Deck 10: Preparing for Your Math Final

Question 1

Choose the one alternative that best completes the statement or answers the question.

Solve the equation by the zero-factor property.

- = 9

A) { 3}
B) {4}
C) {-3, 3}
D) {-4.5, 4.5}

Answer 1

{-3, 3}

Question 2

Choose the one alternative that best completes the statement or answers the question.

Solve the equation by the zero-factor property.

- + 5 = 41

A) { 6}
B) { 20.5}
C) {-6, 6}
D) {-5, 5}

Answer 2

{-6, 6}

Question 3

Choose the one alternative that best completes the statement or answers the question.

Solve the equation by the zero-factor property.

-4 + 5 = 789

A) {-14, 14}
B) { 14}
C) { 394.5}
D) {-15, 15}

Answer 3

{-14, 14}

Question 4

Solve the equation by using the square root property. Simplify all radicals.

- = 19

A)
B) { 361}
C) {±9.5}
D) { ± }

Question 5

Solve the equation by using the square root property. Simplify all radicals.

- = 54

A) { 18}
B) 6
C) ±6
D) ±3

Question 6

Solve the equation by using the square root property. Simplify all radicals.

- = -121

A)
B) {-11}
C) {-60.5}
D) {± 11}

Question 7

Solve the equation by using the square root property. Simplify all radicals.

- =

A)
B)
C)
D)

Question 8

Solve the equation by using the square root property. Simplify all radicals.

- - 13 = 0

A) ±
B)
C) {±6.5}
D) { 169}

Question 9

Solve the equation by using the square root property. Simplify all radicals.

- = 30. 25

A) {± 5.5}
B)
C) {5.5}
D) {± 6.25}

Question 10

Solve the equation by using the square root property. Simplify all radicals.

-7 = 2

A)
B)
C)
D)

Question 11

Solve the equation by using the square root property. Simplify all radicals.

-3 = 33

A) { 12}
B) { 16.5}
C) ±
D) {± 11}

Question 12

Solve the equation by using the square root property. Simplify all radicals.

-3 = 49

A)
B)
C)
D)

Question 13

Solve the equation. Express radicals in simplest form.

-3 - 432 = 0

A) { 12}
B) {± 12}
C) {± 13}
D) { 217.5}

Question 14

Solve the equation. Express radicals in simplest form.

- + 2 = 146

A) {-11, 11}
B) { 73}
C) { 12}
D) {-12, 12}

Question 15

Solve the equation. Express radicals in simplest form.

-2 - 56 = 0

A) 7
B) 4
C) ± 4
D) ± 2

Question 16

Solve the equation. Express radicals in simplest form.

-3 + 2 = 509

A) { 254.5}
B) {-13, 13}
C) { 13}
D) {-14, 14}

Question 17

Solve the equation. Express radicals in simplest form.

--7 - 15 = -267

A) { 6}
B) {-6, 6}
C) { -133.5}
D) {-12, 12}

Question 18

Solve the equation. Express radicals in simplest form.

-3 - 6 = 58

A) { -11, 5}
B)
C)
D)

Question 19

Solve the equation. Express radicals in simplest form.

-4 - 3 = 4

A)
B)
C)
D) { -9, 5}

Question 20

Solve the equation. Express radicals in simplest form.

-(x - 4)² = 49

A) { 7, -7}
B) { 11, -3}
C) { -3, -11}
D) { 53}

Question 21

Solve the equation. Express radicals in simplest form.

-(r + 6)² = 11

A) { , }
B) {-6 + , -6 - }
C) { 5}
D) { 6 + , 6 - }

Question 22

Solve the equation. Express radicals in simplest form.

-(t + 4)² = -14

A) {-4 + , -4 - }
B) { 10}
C) { 4 + , 4 - }
D)

Question 23

Solve the equation. Express radicals in simplest form.

-(x - 6)² = 40

A) ± 2
B) { ± 6
C) 6 ± 2
D) 6 ± 2

Question 24

Solve the equation. Express radicals in simplest form.

