Precal PPSGM Review 2025

A transformed cosine function is often used to represent the graph of the height of a person who rides a Ferris wheel with respect to time. f(t) = a cos b(x - c) + d Which of the transformation parameters effects how quickly the ride rotates?

• a

• c

• d

• b

Examine the function given below. Which of the following statements about the function is incorrect?

• The function has been vertically expanded by a scale factor of 2.

• The function has been horizontally shifted left by 1 unit.

• The function has a horizontal asymptote at y = 0.

• The function has a vertical symptote at x = 0.

When an airplane leaves the runway, its angle of climb is 15° and its speed is 300 feet per second. What is the plane’s altitude relative to the runway in feet after 1 minute?

• 4659 feet

• 15938 feet

• 16,500 feet

• 4421 feet

A pendulum swings between AP and AQ. (Refer to the diagram showing triangle ABC with AP and AQ, where AB = AC = 20 cm, ∠B = ∠C = 50°, and the pendulum swings between points P and Q, forming angles α1 and α2 at the base.) Which of the following statements is true about angles α1 and α2?

• Both angles are equivalent, measuring 121.7°.

• Both angles are equivalent, measuring 58.3°.

• Based on the Ambiguous Case of the Law of Sines, α1 and α2 are either acute or obtuse angles whose measures cannot be ascertained.

• The two angles are supplementary; The measure of α1 = 58.3° and the measure of α2 = 121.7°.

Which of the functions indicate a graph that has been vertically expanded by a scale factor of 3?

• y = log(x + 3)

• y = 3 log(x)

• y = log(3x)

• y = log(x) + 3

A spaceship is moving in the plane of the Sun, Moon, and Earth. It is being acted upon by three forces: - The sun pulls with a force of 90 Newtons at 40°. - The moon pulls with a force of 50 Newtons at 110°. - Earth pulls with a force of 50 Newtons at 230°. In what direction will the spaceship move as a result of these forces?

• θ = 73.5°

• θ = 56.7°

• θ = 63.5°

• θ = 82.3°

Examine the graph below. Which of the following represents the inverse of this function?

• 
• 
• 
• 

Answer explanation

In the original graph there is a y-intercept of (0, -4). The inverse would then have an x-intercept of (-4, 0).

A mapping satellite hovers high above the surface of the Earth, taking measurements. Which of the methods below best determines the distance between the two buildings?

Answer explanation

The scenario is SAS which can be solved using the Law of Cosines.

A triangle has side lengths of 8 m, 5 m, and 11 m. Which of the following formulas can be used to determine most efficiently the measure of the largest angle?

• The angle can not be determined without additional information.

Answer explanation

The largest angle will be across from the largest side. For SSS scenarios, solve for the angle using Law of Cosines.