PAST QUESTIONS 2019

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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. Given that \(X =\) {whole numbers from 4 to 13} and \(Y =\) {multiples of 3 between 2 and 20}, find \(X \cap Y\).


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2. Find the Least Common Multiple (L.C.M) of the following numbers: 3, 5 and 9.

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3. If \(\frac{p + 2q}{p} = \frac{7}{5}\), find the value of \(\frac{q}{p}\).


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Question 2

1. Solve: \(\frac{4x + 5}{5} + \frac{x - 3}{4} = -1\)

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2. The ratio of boys to girls in a school is \(12:25\). If there are \(120\) boys.

   \((i)\) how many girls are in the school?

   \((ii)\) what is the total number of boys and girls in the school?

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3. Simplify: \((8x^2y^3)(\frac{3}{8}xy^4)\)

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Question 3

1. In an examination, 60 candidates passed Integrated Science or Mathematics. If 15 passed both subjects and 9 more passed Mathematics than Integrated Science, find the:

   \((i)\) number of candidates who passed in each subject;

   \((ii)\) probability that a candidate passed exactly one subject.

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2. Factorize: \(xy + 6x + 3y + 18\)

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Question 4

1. Express 250% as a fraction in its lowest term.

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2. 

   Use the diagram to find the value of \(x\).

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3. Simplify: \(2 \div (\frac{15}{64} \div \frac{6}{7})\)

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4. If \(\mathbf{q = \begin{pmatrix} 7\\ -1 \end{pmatrix}}\) and \(\mathbf{r = \begin{pmatrix} 4\\ -5 \end{pmatrix}}\), find \((\mathbf{q} + \mathbf{r})\).

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Solution

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Question 5

1. 

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

   \((i)\) Using a scale of 2 cm to 1 unit on the \(x\) - axis and 2 cm to 2 units on the \(y\) - axis, draw two perpendicular axes \(Ox\) and \(Oy\) on a graph sheet for \(1 \leq x \leq 5\) and \(0 \leq x \leq 14\);

   \((ii)\) Plot the point for each ordered pair, \((x, y)\).

   \((iii)\) Join the points with a straight line;

   \((iv)\) Using the graph sheet, find the gradient of the line in \((a)(iii)\).

   \((v)\) Use the graph to find the equation of the line in \((a)(iii)\).

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2. Simplify: \(32 \times 8 \times 4 \times 2\), leaving your answer in the form \(2^n\).

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Question 6

The marks obtained by students in a class test were:

\(\hspace{0.5cm} 4 \hspace{0.5cm} 8 \hspace{0.5cm} 7 \hspace{0.5cm} 6 \hspace{0.5cm} 7\)
\(\hspace{0.5cm} 2 \hspace{0.5cm} 1 \hspace{0.5cm} 7 \hspace{0.5cm} 4 \hspace{0.5cm} 7\)
\(\hspace{0.5cm} 3 \hspace{0.5cm} 7 \hspace{0.5cm} 6 \hspace{0.5cm} 4 \hspace{0.5cm} 3\)
\(\hspace{0.5cm} 7 \hspace{0.5cm} 5 \hspace{0.5cm} 2 \hspace{0.5cm} 7 \hspace{0.5cm} 2\)
\(\hspace{0.5cm} 5 \hspace{0.5cm} 4 \hspace{0.5cm} 8 \hspace{0.5cm} 3 \hspace{0.5cm} 2\)

1. Construct a frequency distribution table for the data.

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2. Find the:

   \((i)\) mode of the distribution.

   \((ii)\) median mark of the test.

   \((iii)\) mean mark.

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Solution

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