Unit 1 MCQ AP Precalculus Exam Review (1 - 63)

The given graph models Mr. Passwater’s distance from his home over time. Time, in hours, is the independent variable and the distance from home, in miles, is the dependent variable. Which of the following verbal descriptions would be appropriate for the given graph?

• Mr. Passwater leaves school and drives toward his house at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat dinner. After eating dinner, Mr. Passwater leaves and drives until he reaches his house, driving at a constant rate that is faster than the rate he was driving when he first left school.

• Mr. Passwater leaves school and drives toward his house, increasing his speed as he drives. Then, he drives at a constant rate for a period of time. Finally, he increases his speed again and drives until he reaches his home.

• Mr. Passwater leaves his house and drives at a constant rate to a nearby restaurant. After stopping for a period of time to eat lunch, Mr. Passwater drives back to his home at a constant rate that is faster than his rate when driving to the restaurant.

• Mr. Passwater leaves his house and drives to a restaurant at a constant rate. Then, he stops to eat at a restaurant for a period of time to eat breakfast. After eating breakfast, Mr. Passwater leaves and drives until he reaches his school, driving at a constant rate that is faster than the rate he was driving when he first left his house.

Tags

CCSS.HSF.IF.B.4

At time t = 0, water begins pouring into an empty container at a constant rate. The water pours into the container until it is full. As the water begins to pour into the container at a constant rate, the depth of water in the container increases at an increasing rate for a period of time, and then the depth of water increases at a decreasing rate until the container is full. Which of the following containers would be appropriate for the given scenario?

• Container A

• Container B

• Container C

• Container D

Answer explanation

The container narrows then widens, increasing rate to decreasing rate.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.MG.A.1

For his birthday, Mr. Passwater decides to go skydiving. As Mr. Passwater begins falling toward the ground below, the distance he falls increases at an increasing rate until he pulls his parachute. Once his parachute opens, the distance he falls increases at a decreasing rate until he safely lands on the ground. Which of the following graphs could depict this situation, where time, in seconds, is the independent variable and the total distance he has fallen, in feet, is the dependent variable?

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Answer explanation

The distance he falls increases at an increasing rate(concave up), then the distance he falls increases at a decreasing rate(concave down).

Tags

CCSS.HSF.IF.B.4

For his birthday, Mr. Passwater decides to go skydiving. As Mr. Passwater begins falling toward the ground below, the distance he falls increases at an increasing rate until he pulls his parachute. Once his parachute opens, the distance he falls increases at a decreasing rate until he safely lands on the ground. Which of the following graphs could depict this situation, where time, in seconds, is the independent variable and his distance from the ground, in feet, is the dependent variable?

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• 

Answer explanation

The distance to the ground is decreasing and becomes zero. He is approaching the ground at an increasing rate (more negative is concave down) then at a decreasing rate (less negative is concave up)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The figure shows a conical tank with water pouring into it. At t = 0, water begins to pour into the empty tank. The rate that water pours into the tank varies in such a way that the depth of the water inside the tank increases at a constant rate with respect to time. Which of the following graphs could depict this situation, where the depth of the water inside the tank, in feet, is the independent variable and the volume of water inside the tank, in cubic feet, is the dependent variable?

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Answer explanation

The volume increases at a decreasing rate (concave down)

Tags

CCSS.8.EE.B.5

Use the graph of f below for this problem. How many points of inflection does the graph of f have for 0 ≤ x ≤ 9?

• (A) 1

• (B) 2

• (C) 3

• (D) 4

Answer explanation

There are points of inflection at approximately x≈1 (concave down to up), x≈3 (concave up to down) and x≈5 (concave down to up).

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which of the following statements about the graph of f is correct for the interval 7 ≤ x < 9?

• (A) f is positive and increasing.

• (B) f is positive and decreasing.

• (C) f is negative and increasing.

• (D) f is negative and decreasing.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which of the following statements about the graph of f is correct for the interval 1 < x < 3?

• (A) f is increasing at an increasing rate.

• (B) f is increasing at a decreasing rate.

• (C) f is decreasing at an increasing rate.

• (D) f is decreasing at a decreasing rate.

Tags

CCSS.HSF.IF.B.4

Which of the following statements about the graph of f is correct for the interval 0 < x < 1?

• (A) f is increasing and the graph of f is concave up.

• (B) f is increasing and the graph of f is concave down.

• (C) f is decreasing and the graph of f is concave up.

• (D) f is decreasing and the graph of f is concave down.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which of the following statements about the graph of f is correct for the interval 5 < x < 7?

• (A) The rate of change of f is positive and increasing.

• (B) The rate of change of f is positive and decreasing.

• (C) The rate of change of f is negative and increasing.

• (D) The rate of change of f is negative and decreasing.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6