The roots of 8x^2 - 6x = 9 are x_1 and x_2. What is the value of (x_1 + 1)(x_2 +2)?

A. \dfrac{3}{2}

B. \dfrac{5}{8}

C. \dfrac{7}{8}

D. -\dfrac{3}{4}

What is the greatest possible integer value for k such that the equation (1 - 5k)x^2 + 6x - 2 = 0 has two distinct real roots?

A. -2

B. 0

C. 1

D. -1

Given f(x) = 2^{5x-3}, what is the product of f(x) and f(2 - x)?

A. 1024

B. 16

C. 256

D. 8

Determine the value of x such that 3^x - 3^{x-2} = \dfrac{24}{729}.

A. x = 8

B. x = 3

C. x = -4

D. x = -3

Determine the integer values of x and y so that 3^{x + 1} + 3^x = 4^{y + 2} - 7(4^y).

A. x = 0, y = 0

B. x = 1, y = 2

C. x = 2, y = 1

D. x = -1, y = -2

Consider the function y = ax^r. What is the value of r so that y = 6 when x = 4, and y = 24 when x = 64?

A. \dfrac{1}{2}

B. \dfrac{1}{4}

C. 4

D. 2

If cos A = \dfrac{4}{5} such that \pi < A < 2\pi, what is the value of tan A?

A. \dfrac{4}{3}

B. -\dfrac{4}{3}

C. \dfrac{3}{4}

D. -\dfrac{3}{4}

Consider \triangle ABC, with vertices A(2, 2), B(0, 0), and C(4, -2). What is the measure of \angle C to the nearest degree?

A. 37^{\circ}

B. 48^{\circ}

C. 53^{\circ}

D. 65^{\circ}

In the diagram, O is the centre of the circle, \angle OAB = 25^{\circ}, and \angle OCB = 48^{\circ}. Determine the measure of \angle ABC.

A. 48^{\circ}

B. 63^{\circ}

C. 23^{\circ}

D. 55^{\circ}

Determine the sum of four natural a, b, c, and d if a^3 + b^3 = 1729 and c^3 + d^3 = 1729.

A. 24

B. 32

C. 28

D. 36

What is the ones digit for the value 8^{1001}?

If x = a + b and y = a - b, express (\dfrac{3x - 21y}{6x + 12 y})^2 \div \dfrac{x^2 -49y^2}{2x^2 + 8xy + 8y^2} in terms of a and b, in simplified form.

Determine the least number that can be expressed as the sum of two perfect squares in two different ways. Justify your answer.

Determine the value of (1 + 3 + 5 + ... + 49) - (2 + 4 + 6 + ... + 50).

How many rectangles are in this diagram?