Mathematics 30-2

A student checks ten examples, observes the same pattern, and proposes a general rule. This is primarily

Which value is a counterexample to the claim “If n is an integer, then n² > n”?

The converse of “If a figure is a square, then it has four equal sides” is

In a survey, 28 people chose A, 22 chose B, and 9 chose both. How many chose A or B?

The notation A ∩ B represents elements that are

If the probability of an event is 38, the odds in favour of the event are

If P(A) = 0.37, then P(not A) is

For f(x) = x² − 1 when x < 2 and f(x) = 3x + 2 when x ≥ 2, determine f(2).

The graph of y = 2x − 3 − 4 has vertical and horizontal asymptotes, respectively, at

From eight finalists, gold, silver, and bronze medals are awarded. The number of possible ordered outcomes is represented by

The number of distinguishable arrangements of the letters in BANANA is

A game pays $20 with probability 0.15, pays $5 with probability 0.35, and pays $0 otherwise. If it costs $6 to play, the expected net value for the player is

In a class, 18 students take art, 12 take music, and 7 take both. If an art student is selected, the probability that the student also takes music is

A quantity follows V(t) = 500(0.92)ᵗ. The percentage decrease per period is

Relative to y = f(x), the graph of y = f(x − 4) is translated

A water tank is modelled by V(t) = 850 − 24t. In context, −24 represents

A population increases by 6% each year. The multiplicative growth factor is

A least-squares regression model is ŷ = 2.4x + 5. When x = 8, the observed value is 27.7. What is the residual, and what does it indicate?

The vertex of y = 2(x − 3)² − 5 is

A quadratic has zeros −2 and 5 and passes through (0, −20). What is the value of the function at x = 7?

A periodic quantity has maximum 30 and minimum 14. Its amplitude and midline are

A sensor reading ranges from 14 to 30. It reaches a maximum at t = 2 min and the next maximum at t = 14 min. Which model fits the data?

In V(t) = 18 000(0.82)ᵗ, the quantity decreases each period by

The range of y = −2(x + 1)² + 7 is

An exponential function has f(0) = 3 and f(1) = 12. Which equation represents the function?

In a group, 18 people play an instrument, and 12 of those also sing. The conditional probability that a person sings given that the person plays an instrument is

Independent events A and B have probabilities 0.40 and 0.25. The probability that both occur is

“All members of the club submitted a form. Lina submitted a form. Therefore Lina is a club member.” The reasoning is invalid because it

A universal set contains 120 elements and subset A contains 74. Calculate n(A′).

20 people satisfy condition A and 7 satisfy both A and B. Calculate P(B|A) to three decimal places.

An event occurred 18 times in 45 trials. State the experimental odds against the event in simplest form.

A culture begins with 850 cells and grows by 4.7% per hour. Calculate the population after 4 hours to the nearest whole cell.

For f(x) = 2x² − 3x + 1, calculate f(3).

A sinusoidal quantity has maximum 28 and minimum 12. Calculate its midline.

Calculate the number of ordered arrangements of 3 objects selected from 7 distinct objects.

A game pays $8 with probability 0.20 and loses $3 otherwise. Calculate the expected net value, in dollars.

For f(x) = 4x − 7, calculate f(8).

For f(x) = 2.4x + 15, calculate f⁻¹(27) to one decimal place.

An asset worth $20 000 depreciates by 15% annually. Calculate its value after 3 years to the nearest dollar.

In a group of 80 students, 30 study music, 28 study art, and 12 study both. Calculate the probability that a randomly selected student studies neither subject, as a decimal.