \(OY\)

   \(\hspace{0.5cm} ii)\) Using a scale of 2 cm to 50 grammes on the \(x\)-axis and 2 cm to Gh₵2.00 on the \(y\)-axis draw the graph of the relation \(y = \frac{x}{20}\).

3. Using the graph, find

   \(\hspace{0.5cm} i)\) the cost of 175 grammes of rice;

   \(\hspace{0.5cm} ii)\) the weight of rice that can be bought with Gh₵14.00.

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