AP Calculus AB: Chapter 1 Practice Test
This content blends geometry and real-world rate problems, covering area and volume formulas (like those for semicircles, squares, and cones), and interpreting average rates of change from data and graphs. It includes practical examples involving speed, falling objects, and sales data to strengthen understanding of algebraic and geometric applications.
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.
144 + 18π cm^2
Key Terms
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.
144 + 18π cm^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.
21π ft^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?
None of the above
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?
96 ft / s
What is the average rate of change of the number of red car sales from 1990 to 1992?
−5.5 red cars per year
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?
60 mi / h
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| Term | Definition |
|---|---|
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. | 144 + 18π cm^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. | 21π ft^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? | None of the above |
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? | 96 ft / s |
What is the average rate of change of the number of red car sales from 1990 to 1992? | −5.5 red cars per year |
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? | 60 mi / h |
ΔF/ΔT=7g/s can be interpreted as: | “The average rate of change of F is equal to 7 grams per second.” |
| −2 |
If f (x) = 3x^ 2 − 10, which of the following is the new function defined by g (x) = f (x − 1)? | g (x) = 3x^ 2 − 6x − 7 |
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? | None of the above |
Find the domain of the function f(x)=√x+1/x−1. | (− ∞, −1] ∪ (1, ∞) |
Which equation represents a line that is perpendicular to the given graph and passes through the point (1, 1)? | y=−1/3x+4/3 |
Find the slope of the line passing through the points (1, 1) and (−2, 7). | −2 |
What is the slope of the line defined by 4x−2y+7=0? | m = 2 |
Which of the following is the quadratic function whose graph is the parabola shown? | f(x)=x^2−2x+2 |
What is the distance between the two points (−1, 4) and (2, 5)? | √10 |
Does the parabola described by the function f(x)=3(x^2−2)−6x^2−(2+x^2) open upwards or downwards? | downwards |
What is the equation of the line L that passes through the point (−1, 4) and has an angle of inclination of 135°? | y = −x + 3 |
Sketch the parabola of equation y = x 2 − 6x + 9, and indicate its vertex. | right of y-axis, point at (3,0) and (0,9), opens upward |
What is the range of the function f (x) = 2 sin^2 x − 7? | None of the above |