Evaluate log₃ 1/81

1.   ?    4
2.   ?    -4
3.   ?    1/4
4.   ?    -1/4

Solve the equation (1/4)^x = 2^{-x + 4}

1.   ?    -4
2.   ?    2
3.   ?    -2
4.   ?    4

Express 3e^x-1 = y with x as the subject.

1.   ?    x = 1/3 log^e(y – 1) +1
2.   ?    x = 1/3(log^e y) + 1
3.   ?    x = 3log^e y + 1
4.   ?    x = log^e (y/3) + 1

Solve (½)^x < 10

1.   ?    x < -3.322
2.   ?    x > -3.322
3.   ?    x > 0
4.   ?    x < 0

Solve the quadratic equation 5x² – 3x – 1 = 0

1.   ?    x = 0.8385, -0.2385
2.   ?    No solution
3.   ?    x = 0.4725
4.   ?    x = 1/5, 3/5

Solve y² – 81 = 0

1.   ?    y = ± 3
2.   ?    y = ± 27
3.   ?    y = ± 9
4.   ?    y = 3, -27

Solve x² – 2ax – 3a² = 0

1.   ?    x = a, -3a
2.   ?    x = a/2, - 6a
3.   ?    x = -a/2, 6a
4.   ?    x = -a, 3a

An investor has £1000 to invest at an interest rate of 8% per annum. If the sum accrued, S = P(1+r)ⁿ where P is the original investment, r is the interest rate and n is the number of years invested and the investor wishes to accrue £5000, how many years must he wait?

1.   ?    21
2.   ?    15
3.   ?    25
4.   ?    19

Revenue from a product is R = xP where P is the unit price and x is the number sold. Price is related to the number sold by the function P = 50 – 2x. The total production cost is C = 10x + 150. At what values of x is revenue equal to cost?

1.   ?    x = 0, 25
2.   ?    x = 10, 20
3.   ?    x = 5, 15
4.   ?    x = -5, 10

Solve 6x² – x = 0

1.   ?    x = 0, 6
2.   ?    x = 0, 1/6
3.   ?    x = 1, 6
4.   ?    x = 1/6, -1/6