Chapter Competition Questions
Chapter
Chapter 2
Section
Chapter Competition Questions
Solutions 15 Videos

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}

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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}

Q7

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}

Q8

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}

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Q9

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

Q10

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

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Q11

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.

Q12

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

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Q13

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