Review 10: Mixed Review
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1 CHCCS MATH II FINAL EXAM REVIEW Review 10: Mixed Review 1. Segment PR has an endpoint at (25, -5) and a midpoint of (18, -1). What is the value of the xcoordinate of the other endpoint? 2. Ruthann is buying a home, and the plot of land is triangular. She would like to have a long property line along the street. The given angle, M, is opposite the road side of the plot of land. The following are angle measures of M for four different properties that Ruthann may choose from. Which property has the longest property line on the street? Plot A: 65 Plot B: 89 Plot C: 68 Plot D: The figure below shows the length of side DC equal to 120 units and the length of side DB equal to 160 units. What is the length of segment AC? A. 120 units B. 160 units C. 240 units D. 320 units 4. Ben has a toy light saber, and he wants to construct one proportionally smaller than his. The light on his is 33 in, and the handle is 9 in. If the light on the smaller version is 11 in, how long should the handle be? A. 3 in B. 4 in C. 4.5 in D. 6 in 5. In the triangle below, what is the approximate value of x? A. 4 in B. 4.5 in C. 4.9 in D. 5.1 in 6. Look at the figure shown at the right. What is the length of Segment AB to the nearest tenth of a meter? 7. Look at the figure. What is the length of side AD? A. 6 cm C cm 8. B. 8.5 cm D. 12 cm Look at the figure. What is the distance, in meters, between point B and point C? A. 200 cos 35 B. 200 tan 35 C. 200/cos35 D. 200/sin35
2 9. The vertices of pentagon LMPQR are at L(4, -2), M(5, -2), P(8, -5), Q(6, -7), R(2, -4). The coordinates of the pentagon after two translations are L1(-5, -1), M1(-4, -1), P1(-1, -4), Q1(-3, -6), R1(-7, -3). How was LMPQR translated to create L1M1P1Q1R1? A. To the left by 9 units and 1 unit up B. To the right by 9 units and 1 unit up C. To the left by 1 unit and 9 units up D. To the right by 1 unit and 9 units up 10. Brennan is making a poster for the drama club s new production. It is a regular pentagon with side lengths of 12 inches. The school wants to put up a giant replica of the poster during athletic events. If the length of each side is 8 times the original, how many times larger is the area of the replica than the area of the original? 11. The toddler section in a park is in the shape of a trapezoid. The parallel sides of the section measure 10 m and 14 m. The distance between the parallel sides is 8 m, as shown below. The section was remodeled to have an area that was 96 square units more than the original area. What change in the dimensions of the trapezoid was made to create the remodeled section? A. The height was doubled. B. The height was multiplied by four. C. The length of the parallel sides and the height were doubled. D. The length of the parallel sides and the height were multiplied by four. 12. Gina has designed two triangular flower beds, as shown. Which statement is true for the two flower beds? A. They have different areas. B. They have the same perimeter. C. The length of side BC is equal to 10 feet. D. The length of side PQ is equal to 10 feet. 13. Gina stores her toys in a container that has a cylindrical body and a conical lid, as shown. She wants to cover the entire exterior portion of the container with paper. How much paper, in square feet, would Gina need? A. 16π B. 20π C. 24π D. 28π 14. Simplify (5x 1) + (10x 2 + 7x) - (2x + 4) A. 10x x 5 B. 10x² + 7x + 3 C. 10x x If (-2x 2 +3x -9) is subtracted from (4x 2-6x +9), the result is: A. 6x 2-3x B. 6x 2-9x + 18 C. 2x 2-9x Find the points of intersection of the circle with the line given their equations: (x - 2) 2 + (y + 3) 2 = 4 and 2x + 2y = The sum of two numbers is 17, and their difference is 7. What are the two numbers?
3 18. The price per person to rent a limousine varies inversely with the number of passengers. It costs $90 each for five people. How many people are renting the limousine when the cost per person is $56.25? 19. The volume, V, of a gas varies inversely as the pressure, p, in a container. If the volume of a gas is 200cc when the pressure is 1.6 liters per square centimeter, find the volume (to the nearest tenth) when the pressure is 2.8 liters per sq centimeter. 20. In science, one theory of life expectancy states that the lifespan of mammals varies inversely to the number of heartbeats per minute of the animal. If a gerbil's heart beats 360 times per minute and lives an average of 3.5 years, what would be the life expectancy of a human with an average of 72 beats per minute? Does this theory appear to hold for humans? 21. John makes DVDs of his friend s shows. He has realized that, because of his fixed costs, his average cost per DVD depends on the number of DVDs he produces. The cost of producing x DVDs is given by C(x)= x. a. John wants to figure out how much to charge his friend for the DVDs. He s not trying to make any money on the venture, but he wants to cover his costs. Suppose John made 100 DVDs. What is the cost of producing this many DVDs? How much is this per DVD? b. John is hoping to make many more than 100 DVDs for his friends. Complete the table showing his costs at different levels of production. # of DVDs ,000 10, ,000 1,000,000 Total Cost Cost per DVD c. Explain why the average cost per DVD levels off. d. Find an equation for the average cost per DVD of producing x DVDs. e. Find the domain of the average cost function. f. Using the data points from your table above, sketch the graph of the average cost function. How does the graph reflect that the average cost levels off? If (2x 3) and (x + 5) are multiplied to form the trinomial ax bx c, what is the value of b? A 2 B 7 C 4 D During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 135 o F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by. What is the approximate domain of minutes for which the machine is hotter than the manufacturer suggests? 24. Graph f(x) = sinx for 0<x<2π 25. Graph f(x) = cosx for 0<x<2π
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5 30. The value of a car can be modeled by V(y) = 25000(0.89) y where V(y) gives the value of the car y years after purchase. a. What was the initial value of the car? b. What is the annual rate of depreciation? c. What is the monthly rate of depreciation? d. Write an equivalent model to highlight the monthly rate of depreciation. 31. Simplify the following expressions: 32. Simplify
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