BECE

Year to Practice:
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002A 2002B 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024

PAST QUESTIONS 2004


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


  1. \((i)\) Factorise completely the expression

    \(2xy - 8x + 3y -12\)

    \((ii)\) Evaluate the expression in \((i)\) if \(x = 5\) and \(y = 7\)

    2. Solution







  2. Make \(q\) the subject of the equation

    \(t = \frac{1}{p} + \frac{1}{q}\)

    3. Solution







  3. Given that \(\mathbf{u} = \begin{pmatrix}-5 \\ 9 \end{pmatrix}\) and \(\mathbf{v} = \begin{pmatrix}8 \\ 12 \end{pmatrix}\), find \(3(\mathbf{u} + \frac{1}{2}\mathbf{v})\)

    4. Solution











Question 2


  1. Ama and Kofi shared the profit earned from their business in the ratio \(3:4\). The profit was ₵1,743,000.

    \((i)\) Find how much of the profit each person received.

    \((ii)\) Kofi lent out his share of the profit at a rate of 20% per annum for 2 years. Find the interest on his share.

    \((iii)\) What will be Kofi's total amount at the end of the 2 years?

    2. Solution







  2. Change \(243_{five}\) into a base ten numeral.

    3. Solution











Question 3


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

    \((i)\) triangle \(PQR\) such that \(|PQ| = 8\) cm, angle \(QPR = 60^\circ\) and angle \(PQR = 45^\circ\)

    \((ii)\) Measure \(|QR|\).

    2. Solution







  2. A rectangular water tank has length 60 cm, with width 45 cm and height 50 cm. Find,

    \((i)\) the total surface area of the tank when closed,

    \((ii)\) the volume of the tank,

    \((iii)\) the height of the water in the tank, if the tank contains \(81,000\) cm\(^3\) of water.

    3. Solution











Question 4


  1. A car runs on the average at 45 km to 5 litres of fuel. Calculate how many litres of fuel are required for a journey of 117 km.

    2. Solution







  2. \((i)\) Solve for \(x\) in the inequality

    \(\frac{2}{3}(2x + 5) \leq 8\frac{2}{3}\)

    \((ii)\) Illustrate the solution on the number line.

    3. Solution







  3. A factory increased its production by \(22\frac{1}{2}\%\) and produced 49,000 tonnes. How many tonnes was it producing before?

    4. Solution











Question 5


  1. \((i)\) Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes \(Ox\) and \(Oy\) on a graph sheet.

    \((ii)\) On the same graph sheet, mark the \(x-\)axis from \(-5\) to \(5\) and \(y-\)axis from \(-6\) to \(6\).

  2. Plot the points

    \((i)\) \(P(1, -2)\) and \(Q(4, 5)\)

    \((ii)\) \(P^\prime\) the image of \(P\) under a translation by the vector \(\begin{pmatrix}-5 \\ 0 \end{pmatrix}\) and \(Q^\prime\), the image of \(Q\) by the same vector.

  3. \((i)\) Join \(PQQ^\prime P^\prime\)

    \((ii)\) Measure angles \(PQQ^\prime\) and \(PP^\prime Q^\prime\).

  4. \((i)\) Find the vectors \(\overrightarrow{PQ}\) and \(\overrightarrow{P^\prime Q}\)

    \((ii)\) What is the shape of \(PQQ^\prime P^\prime\)?

    5. Solution











Question 6


  1. The following are the ages in years of members of a group:
    \(8, 11, 8, 10, 6, 7, 3x, 11, 11\)

    If the mean age is 9 years, find

    \((i)\) \(x\),

    \((ii)\) the modal age

    \((iii)\) the median age.

    2. Solution







  2. Draw a bar chart for the distribution.

    3. Solution











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SHS JHS PRI 4 - 6 PASSCO