Evaluate:

log₃27 + log₃6 – log₃54

Two locations on the equator are on longitudes 20°W and 70°E respectively.
If R = 6,370 km and π = 22/7, their distance apart along the equator, correct to 2 significant figures is

Arrange the following numbers in ascending order of magnitude

5/6,  11/13,  0.837

When the food bill for the Jackson's family increased by 20%, the mother reduced the quantity of food bought for the family by 15%.
What is the fractional increase in the food bill of the family now?

Two chords AC and BD of a circle intersect inside the circle at E.
If <BAC = 35°, <CAD = 42° and <ABD = 70°,
find <ACB.

Simplify:

(2^y - 2^{y - 1}) ÷ (2³ × 2^y – 8 × 2^{y – 1})

Correct adjectival order?

A plastic black bag.

The profit on a business was shared between two sisters Tara and Tise in the ratio
3 : 4.
If Tise received $8,000 more than Tara, find the profit shared.

The number 1.5714286, corrected to five decimal places, is

Simplify: 

(9^-1/2 × 81^3/4) ÷ (9^1/2)

Choose the word that best completes the sentence:

Forty cents _____ a great bargain for a doll.

Four handbags and three school bags costs $2000 and cost of handbag is thrice as much as schoolbags. If cost of school bag is 'a' then derived equation will be

Choose the word that best completes the sentence:

He gave us a _______ account of all that you had achieved over there.

If x² - 5x + 6 = (x-a)² + b,

what is the value of b?

Solve for y:

27^y/2  =  3^3/4 × 9^-1/4

Choose the word that best completes the sentence:

You need to open the windows and get rid of the _________ air in here.

If P = {3, 1, 0, 5};
Q = {2, 3, 8, 1, 4} and
R = {7, 6, 5},
then P ∩ Q ∩ R is

Choose the word that best completes the sentence:

The message between the lines _______ what we need to finish before Monday.

Convert 69₁₀ to a number in base two

The 5th and 10th terms of an AP are 0 and 10 respectively, the 20th term is

GATE Academy registers 300 candidates for an examination.
180 of the candidates offer Economics and 70 offer Geography.
80 candidates offer neither Economics nor Geography.
The number of candidates offering both Economics and Geography is

Choose the word that best completes the sentence:

The creator and the distributor of the furniture _____ to sign that petition.

Two sectors of the same circle subtend angles of 75° and 30° at the centre of the circle.

Their areas are in the ratio

Two events M and N are mutually exclusive and P(M) = ¼ and P(N) = 2/3.
P(M∩N) is

A sum of money invested at a simple interest rate R increases to 5/3 times the original sum after 5 years.
The value of R is

The length of a rod was given as 35cm correct to the nearest centimetre. The actual length lies within the range

Evaluate:

0.064^-1/3

Given that sin θ = 4/5,
the value of (1 - cos²θ) 
for 0°< θ < 90° is

Choose the word that best completes the sentence:

Neither of my daughters ______ like me.

What is the probability that the sum of any two numbers drawn from the set
{ 1, 2, 3, 4 } is odd?

A ______ of books. (Fill in the blanks)

Two cities London and Lagos are on latitude 60°N and their longitudes are 17°W and 28°E respectively.
If R = 6,370 km and π = 22/7, the distance between London and Lagos, measured along the parallel of latitude is

Choose the option that best completes the sentence:

The girl needs _____________ balls for that activity.

Correct each of the numbers 38.7152 and 0.05381 to two significant figures and find their product , correct to two significant figures.

Sean opened a savings account with £1,000.00. One year later he deposited £500.00 in the account and deposited a further £500.00 two years after opening the account.

If the interest rate is 8% p.a computed annually, calculate the total amount, to the nearest pounds, in his account three years after opening the account.

Given that tan²θ + sec²θ = 3,
the value of θ
(for 0°<θ<90°) is

The quantity x varies inversely as y, and y varies directly as the square of z. If z is halved, then the value of x is

The first winner in a lottery gets N2,000 while subsequent winners get N50 less than the preceding winner. The winner in the 20th position gets

A pump P can fill a water tank in 5hrs. With a second pump Q also operating, the tank can be filled in 2hrs.

Pump Q operating alone can fill the tank in

If 45_y = 100001₂,
the value of y is

A girl walks 30 m from a point P on a bearing of 040º to a point Q.
She then walks 30 m on a bearing of 140º to a point R.
How far is R from P

A number is selected randomly from the set of integers 1 to 20 inclusive.
What is the probability that the number is equal to or greater than 15?

Evaluate:

81^-1/4  × 36^1/2  ×10⁰

33 of the students in a grade 9 class play either football or table tennis.
If 22 students play football and 18 play table tennis,
how many students play football only?

The number 0.0047049, correct to three significant figures is