PAST QUESTIONS 2022

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Question 1

1. Given that \(P =\) {factors of 36} and \(Q =\) {factors of 54},

   \((i)\) List the members in the sets \(P\) and \(Q\).

   \((ii)\) Find:

   \(\hspace{0.5cm}\) A. \(P \cap Q\)

   \(\hspace{0.5cm}\) B. \(n(P \cap Q)\)

   \(\hspace{0.5cm}\) Γ. The Highest Common Factor (HCF) of 36 and 54.


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Solution

Question 1 \((i)\)

\(P =\) {factors of 36}

\(\Rightarrow P =\) {1, 2, 3, 4, 6, 9, 12, 18, 36}

\(Q =\) {factors of 54}

\(\Rightarrow Q =\) {1, 2, 3, 6, 9, 18, 27, 54}





Question 1 \((ii)\)

\(\hspace{0.5cm}\) A. \(P \cap Q =\) {1, 2, 3, 6, 9, 18}

\(\hspace{0.5cm}\) B. \(n(P \cap Q) = 6\)

\(\hspace{0.5cm}\) Γ. The Highest Common Factor (HCF) of 36 and 54:

\(\hspace{0.8cm}\) Common factors of 36 and 54 \(\Rightarrow\) {1, 2, 3, 6, 9, 18}

\(\hspace{0.8cm}\) Highest common factor \(\Rightarrow 18\)

\(\hspace{0.8cm} \therefore\) the highest common factor of 36 and 54 is 18.





2. Write down the next two terms of the sequence 1, 4, 9, ..., ...


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Solution





3. The median of the ordered set of observations 2, 3, (4\(m\)-3),(3\(m\)+1), 11 and 13 in ascending order is 6. Find the value of m.


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Solution

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Question 2

1. Simplify: \((\frac{1}{3} + \frac{1}{12}) \div (\frac{2}{3} - \frac{5}{8})\)


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Solution





2. Find the product of \((2x - 3)\) and \((2x + 3)\).


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Solution




3. 



In the diagram, \(ABC\) is an equilateral triangle. Find the value of \((x + y)\).


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Solution

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Question 3

1. Given the relation \(L = \frac{2(m^2 - n^2)}{4(m + n)}\)

   \(\hspace{0.5cm} (i)\) simplify \(L\):

   \(\hspace{0.5cm} (ii)\) find the value of \(L\) when \(m = 2\) and \(n = 3\).


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Solution





2. Solve \(\frac{4}{3x} = 7 - \frac{3}{x}\)


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Solution





3. A salesman gets a commission of \(5\frac{1}{2}\%\) of the value of items he sells. The salesman sells 12 textbooks at GH₵ 25.00 per book, 3 scientific calculators at GH₵ 50.00 per calculator and 8 packets of bic pens at GH₵ 50.00 per packet. Calculate the salesman's commission.


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Solution

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Question 4

1. Fred is \((x - 1)\) years old now. How old:

   \(\hspace{0.5cm} (i)\) was he 4 years ago?

   \(\hspace{0.5cm} (ii)\) will he be 8 years from now?

   \(\hspace{0.5cm} (iii)\) is he now, if his age in 8 years time will be three times his age 4 years ago?


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Solution





2. The perimeter of a rectangular cocoa farm is 497 km. The length of the farm is \(2\frac{1}{2}\) times the width. Find the:

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

   \(\hspace{0.5cm} (ii)\) length of the farm.


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Solution

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Question 5

1. Factorize: \((x-y)(3m+n)-(x-y)(m-2n)\)


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Solution





2. Given that \(\mathbf{p} = \begin{pmatrix} 2 - 3x\\5 - 2y \end{pmatrix}, \ \mathbf{q} = \begin{pmatrix} -1\\5 \end{pmatrix}\) and \(\mathbf{p} - \mathbf{q} = \begin{pmatrix} 6\\8 \end{pmatrix}\).

   Find the value of \((x + y)\).


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Solution





3. \(\hspace{0.5cm} (i)\) Find the truth set of \(\frac{x - 1}{2} \leq \frac{1}{2} + x\)

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


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Solution

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Question 6

1. Copy and complete the table for the relation \(y = 5 - 2x\) for \(-3 \leq x \leq 4\)

   

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Solution





2. Using a scale of 2 cm to 1 unit on the \(x\) - axis and 2 cm to 2 units on the \(y\) - axis, draw on a graph sheet two perpendicular axes \(Ox\) and \(Oy\) for \(-5 \leq x \leq 5\) and \(-12 \leq y \leq 12\).


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Solution





3. \(\hspace{0.5cm} (i)\) Using the table, plot all the points of the relation \(y = 5 - 2x\).

   \(\hspace{0.5cm} (ii)\) Draw a straight line through all the points.


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Solution





4. Using the graph, find the:

   \(\hspace{0.5cm} (i)\) value of \(y\) when \(x = -2.6\);

   \(\hspace{0.5cm} (ii)\) value of \(x\) when \(y = -2.8\);

   \(\hspace{0.5cm} (iii)\) gradient of the line.


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Solution

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