Chapter 1 Practice Test

Question 1

The given region is the combination of a semicircle with radius 6 cm and a square with side length 12 cm. Find the area of the given region using the formula for the area of a circle, A = πr^2 where r is the circle’s radius, and the formula for the area of a square, A = s^2 where s is the length of a side of the square. Remember, a semicircle’s area is one half the area of the circle with the same radius.

Answer 1

144 + 18π cm^2

Question 2

The formula for the volume of a cone is V=1/3 Bh, where B is the area of the base. Use this formula to find the volume of the given cone.
Hint: The base of the cone is a circle and the formula for the area of a circle is A = πr2, where r is the circle’s radius.

Answer 2

21π ft^3

Question 3

Marjorie’s school is 2 miles away from her house. If she rides her bicycle to school, and it takes her 20 minutes to get to school, what is her average rate of speed in miles per hour?

Answer 3

None of the above

Question 4

An object is dropped from the top of a tall building. At 2 seconds, it is 64 feet from the top of the building. At 4 seconds, it is 256 feet from the top of the building. What is the average rate the object was traveling in the interval between 2 and 4 seconds?

Answer 4

96 ft / s

Question 5

What is the average rate of change of the number of red 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

−5.5 red cars per year

Question 6

A car starts at mile marker 21, and passes mile marker 33 after 20 minutes. It passes mile marker 38 after 23 minutes, and mile marker 42 after 27 minutes. What is the best estimate of the car’s speed in miles per hour when it passes mile marker 40?

Answer 6

60 mi / h

Question 7

ΔF/ΔT=7g/s can be interpreted as:

Answer 7

“The average rate of change of F is equal to 7 grams per second.”

Question 8

Given the graph of f (x), find the best estimate of f (3).

Answer 8

−2

Question 9

If f (x) = 3x^ 2 − 10, which of the following is the new function defined by g (x) = f (x − 1)?

Answer 9

g (x) = 3x^ 2 − 6x − 7

Question 10

Maria’s height from birth to 12 years is modeled by the function h (t) = 0.26t 2 + 22, where t is her age in years, and h (t) is her height in inches. What is Maria’s height when she is 10 years old?

Answer 10

None of the above

Question 11

Find the domain of the function

f(x)=√x+1/x−1.

Answer 11

(− ∞, −1] ∪ (1, ∞)

Question 12

Which equation represents a line that is perpendicular to the given graph and passes through the point (1, 1)?

Answer 12

y=−1/3x+4/3

Question 13

Find the slope of the line passing through the points (1, 1) and (−2, 7).

Answer 13

−2

Question 14

What is the slope of the line defined by

4x−2y+7=0?

Answer 14

m = 2

Question 15

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

Answer 15

f(x)=x^2−2x+2

Question 16

What is the distance between the two points (−1, 4) and (2, 5)?

Answer 16

√10

Question 17

Does the parabola described by the function f(x)=3(x^2−2)−6x^2−(2+x^2) open upwards or downwards?

Answer 17

downwards

Question 18

What is the equation of the line L that passes through the point (−1, 4) and has an angle of inclination of 135°?

Answer 18

y = −x + 3

Question 19

Sketch the parabola of equation y = x 2 − 6x + 9, and indicate its vertex.

Answer 19

right of y-axis, point at (3,0) and (0,9), opens upward

Question 20

What is the range of the function f (x) = 2 sin^2 x − 7?

Answer 20

None of the above