PAST QUESTIONS 2012

Time yourself to improve on your speed. You are to use not more than 60 minutes for this section.

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Take the test

Highest score: \(\mathbf{\frac{35}{40}}\)

Tracy Amoako

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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. Evaluate \(\frac{0.035 \times 1.02}{0.00015}\), leaving your answer in standard form.

2. An amount of Gh₵4,200.00 was shared between Aba and Kwame. If Aba had \(\frac{5}{7}\) of the amount,

   \(\hspace{0.5cm} i)\) how much did Kwame receive?

   \(\hspace{0.5cm} ii)\) what percentage of Aba's share did Kwame receive?

3. Find the value of \(x\) in the diagram below.

   

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Question 2

1. A car consumes a gallon of petrol for every 30 km drive. The driver of the car set out on a journey of 420 km with 10 gallons of petrol in the fuel tank.

   \(\hspace{0.5cm} i)\) How many gallons of petrol will be needed to complete the journey?

   \(\hspace{0.5cm} ii)\) Find the cost of the petrol used for the journey of 420 km if a gallon of petrol costs GH₵5.50.

2. The average number of spectators at a football competition for the first five days was 3,144. The attendance on the sixth day was 3,990. Find the

   \(\hspace{0.5cm} i)\) total attendance on the first five days

   \(\hspace{0.5cm} ii)\) average attendance for the 6 days.

3. The area enclosed by a square garden is 121 m\(^2\). What is the distance around the garden?

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Question 3

1. The table shows the number of students who scored more than 80% in the listed subjects.

   

   \(\hspace{0.5cm} i)\) Draw a pie chart for the distribution.

   \(\hspace{0.5cm} ii)\) What is the probability that a student chosen at random from the distribution offers Chemistry?

2. A woman bought 210 oranges for Gh₵7.50. She sold all of them at 3 for 15 Gp. Find the

   \(\hspace{0.5cm} i)\) total selling price of the oranges;

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

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Question 4

The marks scored by some students in a Mathematics test are as follows:

\(\hspace{0.5cm}\) 3 \(\hspace{0.5cm}\) 3 \(\hspace{0.5cm}\) 5 \(\hspace{0.5cm}\) 6 \(\hspace{0.5cm}\) 3 \(\hspace{0.5cm}\) 4
\(\hspace{0.5cm}\) 7 \(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 3 \(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 5 \(\hspace{0.5cm}\) 4
\(\hspace{0.5cm}\) 7 \(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 3 \(\hspace{0.5cm}\) 7 \(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 6
\(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 5 \(\hspace{0.5cm}\) 6 \(\hspace{0.5cm}\) 3
\(\hspace{0.5cm}\) 8 \(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 5 \(\hspace{0.5cm}\) 6 \(\hspace{0.5cm}\) 4 \(\hspace{0.5cm}\) 5

1. Construct a frequency distribution table for the scores.

2. Using the table, find for the distribution, the

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

   \(\hspace{0.5cm} ii)\) mean, correct to one decimal place;

   \(\hspace{0.5cm} iii)\) median

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Question 5

1. \(i)\) Find the Least Common Multiple (L. C. M) of 9, 18 and 16.

   \(\hspace{0.5cm} ii)\) Arrange \(\frac{8}{9}\), \(\frac{7}{18}\) and \(\frac{10}{16}\) in ascending order of magnitude.

2. Using a ruler and a pair of compass only,

   \(\hspace{0.5cm} i)\) construct a triangle \(PQR\) with length \(|PQ| = 10\) cm, angles \(QPR = 45^\circ\) and \(PQR = 60^\circ\).

   \(\hspace{0.5cm} ii)\) Construct the perpendicular bisectors of \(PR\) and \(RQ\) to meet at T.

   \(\hspace{0.5cm} iii)\) Measure the length of \(TP\).

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Question 6

\(\hspace{0.5cm} i)\) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes \(Ox\) and \(Oy\) on a graph sheet.

\(\hspace{0.5cm} ii)\) Mark on the same graph sheet, the \(x\)-axis from \(-5\) to \(5\) and \(y\)-axis from \(-6\) to \(6\).

\(\hspace{0.5cm} iii)\) Plot the points \(P(4, 2)\), \(Q(2, 5)\) and \(R(2, 2)\). Join the points \(P, Q, R\) to form triangle \(PQR\).

\(\hspace{0.5cm} iv)\) Using the \(x\)-axis as a mirror line, draw the image \(P_1Q_1R_1\) of the triangle \(PQR\) such that \(P \rightarrow P_1\), \(Q \rightarrow Q_1\), \(R \rightarrow R_1\).

\(\hspace{0.5cm} v)\) Write down the coordinates of \(P_1, Q_1\) and \(R_1\).

\(\hspace{0.5cm} vi)\) Translate triangle \(PQR\) by the vector \(\begin{pmatrix} -1 \\ -1 \end{pmatrix}\) such that \(P \rightarrow P_2\), \(Q \rightarrow Q_2\), \(R \rightarrow R_2\).

\(\hspace{0.5cm} vii)\) Label the vertices of triangle \(P_2Q_2R_2\).

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