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?