PAST QUESTIONS 1998

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.

Take the test

---

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. Simplify the expression
   \(3x^2 + 6xy - 3y^2 + 4x^2 - 8xy + 2y^2\)

Show Solution

Question 1.a.

\(3x^2 + 6xy - 3y^2 + 4x^2 - 8xy + 2y^2\)

Grouping like-terms:

\(3x^2 + 4x^2 + 6xy - 8xy - 3y^2 + 2y^2\)

\(\Rightarrow 7x^2 - 2xy - y^2\)





---








2. \((i)\) Solve the inequality \(3x - 9 \geq 12(x - 3)\).
   \((ii)\) Illustrate your answer on the number line.

Show Solution

Question 1.b.i.

\(3x - 9 \geq 12(x - 3)\)

\(\Rightarrow 3x - 9 \geq 12x - 36\)

Grouping like-terms:

\(\Rightarrow 3x - 12x \geq -36 + 9\)

\(\Rightarrow \hspace{0.7cm} - 9x \geq - 27\)

\(\Rightarrow \hspace{0.5cm} \dfrac{- 9x}{-9} \leq \dfrac{- 27}{-9}\)

\(\Rightarrow \hspace{1.1cm} x \leq 3\)

\(\therefore \underline{\{x:x \leq 3\}}\)





Question 1.b.ii.

Illutrating on the number line:





---








3. If \(p = 7, a = 16, b = 4\) and \(c = 3\),
   evaluate \(p^2 - \dfrac{(a - b)}{c}\)

Show Solution

Solution

\(p = 7\)

\(a = 16\)

\(b = 4\)

\(c = 3\)

\(p^2 - \dfrac{(a - b)}{c}\)

\(\Rightarrow 7^2 - \dfrac{(16 - 4)}{3}\)

\(\Rightarrow 49 - \dfrac{(12)}{3}\)

\(\Rightarrow 49 - 4\)

\(\Rightarrow 45\)

\(\therefore\) \(\underline{p^2 - \frac{(a - b)}{c} \ \text{is} \ 45}\)





---

---

Question 2

1. Using a pair of compasses only;

   \((i)\) Construct a triangle \(PQR\) such that \(|PQ| = 8\) cm, \(\angle RPQ = 90^\circ\) and \(\angle PQR = 30^\circ\). Measure \(|RQ|\)

   \((ii)\) Construct the perpendicular bisector (mediator) of \(RQ\). Let it meet \(RQ\) at \(O\).

2. With \(O\) as center and radius \(OP\), draw a circle. Measure \(|OP|\).

3. What is the special name for the chord \(RQ\)?

Show Solution

Solution





---

---

Question 3

1. A farmer travelled from Bakwa to Pabam, the distance between the two towns is 51 km. At Pabam he covered an additional 40 km on official duties. He returned to Bakwa the next day.

   \((i)\) Find the total distance covered by the man.

   \((ii)\) If the car used one litre of petrol to cover 20 km, find the amount of petrol used for the whole journey.

   \((iii)\) If a litre of petrol cost ₵522.00, calculate the total cost of petrol used for the journey.

Show Solution

Solution





---








2. A woman sold an article for ₵200,000.00 and made a profit of 25%. Find the cost price of the article.

Show Solution

Solution





---

---

Question 4

1. The pie chart shows angles representing the number of candidates who applied for admission into four programmes at a Senior Secondary School. The number of pupils who applied were 1080. Find

   \((i)\) the angle \(x^\circ\) representing the Vocational Programme.

   \((ii)\) the number of candidates who applied for Business Programme.

   \((iii)\) correct to the nearest whole number, the percentage of the number of applicants who applied for General Programme.

   
Show Solution

Solution





---








2. The table below shows the distribution of the masses of pupils in a school. On a graph paper, draw a bar chart for the distribution.

   
Show Solution

Solution





---

---

Question 5

1. Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes \(OX\) and \(OY\) on a graph sheet. On the same sheet, mark the \(x-\)axis from \(-8\) to \(8\) and the \(y-\)axis from \(-8\) to \(8\).

   \((i)\) Plot \(P(-2, 3)\) and \(Q(6, 4)\). Join \(PQ\).

   \((ii)\) Draw the image \(P_1Q_1\) of \(PQ\) under the anticlockwise rotation through \(90^\circ\) about the origin where \(P \rightarrow P_1\) and \(Q \rightarrow Q_1\)

   \((iii)\) Draw the image \(P_2Q_2\) of \(PQ\) under a clockwise rotation through \(90^\circ\) about the origin where \(P \rightarrow P_2\) and \(Q \rightarrow Q_2\).

Show Solution

Solution





---








2. The base radius of a closed cylinder is 4 cm and height of 7 cm. Calculate the total surface area.

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

Show Solution

Solution





---

---