Mathematics 30-1

The point (6, 5) lies on y = f(x). Which point lies on y = −2f(2(x − (1))) + (-3)?

What is the domain of f(x) = √(x − (3))?

For f(x) = 3x − 7, determine f⁻¹(11).

Let f(x) = 3x − 2 and g(x) = x² + 1. What is (f ∘ g)(2)?

If P(2) = 0, which expression must be a factor of P(x)?

A polynomial graph touches the x-axis at x = −1 and turns around, but crosses the x-axis at x = 3. Which factorization is consistent with this behaviour?

What is the remainder when P(x) = x³ − 2x + 5 is divided by x − 2?

For f(x) = (x² − 9)/(x² − x − 6), the graph has

In P(t) = 850(1.04)ᵗ, the annual percentage growth rate is

Given log₃x = 2 and log₃y = −1, determine log₃(x³√y/3⁴).

Solve 2^(x + 1) = 2^5.

If θ is in quadrant II and sin θ = 513, then cos θ is

The reference angle for 140° is

Which identity is valid wherever both sides are defined?

A periodic quantity has maximum 14, minimum 2, period 8, and a minimum at x = 1. Which equation models the quantity?

A circle has radius 6 cm and central angle 1.2 rad. The intercepted arc length is

How many distinguishable arrangements are possible using all letters of LEVEL?

A 4-person committee is selected from 9 people. Two of the people are team captains. How many committees contain at least one captain?

Determine sin 90° exactly.

The coefficient of x³ in (1 + x)⁷ is

A bag contains 5 blue and 3 gold tiles. Two tiles are selected without replacement. The probability that both are gold is

To make f(x) = (x − 2)² one-to-one while retaining the right half of its graph, its domain should be restricted to

Relative to y = |x|, the graph y = −3|x + 2| + 5 is

For (x − 1)/(x + 2) > 0, the solution set is

A polynomial has odd degree and a negative leading coefficient. Its graph must

The inverse of y = 5ˣ is

A quantity has maximum 18, minimum 6, and period 10. One model with a maximum at x = 0 is

Six different books are arranged on a shelf. If two particular books must remain together, the number of arrangements is

Solve log₂(2x + 1) = 5.

For P(x) = 2x³ − 3x² + 4x − 5, calculate the remainder when P(x) is divided by x − 2.

How many solutions does sin θ = 0.500 have on 0° ≤ θ < 360°?

Determine the coefficient of x^3 in (1 + x)^7.

Solve 2^(x − 1) = 64.

Calculate the arc length, in centimetres, for radius 8 cm and central angle 1.25 rad.

How many solutions does sin x = 12 have on 0 ≤ x < 4π?

$1 500 grows at 4.0% compounded annually for 6 years. Calculate the value to the nearest cent.

The point (3, 7) lies on y = f(x). Determine the x-coordinate of the corresponding point on y = f(2(x − (1))).

Determine the y-intercept of f(x) = (3x + 2)/(x + 5).

Two cards are drawn without replacement from five red and three black cards. Calculate the probability that both are red, as a decimal to three places.

Calculate the period, in degrees, of y = sin(2θ).