Multiply 3.4 × 10⁻⁵ by 7.1 × 10⁸ and leave the answer in standard form.

Given that P = {p : 1 < p < 20}, where p is an integer and R = {r : 0≤ r ≤25, where r is a multiple of 4}. Find P ∩ R.

The First term of an Arithmetic Progression (A.P) is 2 and last term is 29. If the common difference is 3, how many terms are in the A.P?

Express in index form: logₐ x + logₐ y = 3.

Simplify: (2p - q)² - (p + q)².

If (3 - 4√2)(1 + 3√2) = a + b√2, find the value of b.

Find the time for which $1,250.00 will amount to $2,031.25 at 12.5% per annum simple interest.

If log₃(2x − 1) = 5, find the value of x.

The population of a town increases by 3% every year. In the year 2000, the population was 3,000. Find the population in the year 2003.

A trader gave a change of #540.00 instead of #570.00 to a customer. Calculate the percentage error

An interior angle of a regular polygon nis 168º. Find the number of sides of the polygon

If 3x - 2y = -5 and x + 2y = 9, find the value of {x - y}/{x + y}.

A variable W varies partly as M and partly inversely as P. Which of the following correctly represents the relation with K1 and K2 constants?

A cylindrical metallic barrel of height 2.5m and radius 0.245 is closed at one end. Find, correct to one decimal place, the total surface area of the barrel. [Take π= 22/7].

Make R the subject of the relation

V = πl(R² − r²).

Consider the following statements:

m : Edna is respectful

n : Edna is brilliant

If m ==> n, which of the following is valid?

A number is added to both the numerator and the denominator of the fraction 5/8. If the result is 1/2, find the number.

Gifty, Justina and Frank shared 60 oranges in the ratio 5 : 3 : 7 respectively. How many oranges did Justina receive?

Find the quadratic equation whose roots are 2/3 and -1.

A piece of rod of length 44m is cut to form a rectangular shape such that the ratio of the length to the breadth is 7 : 4. Find the breadth.

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A ladder 15m long leans against a vertical pole, making an angle of 72º with the horizontal. Calculate, correct to one decimal place, the distance between the foot of the ladder and the pole.

In the diagram, O is the centre of the circle. If |OA| = 25cm and |AB| = 40cm, find |OH|.

Given that P is 25m on a bearing of 330º from Q, how far south of P is Q

A car valued at $600,000.00 depreciates by 10% each year. What will be the value of the car at the end of two years?

The length and breadth of a cuboid are 15cm and 8cm respectively. If the volume of the cuboid is 1,560cm³, calculate the total surface area.

The number 1621 was subtracted from 6244 in base x. If the result was 4323, find x.

Factorize completely: 27x² - 48y².

In the diagram, < SQR = 52º and <PQS = 16º. Find the value of the angle marked y.

In the diagram, JKL is a tangent to circle GHIK at K. <LKG= 38º and <LKG=87º, calculate the value of angle marked x

A cone and a cylinder are of equal volume. The base radius of the cone is twice the radius of the cylinder. What is the ratio of the height of the cylinder to that of the cone?

Find, correct to the nearest whole number, the value of h in the diagram.

The gradient of the line joining the points P(2, -8) and Q(1, y) is -4. Find the value of y.

In the diagram, PQ || RS, <WYZ = 44º and <WXY = 50º. Find <WTX.

The perimeter of a rectangular garden is 90m. If the width is 7m less than the length, find the length of the garden.

Four of the angles of a hexagon sum up to 420º. If the remaining angles are equal, find the value of each of the angles.

Find the value of x in the diagram.

The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 40, 48 and 50. Use the information to answer questions 39 and 40.

Calculate the mean mass.

The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 40, 48 and 50. Use the information to answer questions 39 and 40.

Calculate the variance of the distribution.

Two opposite sides of a rectangle are (5x + 3)m and (2x + 9)m. If an adjacent side is (6x - 7)m, find in m², the area of the rectangle.

A die is tossed once. Find the probability of getting a prime number.

The area of a sector of a circle with radius 7cm is 51.3cm². Calculate, correct to the nearest whole number, the angle of the sector. [Take π= 22/7].

A cliff on the bank of a river is 87m high. A boat on the river is 22m away from the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

In the diagram TU is a tangent to the circle SPQR at P. If < PTS = 44º, < SQP = 35º, find <PST.

The probability that Amaka will pass an examination is 3/7 and that Bala will pass is 4/9. Find the probability that both will pass the examination.

Which of the following points lies on the line 3x - 8y = 11?

Find the range of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15 and 25.

The fourth and eighth terms of an Arithmetic Progression are 16 and 40 respectively. Find the common difference.