PAST QUESTIONS 1999

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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. Kofi and Kojo were given ₵38,000.00 to share. Kojo had ₵7,500.00 more than Kofi. Find,

   \((i)\) Kofi's share

   \((ii)\) Kojo's share

Show Solution

Question 1a

\((i)\) Amount to be shared \(= ₵38,000\)

Let Kofi's share \(= x\)

then Kojo's share \(= x + ₵7,500\)

\(\Rightarrow x + (x + ₵7,500) = ₵38,000\)

\(\Rightarrow 2x + ₵7,500 = ₵38,000\)

\(\Rightarrow 2x = ₵38,000 - ₵7,500\)

\(\Rightarrow 2x = ₵30,500\)

\(\Rightarrow \dfrac{2x}{2} = \dfrac{₵30,500}{2}\)

\(\Rightarrow x = ₵15,250.00\)

\(\therefore\) Kofi's share is \(₵15,250.00\)





\((ii)\) Kojo's share
\(\Rightarrow x + ₵7,500\)

\(\Rightarrow ₵15,250 + ₵7,500\)

\(\Rightarrow ₵22,750.00\)

\(\therefore\) Kojo's share is \(₵22,750.00\)





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2. A trader paid ₵1,500.00 for 6 drinking cups. One of the cups got broken. He sold the remaining 5, making a profit of 10%. Calculate

   \((i)\) The cost price of each of the six cups.

   \((ii)\) The selling price of each of the five cups.

   \((iii)\) The profit made on each of the cups sold.

Show Solution

Question 1.b

\((i)\) Cost price of 1 of the 6 cups:

If 6 cups \(= ₵1,500\)

\(\Rightarrow\) 1 cup \(= \frac{1}{6} \times ₵1,500\)

\(\Rightarrow \dfrac{₵1,500}{6}\)

\(\Rightarrow ₵250\)

\(\therefore\) 1 of the 6 cups costs ₵250.00





\((ii)\) Profit made \(= 10\%\)

let the Cost Price \(= 100\%\)

\(\Rightarrow\) Selling Price \(= 100\% + 10\%\)

\(\Rightarrow\) Selling Price \(= 110\%\)

If CP, \(100\% \Rightarrow ₵1,500\)

Then SP, \(110\% \Rightarrow \dfrac{110\%}{100\%} \times ₵1,500\)

\(\Rightarrow 11 \times ₵150\)

\(\Rightarrow ₵1,650\)

Selling Price for each of the 5 cups:

\(\Rightarrow \dfrac{₵1,650}{5} \)

\(\Rightarrow ₵330.00 \)

\(\therefore\) The selling price of each of the 5 cups was ₵330.00





\((iii)\) Profit made on the 5 cups:

\(\Rightarrow ₵1,650 - ₵1,500\)

\(\Rightarrow ₵150\)

Profit made on each of the 5 cups:

\(\Rightarrow \dfrac{₵150}{5}\)

\(\Rightarrow ₵30\)

\(\therefore\) the profit made on each of the 5 cups was ₵30.00





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Question 2

1. Solve the inequality \(\dfrac{2x - 1}{4} - \dfrac{x - 2}{3} \geq 1\)

Show Solution

Question 2a

\(\dfrac{2x - 1}{4} - \dfrac{x - 2}{3} \geq 1\)

Multiplying through by 12:

\(\Rightarrow\) \(12 \times \dfrac{2x -1}{4}\)\(- \dfrac{x - 2}{3} \times 12\) \(\geq 1 \times 12\)

\(\Rightarrow\) \(3(2x - 1)\)\(- 4(x - 2)\) \(\geq 12\)

\(\Rightarrow 6x - 3 - 4x + 8 \geq 12\)

\(\Rightarrow 6x - 4x \geq 12 - 8 + 3\)

\(\Rightarrow 2x \geq 7\)

\(\Rightarrow \dfrac{2x}{2} \geq \dfrac{7}{2}\)

\(\Rightarrow x \geq 3\frac{1}{2}\)

\(\Rightarrow\) \(\therefore \{x:x \geq 3\frac{1}{2}\}\)





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2. Find the value of the expression \(2x - 3y\) if \(x = \frac{1}{3}\) and \(y = -\frac{1}{2}\).


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Solution





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3. 25 students in a class took an examination in Mathematics and Science. 17 of them passed in Science and 8 passed in both Mathematics and Science. 3 students did not pass in any of the subjects.

   \((i)\) How many passed in Mathematics?

   \((ii)\) The probability of meeting a student who passed in one subject only.


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Solution





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Question 3

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

   \((i)\) construct triangle \(ABC\) such that \(|AB| = 10\) cm, \(\angle ABC = 30^\circ\) and \(|BC| = 8\) cm. Measure \(\angle ABC\).

   \((ii)\) construct a perpendicular from \(C\) to meet line \(AB\) at \(D\). Measure \(CD\).

2. Calculate the area of triangle \(ABC\).

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Solution





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Question 4

1. Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes \(Ox\) and \(Oy\) on a graph sheet. On the same graph sheet, mark the \(x-\)axis from \(-10\) to \(10\) amd the \(y-\)axis from \(-12\) to \(12\). Plot the points \(A(0, 10)\), \(B(-6, -2)\), \(C(4, 3)\) and \(D(-3, -11)\). Use the ruler to join the points \(A\) to \(B\) and also \(C\) to \(D\).

2. \((i)\) Draw the line \(x = -2\) to meet \(AB\) at \(P\) and \(CD\) at \(Q\).

   \((ii)\) Use the protractor to measure angles \(BPQ\) and \(PQC\).

   \((iii)\) What is the common name given to angles \(BPQ\) and \(PQC\)

   \((iv)\) State the relationship between lines \(AB\) and \(CD\).

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Solution





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Question 5

The table below shows the marks scored out of 10 by some candidates in a test.

1. From the table, find

   \((i)\) the modal mark

   \((ii)\) how many students took the test.

   \((iii)\) the mean mark for the test.

2. If 20% of the candidates failed,

   \((i)\) how many failed?

   \((ii)\) What is the least mark a candidate should score in order to pass?

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Solution





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