AP Calculus AB: Chapter 1 Test
This content focuses on applying geometric formulas (area of semicircles, triangles, and volume of cones) and understanding average rates of change in various real-world contexts, such as motion, sales trends, and growth models. It reinforces interpreting function notation, unit conversions, and estimating values from graphs and data.
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.
8+2π cm^2
Key Terms
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.
8+2π cm^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.
75π ft^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?
48 min
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?
1,520 ft / s
What is the average rate of change of the number of Chevy car sales from 1990 to 1992?
None of the above
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?
0.005 in / s
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| Term | Definition |
|---|---|
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. | 8+2π cm^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. | 75π ft^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? | 48 min |
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? | 1,520 ft / s |
What is the average rate of change of the number of Chevy car sales from 1990 to 1992? | None of the above |
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? | 0.005 in / s |
ΔV/ΔT=12cm^3/min can be interpreted as: | “The average rate of change of the volume V is equal to 12 cubic centimeters per minute.” |
Given the graph of g (x), find the best estimate of g (4). | 1 |
If g (x) = −2x + 7, which of the following is the new function defined by h (x) = g (2x ^2 + 1)? | h (x) = −4x^ 2 + 5 |
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? | 15 years |
A function is defined as f (x) = x ^2 − 5x + 3. Evaluate f (0) | f (0) = 3 |
Which equation represents a line that is perpendicular to the given graph and passes through the point (2, 0)? | y=−3/2x+3 |
Find the slope of the line passing through the points (−1, 2) and (3, 10). | None of the above |
What is the slope of the line defined by −3x+6y−5=0? | None of the above |
Which of the following is the quadratic function whose graph is the parabola shown? | None of the above |
What is the distance between the two points (1, 5) and (−3, 10)? | √41 |
Does the parabola described by the function f(x)=−2(x^2+7)−4x^2−9(5−x^2) open upwards or downwards? | upwards |
The graph indicates the regions created by the lines L1, L2, and L3, whose equations are given below. L1: y + x = 1 In which region does the point (2, 2) lie? | Region D |
What is the equation of the line L that passes through the point (−2, 2) and has slope 2? | y = 2x + 6 |
Sketch the parabola of equation y = −x^ 2 + 4x − 8, and indicate its vertex. | v (2,-4), fourth quadrant |