BECE

Year to Practice:
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PAST QUESTIONS 2003


Section A

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

Click on the link below when you are ready.





Section B

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.





Question 1


    \(ξ\) = {1, 2, 3, 4, ..., 18};

    \(A\) = {Prime numbers} and

    \(B\) = {Odd numbers greater than 3}

  1. If \(A\) and \(B\) are subsets of the universal set, \(ξ\), list the members of \(A\) and \(B\).

  2. Find the set

    \((i)\) \(A \cap B\)
    \((ii)\) \(A \cup B\)

  3. \((i)\) Illustrate \(ξ\), \(A\) and \(B\) on a Venn diagram

    \((ii)\) Shade the region for prime factors of 18 on the Venn diagram.


    4. Solution









Question 2


  1. If \(2n - 5m + 10 = 0\), find

    \((i)\) \(m\), when \(n = 2\)

    \((ii)\) \(n\), when \(m = 5\)

    2. Solution







  2. Simplify \(\frac{6.4 \times 0.25 \times 16}{0.8 \times 0.5}\) leaving your answer in standard form.

    3. Solution







  3. A number of sweets were shared among 8 children and each child received 30. If 12 children shared the same number of sweets, how many will each receive?

    4. Solution









Question 3


    The table shows the distribution of the ages (in years) of children in a nursery school.

    The table as described above.

  1. Find

    \((i)\) the modal age

    \((ii)\) the mean age.

  2. Draw a bar chart for the distribution.

  3. What is the probability that a child chosen from the school is 4 years old?

    4. Solution









Question 4


  1. If \(\mathbf{p} = \begin{pmatrix}4 \\ 5 \end{pmatrix}\), \(\mathbf{q} = \begin{pmatrix}0 \\ -2 \end{pmatrix}\) and \(\mathbf{r} = \begin{pmatrix}-3 \\ 7 \end{pmatrix}\),

    Find \(\mathbf{p} + 2\mathbf{q} + \mathbf{r}\)

    2. Solution







  2. Find the solution set of the inequality \(x - \frac{4}{5} \leq \frac{1}{5}\), if the domain is the set \(\{-2, -1, 0, 1, 2\}\)

    3. Solution







  3. A rectangular sheet of metal has length 44 cm and breadth 10 cm. It is folded to form a cylinder with the breadth becoming the height. Calculate

    \((i)\) the radius of the cylinder formed;

    \((ii)\) the volume of the cylinder.

    [Take \(\pi = \frac{22}{7}\)]

    4. Solution











Question 5


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

    \(\hspace{0.5cm} i)\) Construct the triangle \(ABC\) with \(|AB| = 8\) cm, \(|BC| = 8\) cm and \(|AC| = 7\) cm.

    \(\hspace{0.5cm} ii)\) Bisect \(ABC\) and let the bisector meet \(AC\) at \(D\). Produce \(|BD|\) to \(P\) such that \(|BD| = |DP|\). Join \(AP\) and \(CP\).

    2. Solution











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