PAST QUESTIONS 2017

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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 class of 30 girls, 17 play football, 12 play hockey and 4 play both games.

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

   \(\hspace{0.5cm} ii)\) How many girls play:

   \(\hspace{1cm} \alpha)\) one or two of the games?

   \(\hspace{1cm} \beta)\) none of the games?

2. \( \)

   

   In the diagram, \(ABCD\) is a circle of radius 14 cm and center \(O\). Line \(BO\) is perpendicular to line \(AC\). Calculate, the total area of the shaded portions.

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

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Question 2

1. Two consecutive odd numbers are such that seven times the smaller, subtracted from nine times the bigger, gives 144. Find the two numbers.

2. A paint manufacturing company has a machine which fills 24 tins with paint in 5 minutes.

   \(\hspace{0.5cm} i)\) How many tins will the machine fill in

   \(\hspace{1cm} \alpha)\) 1 minute, correct to the nearest whole number?

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

   \(\hspace{0.5cm} ii)\) How many hours will it take to fill 1440 tins?

3. Given that \(s = \frac{n}{2}[2a + (n - 1)d]\), \(a = 3\), \(d = 4\) and \(n = 10\), find the value of \(s\).

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Question 3

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

   \(\hspace{0.5cm} i)\) a triangle \(ABC\) with \(|BC| = 9\) cm, \(|AC| = 8\) cm and \(|AB| = 6\) cm;

   \(\hspace{0.5cm} ii)\) the perpendicular bisector of line \(BC\);

   \(\hspace{0.5cm} iii)\) the bisector of angle \(ACB\).

2. Label the point of intersection of the two bisectors as \(Y\).

3. Draw a line to join \(B\) and \(Y\).

4. Measure:

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

   \(\hspace{0.5cm} ii)\) \(|YC|\);

   \(\hspace{0.5cm} iii)\) the base angles of triangle \(BYC\).

5. What type of triangle is \(BYC\)?

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Question 4

1. The table below show the ages of students admitted in a hospital.

   

   Use the information to answer the following questions:

   \(\hspace{0.5cm} i)\) What is the modal age?

   \(\hspace{0.5cm} ii)\) Calculate, correct to two decimal places, the mean age of the students.

2. Rice is sold at Gh₵56.00 per bag of 50 kg. A trader bought some bags of rice and paid Gh₵1,344.00.

   \(\hspace{0.5cm} i)\) How many bags of rice did the trader buy?

   \(\hspace{0.5cm} ii)\) If the trader retailed the bags of rice at Gh₵1.40 per kg, how much profit was made on 1 kg of rice?

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Question 5

1. Using a scale of 2 cm to 1 unit on both axes, draw on a graph sheet two perpendicular axes \(Ox\) and \(Oy\) for \(-5 \leq x \leq 5\) and \(-5 \leq y \leq 5\)

   \(\hspace{0.5cm} i)\) Plot, indicating the coordinates of all points \(A(2, 3)\) and \(B(-3, 4)\). Draw a line passing through the points \(A\) and \(B\).

   \(\hspace{0.5cm} ii)\) Plot on the same graph sheet, indicating the coordinates of the points \(C(4, 2)\) and \(D(-2, -3)\). Draw a straight line passing through the points to meet line \(\overline{AB}\).

2. Using the graphs in \(5(a)\):

   \(\hspace{0.5cm} i)\) find the values of \(y\) when \(x = -2\);

   \(\hspace{0.5cm} ii)\) measure the angle between the lines \(AB\) and \(CD\).

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Question 6

1. If \(\mathbf{m} = \begin{pmatrix} 2x + 1 \\ 2 - 3y\end{pmatrix}\), \(\mathbf{n} = \begin{pmatrix} 6 \\ -8\end{pmatrix}\) and \((\mathbf{m + n}) = \begin{pmatrix} 9 \\ -12\end{pmatrix}\), find the:

   \(\hspace{0.5cm} i)\) values of \(x\) and \(y\);

   \(\hspace{0.5cm} ii)\) components of \(\mathbf{m}\).

2. \(i)\)Solve the inequality:

   \(\hspace{0.5cm}\) \(\frac{3}{4}(x + 1) + 1 \leq \frac{1}{2}(x - 2) + 5\)

   \(\hspace{0.5cm} ii)\) Illustrate the answer in \(b(i)\) on a number line.

3. \(\)

   

   In the diagram, \(\overline{AB}\) is parallel to \(\overline{CD}\).

   Find the value of:

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

   \(\hspace{0.5cm} ii)\) \(y\).

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