1.Write the Following Quadratic Equations in Standard Form and Identify A, B and C

MTH 65 MODULE 4 REVIEW

Name ______

1.Write the following quadratic equations in standard form and identify a, b and c.

a) 5u2 –7 = 3u

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b) -3x2 –2x = 4x + 6

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c) 2x(5x + 7) = 3x - 1______

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2. Solve the following quadratic equations using the quadratic formula. Show your work. If there are no real solutions, say so. If there are real solutions give your answer as exact values. (You may use your calculator to check your solutions.)

a) 2x2 – 3x + 7 = 0______

b) a2 + 5a = -6______

c) 2x2 = 3x + 1______

3. Solve the following quadratic equations by graphing with your calculator. Your answers should be accurate to two decimal places. If there are no real solutions, say so.

a) 0 = x2 - 3x – 3 ______

b) –0.6v2 = 1.3v – 2.4______

c) 11x2 – 12 x + 15 = 0______

4. Solve the following quadratic equations using the square root method. Give your answers as both exact values and, if necessary, approximated to two decimal places. If there are no real solutions, say so. (You may use your calculator to check your solutions.)

a) 2b2 = 18

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b) 3z2 + 18 = 7______

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c) .13x2 = 0.05______

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5. For the following quadratic equations, find the discriminant and use it to determine the number of real solutions the equation will have. Do not find the solutions.

a) 3x + 2 = x2______

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b) 2a2 – 2a + 2 = 0______

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c) 2z2 – 4z + 2 = 0______

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6. The volume of a cylinder is found using the formula V = r2h. If the volume of a cylinder is 342 cubic inches and its height is 5 inches, what is its radius?

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7. The height of an apple falling from a branch 28 feet high can be modeled by the equation h(t) = -16 t2 + 28. Where h(t) is the height of the apple t seconds after it starts to fall from the branch. How long will it take the apple to hit the ground? (Assume the apple will not hit anything on the way down.)

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8. The height of an apple tossed into the air from a height of 5 feet and initial velocity 12 ft/sec is given by the equation h(t) = -16 t2 + 12t + 5. Where h(t) is the height of the apple t seconds after it is tossed in the air. How long will it take the apple to reach a height of 6 feet?

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How many solutions did you find? Explain what this means in terms of the problem.

9. Tina is designing a quilt where a rectangular piece must be 8 and a half inches longer than its width and the area of the rectangle must be 42 square inches. Find the dimensions of the rectangle.

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10. State the Pythagorean theorem.

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11.Find the length of the missing sides of the triangles.

117

a) b)

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12. Is a triangle with sides 7.5, 19.5 and 18 a right triangle? Why or why not?

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13. Will a walking stick 26 inches long fit in a box that is 2 feet by 6 inches? Justify your answer.

14. Find the distance between the pairs of points.

a) (-2, -9) and (3, -7)

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b) (7, -6) and (8, 1)

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15. For the following data sets, find the mean, median and standard deviation.

a) 9.2, 6.7, 7.9, 5.5, 3.3, 2.1, 5.3

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b) 63, 59, 78, 68, 69, 76

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16. The average height of sunflower plants grown by students in a horticulture class is 12.4 feet and the standard deviation is 2.3 feet. Sally’s plant was 12.2 feet tall and Kyle’s was 15.5 feet tall. Use the class mean and standard deviation to discuss how the height of each student’s plant compared to the rest of the class. Be sure to use complete sentences.

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17. Which sides of the triangle are the opposite, adjacent and hypotenuse for angle A?

18. For the following triangle, find the sine, cosine and tangent for both angle A and angle B.

Sin A = _____Sin B = _____

Cos A = _____Cos B = _____

Tan A = _____Tan B = _____

19. Use a calculator to find each ratio to 4 decimal places.

a) sin 23______

b) tan 30______

c) cos 45______

20. A guy wire is attached to the top of a radio antenna and anchored to the ground at a point 7 meters from the base of the antenna. If the wire makes an angle of 75 with the ground, how tall is the antenna? How long is the guy wire?

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