In an examination, the result of a certain school is as shown in the histogram above. How many candidates did the school present?
- A. 12
- B. 16
- C. 18
- D. 19
The pie chart shows the income of a civil servant in a month. If his monthly income is N6000, find his monthly basic salary
- A. N2050
- B. N2600
- C. N3100
- D. N3450
In the figure, XYZ is a triangle with XY = 5cm, XZ = 2cm and XZ is produced to E making the angle < YZE = 150o. If the angle XYZ = \(\theta\), calculate the value of sin\(\theta\)
- A. \(\frac{3}{5}\)
- B. \(\frac{1}{2}\)
- C. \(\frac{2}{5}\)
- D. \(\frac{1}{5}\)
Find the volume of the prism
- A. 990cm3
- B. 880cm3
- C. 550cm3
- D. 495cm3
The figure shows circles of radii 3cm and 2cm with centres at X and Y respectively. The circles have a transverse common tangent of length 25cm. Calculate XY
- A. \(\sqrt{630}\)cm
- B. \(\sqrt{626}\)cm
- C. \(\sqrt{615}\)cm
- D. \(\sqrt{600}\)cm
Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
- A. 2
- B. 3
- C. \(\sqrt{10}\)
- D. \(\sqrt{11}\)
A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number
- A. \(\frac{5}{11}\)
- B. \(\frac{1}{2}\)
- C. \(\frac{6}{11}\)
- D. \(\frac{7}{10}\)
In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges, if one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?
- A. \(\frac{17}{30}\)
- B. \(\frac{11}{30}\)
- C. \(\frac{6}{30}\)
- D. \(\frac{5}{30}\)
Find the difference between the range and the variance of the following set of numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7 where \(\sum d^2\) = 60
- A. 2
- B. 3
- C. 4
- D. 6
\(\begin{array}{c|c} Age & 20 & 25 & 30 & 35 & 40 & 45\\
\hline Number of people & 3 & 5 & 1 & 1 & 2 & 3\end{array}\)
Find the median age of the frequency distribution in the table above.
- A. 20
- B. 25
- C. 30
- D. 35
If \(y = x(x^4 + x + 1)\), evaluate \(\int \limits_{0} ^{1} y \mathrm d x\).
- A. \(\frac{11}{12}\)
- B. 1
- C. \(\frac{5}{6}\)
- D. zero
Integrate \(\frac{1}{x}\) + cos x with respect to x
- A. -\(\frac{1}{x^2}\) + sin x + k
- B. x + sin x - k
- C. x - sin x + k
- D. -\(\frac{1}{x^2}\) - sin x + k
\(\frac{d}{dx}\) cos(3x\(^2\) – 2x) is equal to
- A. -sin(6x - 2)
- B. -sin(3x2 - 2x)dx
- C. (6x - 2) sin(3x2 - 2x)
- D. -(6x - 2)sin(3x2 - 2x)
Differentiate \(\frac{6x^3 – 5x^2 + 1}{3x^2}\) with respect to x
- A. \(\frac{2 + 2}{3x^3}\)
- B. 2 + \(\frac{1}{6x}\)
- C. 2 - \(\frac{2}{3x^3}\)
- D. \(\frac{1}{5}\)
In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ.
- A. √23cm
- B. √13cm
- C. 2√5cm
- D. 2√3cm
The angle of elevation of a building from a measuring instrument placed on the ground is 30o. If the building is 40m high, how far is the instrument from the foot of the building?
- A. \(\frac{20}{√3}\)m
- B. \(\frac{40}{√3}\)m
- C. 20√3m
- D. 40√3m
Find the distance between the point Q (4,3) and the point common to the lines 2x – y = 4 and x + y = 2
- A. 3√10
- B. 3√5
- C. √26
- D. √13
A point P moves so that its equidistant from point L and M. If LM is16cm, find the distance of P from LM when P is 10cm from L
- A. 12cm
- B. 10cm
- C. 8cm
- D. 6cm
The angle between the positive horizontal axis and a given line is 135o. Find the equation of the line if it passes through the point (2,3)
- A. x - y = 1
- B. x + y = 1
- C. x + y = 5
- D. x - y = 5
A cone with a sector angle of 45° is cut out of a circle of radius r cm. Find the base radius of the cone.
- A. \(\frac{r}{16}\) cm
- B. \(\frac{r}{6}\) cm
- C. \(\frac{r}{8}\) cm
- D. \(\frac{r}{2}\) cm
An arc of a circle subtends an angle 70o at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.(\(\pi\) = \(\frac{22}{7}\))
- A. 22cm2
- B. 44cm2
- C. 66cm2
- D. 88cm2