PAST QUESTIONS 2001

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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. \(M\) is a set consisting of all positive integers between 1 and 10. \(P\) and \(Q\) are subsets of \(M\) such that \(P = \) {factors of 6} and \(Q = \) {Multiples of 2}.

   \(i)\) List the elements of \(M, P\) and \(Q\).

   \(ii)\) Represent \(M, P\) and \(Q\) on a Venn diagram.

   \(iii)\) Find \(P \cap Q\)

2. Solve the inequality

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

   \(\hspace{0.5cm} ii)\) Illustrate your answer on the number line.

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Question 2

1. Express \(131_{five}\) as a binary numeral.

2. Three children Kwabena, Esi and Yaw were given 160 oranges to share. Kwabena got \(\frac{1}{4}\) of the oranges. Esi and Yaw shared the remainder in the ratio \(3: 2\) respectively.

   \(i)\) Find how many oranges Esi recieved.

   \(ii)\) How many oranges did Yaw recieve than Kwabena?

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Question 3

1. Using a ruler and a pair of compasses only, construct triangle \(XYZ\), such that \(|XY| = 6\) cm, \(|XZ| = 8\) cm and \(|YZ| = 10\) cm.

2. \((i)\) Construct the mediator of line \(YZ\)

   \(ii)\) Construct the mediator of line \(XZ\)

   \(iii)\) Locate \(O\) the point of intersection of the mediators of lines \(YZ\) and \(XZ\).

   \(iv)\) With the center \(O\) and radius \(OY\), draw a circle.

3. Measure the radius of the circle you have drawn in \((b)\) \((iv)\) above, hence calculate the circumference of the circle.
   \(\hspace{0.5cm}\)[Take \(\pi = 3.14\)]

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Question 4

1. \(i)\) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes \(Ox\) and \(Oy\) on a graph sheet.

   \(ii)\) On the same graph sheet, mark the \(x-\)axis from \(-5\) to \(5\) and the \(y-\)axis from \(-6\) to \(6\).

2. On the same graph sheet plot the points \(A(2, 5)\), \(B(4, 3)\) and \(C(1, 1)\). Join the points \(A, B\) and \(C\) to form a triangle.

3. Reflect triangle \(ABC\) in the \(y-\)axis such that \(A \rightarrow A_1\), \(B \rightarrow B_1\) and \(C \rightarrow C_1\). Label the vertices of triangle \(A_1B_1C_1\).

4. Translate triangle \(A_1B_1C_1\) by the vector \(\begin{pmatrix}3 \\ -4 \end{pmatrix}\) such that \(A_1 \rightarrow A_2\), \(B_1 \rightarrow B_2\) and \(C_1 \rightarrow C_2\)

5. Join the vertices \(A_1B_1B_2\) and \(C\). Name the figure formed.

6. Find \(\overrightarrow{A_1B_1}\)

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Question 5

1. A cylinder closed at one end has radius 7 cm and height 20 cm.

   \(i)\) Find its total surface area.

   \(ii)\) If the cylinder is filled with water to a depth of 5 cm, calculate the volume of water in it.

2. Evaluate \(\frac{0.07 \times 0.6}{0.014 \times 0.03}\) leaving your answer in standard form.

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