Express 0.0000407, correct to 2 significant figures.

If x varies inversely as y and y varies directly as z, what is the relationship between x and z?

Evaluate: {3(1/4) x 1(3/5)}/ {11 (1/3) - 5 (1/3)}

Fig. 1 and Fig. 2 are the addition and multiplication tables respectively in modulo 5. Use these tables to solve the equation (n ⊕ 4) ⊕ 3 = 0 (mod 5)

The ages of Tunde and Ola are in the ratio 1 : 2. If the ratio of Ola's age to Musa's age is 4 : 5, what is the ratio of Tunde's age to Musa's age?

If M = {x : 3 ≤ x < 8} and N = {x : 8 < x ≤ 12}, which of the following is True?

I. 8 ∈ M∩N

II. 8 ∈ M∪N

III. M ∩N = ø

Given that a = log 7 and b = log 2, express log 35 in terms of a and b

if x = 2/3 and y = -6, evaluate xy - y/x.

Solve the equation: (1/5x) + (1/x) = 3

A sum of #18,100.00 was shared among 5 boys and 4 girls with each boy taking #20.00 more than each girl. Find a boy's share.

One factor of 7x² + 33x - 10 is

Solve: -1/4 < 3/4(3x - 2) < (1/2)

Simplify: 3x - (p - x) - (r - p).

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 π = 22/7].

Water flows out of a pipe at a rate of 40πcm³ per second into an empty cylindrical container of base radius 4cm}. Find the height of water in the container after 4 seconds.

The dimensions of a water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres.

If the total surface area of a solid hemisphere is equal to its volume, find the radius.

Which of the following is true about parallelograms?

The diagram shows a circle centre O. If < STR = 29º and < RST = 46º, calculate the value of <STO.

In the diagram above, XY is a straight line, <POX = <POQ and <ROY = <QOR. Find the value of <POQ + <ROY.

The diagram above shows a circle centre O. If <ZYW = 33º, find <ZWX.

In the diagram above, PQ and PS are tangents to the circle centre O. If < PSQ = mº, <SPQ = nº and <SQR = 33º, find the value of (m + n)º

Calculate the gradient (slope) of the line joining points (-1, 1) and (2, -2).

If P(2, 3) and Q(2, 5) are points on a graph, calculate the length PQ.

A bearing of 320º expressed as a compass bearing is

Given that cos 30º = sin 60º = √3/2 and sin 30º = cos 60º = 1/2, evaluate (tan 60º - 1)/(1 - tan 30º)

A stationary boat is observed from a height of 100m. If the horizontal distance between the observer and the boat is 80m, calculate, correct to two decimal places, the angle of depression of the boat from the point of observation.

The average age of a group of 25 girls is 10 years. If one girl, aged 12 years and 4 months joins the group, find, correct to one decimal place, the new average age of the group.

The bar chart shows the statistics of the number of passes and failures in an examination in a school from 2001 to 2004. What is the ratio of the total number of passes to the total number of failures?

The table above gives the distribution of marks obtained by a number of pupils in a class test.

Use this information to answer questions 30 and 31.

Find the median of the distribution.

The table above gives the distribution of marks obtained by a number of pupils in a class test.

Use this information to answer questions 30 and 31.

Find the first quartile

In a class of 45 students, 28 offer Chemistry and 25 offer Biology. If each student offers at least one of the two subjects, calculate the probability that a student selected at random from the class offers Chemistry only.

In what number base was the addition 1 + nn = 100, where n > 0, done?

Simplify: √2(√6 + 2√2) - 2√3

Three exterior angles of a polygon are 30º, 40º and 60º. If the remaining exterior angles are 46º each, name the polygon.

In the diagram, NQ // TS, <RTS = 50º and <PRT = 100º. Find the value of <NPR.

Find the 6th term of the sequence: 2/3, 7/15, 4/15, ...

The diagonal of a square is 60cm. Calculate its perimeter.

The roots of a quadratic equation are -1/2 and 2/3. Find the equation.

Make x the subject of the relation d = √(6/x - y/2)

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 is cold"?

Find the value of m in the diagram.

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?

If the simple interest on a certain amount of money saved in a bank for 5 years at 2 1/2% per annum is #500.00, calculate the total amount due after 6 years at the same rate.

Calculate the variance of 2, 3, 3, 4, 5, 5, 5, 7, 7 and  9.

A circular pond of radius 4m has a path of width 2.5 round it. Find, correct to two decimal places, the area of the path. [Take π = 22/7].

The graph of y = ax² + bx + c is shown in the diagram. Find the minimum value of y.

In the diagram, RP is a diameter of the circle RSP, RP is produced to T and TS is a tangent to the circle at S. If < PRS = 24º, calculate the value of < STR.