(a) Using a ruler and a pair of compasses only, construct: (i) a triangle ABC such that |AB| = 5cm, |AC| = 7.5cm and < CAB = 120°; (ii) the locus \(l_{1}\) of points equidistant from A and B; (iii) the locus \(l_{2}\) of points equidistant from AB and AC which passes through triangle ABC .

(b) Label the point P where \(l_{1}\) and \(l_{2}\) intersect.

(c) Measure |CP|.

The sketch shows a plot of land .

(a) Using a scale of 1 cm to 10m, draw an accurate diagram of the plot ;

(b) Construct : (i) The locus \(l_{1}\) of points equidistant from AC and BC ; (ii) the locus \(l_{2}\) of points 60m from A.

(c) A tree T inside the plot is on both \(l_{1}\) and \(l_{2}\). Locate T and find |TC| in metres.

(d) A flagpole, P is to be placed such that it it is nearer AC than BC and more than 60m from A. Shade the regions where P can be located.

Which of the following is nor a measure of central tendency?

• A. Mean
• B. Variance
• C. Median
• D. Mode

A can of Cola was labeled as containing 330ml of fluid but was found to contain 341ml. What was the percentage error?

• a.33.0%
• b. 34.1%
• c. 3.33%
• d. 3.41%

A trader bought 100 tubers at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain percent.

• A. 3.6%
• B. 3.5%
• C. 3.4%
• D. 2.55%

Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart?

• A. 1:00 pm
• B. 12:00 noon
• C. 11:00 am
• D. 10:00 am

Evaluate \(\frac{0.8 \times 0.43 \times 0.031}{0.05 \times 0.72 \times 0.021}\). Correct to four significant figures

• A. 14.09
• B. 14.1
• C. 14.12
• D. 14.11

(a) A sector of a circle of radius 8cm subtends an angle of 90° at the centre of the circle. If the sector is folded without overlap to form the curved surface of a cone, find the :

(i) base radius ; (ii) height ; (iii) volume of the cone. [Take \(\pi = \frac{22}{7}\)].

(b) A map is drawn to a scale of 1 : 20,000. Use it to calculate the : (i) distance, in kilometres, represented by 4.5 cm on the map ;

Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction

• A. \(\frac{x - 7}{x^2 + x - 6}\)
• B. \(\frac{x - 1}{x^2 + x - 6}\)
• C. \(\frac{x - 2}{x^2 + x - 6}\)
• D. \(\frac{x - 27}{x^2 + x - 6}\)

Find the sum to infinity to the following series 3 + 2 + \(\frac{4}{3}\) + \(\frac{8}{9}\) + \(\frac{16}{17}\) + .....

• A. 1270
• B. 190
• C. 18
• D. 9