Chapter 1 Test

Question 1

The given region is the combination of a semicircle with radius 2 cm and a right isosceles triangle with base length 4 cm. Find the area of the given region using the formula for the area of a circle, A = πr2 where r is the circle’s radius, and the formula for the area of a triangle, A = bh/2 where b and h are the lengths of the triangle’s base and height, respectively. Remember, a semicircle’s area is one half the area of the circle with the same radius.

Answer 1

8+2π cm^2

Question 2

The formula for the volume of a cone is V=1/3Bh, where B is the area of the base. Use this formula to find the volume of the given cone.

Answer 2

75π ft^3

Question 3

The community center is 4 miles away from George’s house. If he rides his skateboard to the center, and he is traveling at an average rate of 5 miles per hour, how many minutes will it take him to get to the community center?

Answer 3

48 min

Question 4

A projectile is fired straight up into the air. At 1 second, it has reached a height of 1,584 feet. At 4 seconds, it has reached a height of 6,144 feet. What is the average rate the projectile was traveling in the interval between 1 and 4 seconds?

Answer 4

1,520 ft / s

Question 5

What is the average rate of change of the number of Chevy car sales from 1990 to 1992?

Model 	Year 	Color 	Sales
Chevy 	1990 	red 	5
Chevy 	1990 	white 	87
Chevy 	1990 	blue 	62
Chevy 	1991 	red 	54
Chevy 	1991 	white 	95
Chevy 	1991 	blue 	49
Chevy 	1992 	red 	31
Chevy 	1992 	white 	54
Chevy 	1992 	blue 	71
Ford 	1990 	red 	64
Ford 	1990 	white 	62
Ford 	1990 	blue 	63
Ford 	1991 	red 	52
Ford 	1991 	white 	9
Ford 	1991 	blue 	55
Ford 	1992 	red 	27
Ford 	1992 	white 	62
Ford 	1992 	blue 	39

Answer 5

None of the above

Question 6

A caterpillar travels 1 inch during the first 5 minutes it is observed. It travels 1.5 inches during the next 5 minutes. What is the best estimate of the caterpillar’s speed, in inches per second, 7 minutes into its observation?

Answer 6

0.005 in / s

Question 7

ΔV/ΔT=12cm^3/min can be interpreted as:

Answer 7

“The average rate of change of the volume V is equal to 12 cubic centimeters per minute.”

Question 8

Given the graph of g (x), find the best estimate of g (4).

Answer 8

1

Question 9

If g (x) = −2x + 7, which of the following is the new function defined by h (x) = g (2x ^2 + 1)?

Answer 9

h (x) = −4x^ 2 + 5

Question 10

Rob’s height from birth to 15 years is modeled by the function h (t) = 0.24t^  2 + 22, where t is his age in years, and h (t) is his height in inches. At what age is Rob 76 inches tall?

Answer 10

15 years

Question 11

A function is defined as f (x) = x ^2 − 5x + 3. Evaluate f (0).

Answer 11

f (0) = 3

Question 12

Which equation represents a line that is perpendicular to the given graph and passes through the point (2, 0)?

Answer 12

y=−3/2x+3

Question 13

Find the slope of the line passing through the points (−1, 2) and (3, 10).

Answer 13

None of the above

Question 14

What is the slope of the line defined by −3x+6y−5=0?

Answer 14

None of the above

Question 15

Which of the following is the quadratic function whose graph is the parabola shown?

Answer 15

None of the above

Question 16

What is the distance between the two points (1, 5) and (−3, 10)?

Answer 16

√41

Question 17

Does the parabola described by the function f(x)=−2(x^2+7)−4x^2−9(5−x^2) open upwards or downwards?

Answer 17

upwards

Question 18

The graph indicates the regions created by the lines L1, L2, and L3, whose equations are given below.

L1: y + x = 1
L2: x − y = 1
L3: 2y − x = 1

In which region does the point (2, 2) lie?

Answer 18

Region D

Question 19

What is the equation of the line L that passes through the point (−2, 2) and has slope 2?

Answer 19

y = 2x + 6

Question 20

Sketch the parabola of equation

y = −x^ 2 + 4x − 8, and indicate its vertex.

Answer 20

v (2,-4), fourth quadrant