The figure is an example of the construction of a
- A. perpendicular bisector of a given straight line QR
- B. perpendicular from a given point to a given line QR
- C. perpendicular to a line from a given point P on that line
- D. given angle
Three angles of a nonagon are equal and the sum of six other angles is 1110o. Calculate the size of one of the equal angles.
- A. 210o
- B. 150o
- C. 105o
- D. 50o
In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio of the area of triangle PQR to the area of the trapezium QRST.
- A. 4:9
- B. 4:5
- C. 1:3
- D. 2:3
In the diagram, POQ is a diameter, 0 is the centre of the circle and TP is a tangent. Find the value of x
- A. 30o
- B. 40o
- C. 45o
- D. 50o
An (\(n – 2)^2\) sided figure has n diagonals. Find the number n diagonals for a 25-sided figure
- A. 7
- B. 8
- C. 9
- D. 10
Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium
- A. \(\frac{3}{5}\)
- B. \(\frac{2}{5}\)
- C. \(\frac{4}{5}\)
- D. \(\frac{1}{5}\)
Below are the scores of group of students in a music test
\(\begin{array}{c|c}scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No, of students} & 3 & 6 & 10 & 8 & 6 & 5 & 2 & 4 & 12\end{array}\)
If CF(x) is the number of students with scores less than or equal to x, find CF(6)
- A. 40
- B. 38
- C. 33
- D. 5
The numbers 3, 2, 8, 5, 7, 12, 9 and 14 are the marks scored by a group of students in a class test. If P is scored by an group of students in a class test. If P is the mean and Q the median, the P + Q is
- A. 18
- B. 17\(\frac{1}{2}\)
- C. 16
- D. 15
The goals scored by 40 football teams from three league divisions are recorded below
\(\begin{array}{c|c} \text{Number of goals} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline frequency & 4 & 3 & 15 & 16 & 1 & 0 & 1\end{array}\)
What is the total number of goals scored by all the terms?
- A. 21
- B. 40
- C. 91
- D. 96
Taking the period of day light on a certain day to be from 5.30a.m to 7.00p.m. Calculate the angle of a pie chart designed to show the periods of the day light and of darkness on that day
- A. 187o30'
- B. 172o30'
- C. 135o225o
- D. 202o30' 157o 30'
What is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cm and with centre 0
- A. A circle of radius 4 cm and with centre O
- B. The perpendicular bisector of the chords
- C. a straight line passing through centre O
- D. A circle of radius 6 cm and with centre O
The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 4\(\sqrt3\)cm
- A. 6cm
- B. 5cm
- C. 4cm
- D. 3cm
What is the circumference of latitude 0°S if R is the radius of the earth?
- A. R cos\(\theta\)
- B. 2\(\pi\) R cos \(\theta\)
- C. R sin \(\theta\)
- D. 2\(\pi\) R sin \(\theta\)
A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room
- A. \(\frac{5}{17}\)
- B. \(\frac{8}{17}\)
- C. \(\frac{8}{15}\)
- D. \(\frac{12}{17}\)
From two points x and y, 8m apart, and in line with a pole, the angle of elevation of the top of the pole are 30o and 60o respectively. Fins the height of the pole assuming that x, y and the foot of the pole are the same horizontal plane and x and y are on the same side of the pole.
- A. \(\sqrt{6}\)
- B. 4\(\sqrt{3}\)
- C. \(\sqrt{3}\)
- D. \(\frac{12}{\sqrt{3}}\)
If tan \(\theta\) = \(\frac{m^2 – n^2}{2mn}\) find sec\(\theta\)
- A. \(\frac{m^2 + n^2}{(m^2 - n^2)}\)
- B. \(\frac{m^2 + n^2}{2mn}\)
- C. \(\frac{mn}{2(m^2 + n^2)}\)
- D. \(\frac{m^2n^2}{2(m^2 - n^2)}\)
The sine, cosine and tangent of 210o are respectively
- A. \(\frac{1}{2}\), \(\frac{\sqrt{3}}{2}\), \(\frac{\sqrt{3}}{2}\)
- B. \(\frac{1}{2}\), \(\frac{\sqrt{3}}{2}\), \(\frac{\sqrt{3}}{3}\)
- C. \(\frac{1}{2}\), \(\frac{\sqrt{3}}{2}\), \(\frac{\sqrt{3}}{2}\)
- D. \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)
Two chords QR and NP of a circle intersect inside the circle at x. If RQP = 37o, RQN = 49o and QPN = 35o, find PRQ
- A. 35o
- B. 37o
- C. 49o
- D. 59o
Three angles of a nonagon are equal and the sum of six other angles is 1110o. Calculate the size of one of the equal angles
- A. 210o
- B. 150o
- C. 105o
- D. 50o
Find the eleventh term of the progression 4, 8, 16…..
- A. 213
- B. 212
- C. 211
- D. 210