Two bottles are drawn with replacement from a crate containing 8 Coke, 12 Fanta, and 4 Sprite bottles. What is the probability that the first is coke and the second is not coke?
- A. \(\frac{1}{12}\)
- B. \(\frac{1}{6}\)
- C. \(\frac{2}{9}\)
- D. \(\frac{3}{8}\)
Given that t = \(2 ^{-x}\), find \(2 ^{x + 1}\) in terms of t.
- A. \(\frac{2}{t}\)
- B. \(\frac{t}{2}\)
- C. \(\frac{1}{2t}\)
- D. t
Consider the statements: p it is hot, q: it is raining
Which of the following symbols correctly represents the statement “It is raining if and only if it it is cold”?
- A. p \(\iff\) \(\sim\)q
- B. p \(\iff\) q
- C. \(\sim\)p \(\iff\) \(\sim\)q
- D. q \(\iff\) \(\sim\)p
Make x the subject of the relation d = \(\sqrt{\frac{6}{x} – \frac{y}{2}}\)
- A. x = \(\frac{6 + 12}{d^2 + y}\)
- B. x = \(\frac{12}{d^2 - y}\)
- C. x = \(\frac{12}{y} - 2d^2\)
- D. x = \(\frac{12}{2d^2 + y}\)
The roots of a quadratic equation are \(\frac{-1}{2}\) and \(\frac{2}{3}\). Find the equation.
- A. \(6x^2 - x + 2 = 0\)
- B. \(6x^2 - x - 2 = 0\)
- C. \(6x^2 + x - 2 = 0\)
- D. \(6x^2 + x + 2 = 0\)
Find the 6th term of the sequence \(\frac{2}{3} \frac{7}{15} \frac{4}{15}\),…
- A. -\(\frac{1}{3}\)
- B. -\(\frac{1}{5}\)
- C. -\(\frac{1}{15}\)
- D. \(\frac{1}{9}\)
Simplify the expression \(\frac{a^2 b^4 – b^2 a^4}{ab(a + b)}\)
- A. \(a^2 - b^2\)
- B. \(b^2 - a^2\)
- C. \(a^2b - ab^2\)
- D. \(ab^2 - a^2b\)
Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.
- A. decagon
- B. nonagon
- C. octagon
- D. hexagon
Simplify; \(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) – 2\sqrt{3}\)
- A. 4
- B. \(\sqrt{3} + 4\)
- C. 4 \(\sqrt{2}\)
- D. 4\(\sqrt{3} + 4\)
In what number base was the addition 1 + nn = 100, where n > 0, done?
- A. n - 1
- B. n + 1
- C. n
- D. n + 2
The average age of a group of 25 girls is 10year. If one girl, aged 12 years and 4 months joins the group, find the new average age of the group
- A. 10.1 years
- B. 9.3 years
- C. 8.7 years
- D. 8 . 3 years
Given that cos 30\(^o\) = sin 60\(^o\) = \(\frac{3}{2}\) and sin 30\(^o\) = cos 60\(^o\) = \(\frac{1}{2}\), evaluate \(\frac{tan 60^o – 1}{1 – tan 30^o}\)
- A. \(\sqrt{3 - 2}\)
- B. 2 - \(\sqrt{3}\)
- C. \(\sqrt{3}\)
- D. -2
A bearing of 320\(^o\) expressed as a compass bearing is
- A. N 50\(^o\) W
- B. N 40\(^o\) W
- C. N 50\(^o\) E
- D. N 40\(^o\) E
If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ
- A. 6 units
- B. 5 units
- C. 4 units
- D. 2 units
Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)
- A. -1
- B. \(\frac{-1}{2}\)
- C. \(\frac{1}{2}\)
- D. 1
Which of the following is true about parallelogram?
- A. opposite angles are supplementary
- B. opposite angles are complementary
- C. opposite angles are equal
- D. opposite angles are reflex angles
If the total surface area of a solid hemisphere is equal to its volume, find the radius
- A. 3.0cm
- B. 4.5cm
- C. 5.0cm
- D. 9.0cm
The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres
- A. 4.55 litres
- B. 7.50 litres
- C. 8.10 litres
- D. 9.55 litres
Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.
- A. 10 cm
- B. 14 cm
- C. 16 cm
- D. 20 cm
An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)]
- A. 29\(^o\)
- B. 57\(^o\)
- C. 65\(^o\)
- D. 115\(^o\)
Simplify; 3x – (p – x) – (r – p)
- A. 2x - r
- B. 2x + r
- C. 4x - r
- D. 2x - 2p - r