PAST QUESTIONS 2021

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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

In the Venn diagram, \(M\) and \(N\) are intersecting sets in the universal set \(\mu\).

1. Express \(n(M)\) and \(n(N)\) in terms of \(x\).


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2. Given that \(n(M) = n(N)\), find the:

   \((i)\) value of \(x\).

   \((ii)\) \(n(\mathcal{\mu})\).


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3. Simplify: \(2^6 \div (2^2 \times 2^1) \div 2^5\)


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Question 2

1. Factorize the expression \(5ay - by + 15a - 3b\).


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2. Solve \(\frac{6}{4p - 1} = \frac{4}{3(p + 4)}\)


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3. Esi and Kofi shared an amount of Gh₵21,000.00 in the ratio of \(2:5\) respectively. How much more did Kofi receive than Esi?


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Question 3

1. If \(\mathbf{r} = \begin{pmatrix} -4 \\ -5 \end{pmatrix}\) and \(\mathbf{m} = \begin{pmatrix} -1 \\ -2 \end{pmatrix}\), find \(\mathbf{p}\) given that \(\mathbf{p} = \mathbf{r} - \mathbf{m}\).


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2. The sum of two numbers is 81. If the second number is twice the first, find the second number.


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3. The floor of a rectangular hall is of length 9 m and width 4 m. How may tiles of 20 cm by 30 cm can be used to cover the floor completely?


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Question 4

1. Antwiwaa bought 25 mangoes, 7 of which were unripe. What percentage of the mangoes were ripe?


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2. 

The mapping show the relationship between \(x\) and \(y\). Find the

\((i)\) rule of the mapping;

\((ii)\) values of \(m\) and \(n\).


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3. A bus left town \(X\) at 6:30 am and arrived at town \(Y\) at 1:00 pm. If the bus travelled at an average speed of 100 km per hour, calculate the distance from town \(X\) to town \(Y\).


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Question 5

1. Simplify: \((4x + 2)(x - 2) - 3x^2.\)


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2. The following are the angles formed at the centre of a circle: \(40^\circ, 60^\circ, 100^\circ, 3x^\circ\) and \(5x^\circ\). Find the value of \(x\).


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3. The cost \((C)\) in Ghana Cedis of producing a book of \(x\) pages is given as \(C = 25 + 0.6x\).

   \((i)\) Find the cost of producing a book with 220 pages.

   \((ii)\) How many pages are in a book produced at a cost of Gh₵ 145.00?


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Question 6

The table shows the number of marbles students sent to class for Mathematics lesson.

1. Copy and and complete the table.


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2. How many:

   \((i)\) students were in the class?

   \((ii)\) marbles were brought altogether?

   \((iii)\) marbles did most of the students bring?


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3. Calculate correct to the nearest whole number, the mean number of marbles brought for the lesson.


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