-(2m - 3)² = 121

A) { 7, -4}
B) { 4, -7}
C) { 8, -14}
D) { 14, -8}

Question 25

Solve the equation. Express radicals in simplest form.

-( 4x + 2)² = 36

A) {1, 2}
B) {1, -2}
C) { 10, -10}
D) {0, 1}

Question 26

Solve the equation. Express radicals in simplest form.

- = 23

A)
B)
C)
D)

Question 27

Solve the equation. Express radicals in simplest form.

-(3x + 6)² = 28

A)
B)
C)
D)

Question 28

Solve the equation. Express radicals in simplest form.

-( 5 - 80 = 0

A)
B)
C)
D)

Question 29

Solve the equation. Express radicals in simplest form.

- = 125

A) { -16 + 10 , -16 - 10 }
B) { 10 - 16 , 10 + 16}
C) { , }
D) { 16 + 10 , 16 - 10 }

Question 30

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-(m + 3.84)² = 20.25

A) { 2.54, -6.46}
B) { 0.66, -8.34}
C) { 4.05, -4.05}
D) { 0.66}

Question 31

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-( 2.12m - 7.90)² = 3.57

A) {-2.83, 4.62}
B) { 4.62, -4.62}
C) { 4.62, 2.83}
D) { 3.23, 0.63}

Question 32

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-( 2.03p + 6.11)² = 8.07

A) { 4.41, -1.61}
B) { 0.69, -0.69}
C) { 1.61, -1.61}
D) {-1.61, -4.41}

Question 33

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-If P dollars is invested in an account at an annual interest rate of r, with interest compounded annually, after 2 years the amount A in the account is given by A = P . Use this formula to determine the interest rate if $ 5000 grows to $ 5618 in 2 years, with interest compounded annually.

A) 1.12%
B) 1.06%
C) 0.06%
D) 6%

Question 34

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-The area of a circle is found by the equation A = $\pi$ . If the area A of a certain circle is 9 $\pi$ square centimeters, find its radius r.

A) r = 3 $\pi$ cm
B) r = 3 cm
C) r = 3 cm
D) r = ± 3 cm

Question 35

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-The surface area S of a sphere with radius r is given by the formula If a sphere has surface area square inches, what is its radius?

A) 81 in.
B) 9 $\pi$ in.
C) 9 in.
D) 18 in.

Question 36

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-A construction worker tosses a scrap piece of lumber from the roof of a building. How long does it take the piece of lumber to reach the ground 81 feet below? Use the formula where d is the distance (in feet) a freely falling object falls in t seconds. Give your answer as a fraction.

A) sec
B) sec
C) sec
D) sec

Question 37

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-The distance traveled by a falling object is given by d = 16 , where d is the distance (in feet) the object falls in t seconds. How long would it take an object to fall freely from a bridge above the water? Round your answer to the nearest tenth of a second.

A) 12,673,600.0 sec
B) 7.5 sec
C) 119.3 sec
D) 55.6 sec

Question 38

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-The distance traveled by a falling object is given by d = 16 , where d is the distance (in feet) the object falls in t seconds. A stuntman jumps from a rooftop 330 ft off the ground. How long will it take him, falling freely, to reach the ground? Round your answer to the nearest tenth of a second.

A) 4.5 sec
B) 72.7 sec
C) 10.3 sec
D) 20.6 sec

Question 39

Use a calculator to solve the equation. Round to the nearest hundredth, if necessary.

-A rock falls from a tower that is 73.5 m high. As it is falling, its height is given by the formula How many seconds will it take for the rock to hit the ground Round to the nearest tenth, if necessary.

A) 1102.5 sec
B) 8.3 sec
C) 8.6 sec
D) 3.9 sec

Question 40

Decide whether the statement is true or false. If it is false, tell why.

-If k = 0, then x² = k will have exactly one real solution.

A) False; the equation will have two real solutions.
B) False; the equation will have no real solution.
C) True

Question 41

Decide whether the statement is true or false. If it is false, tell why.

-If k is a positive integer, then x² = k will have one rational and one irrational solution.

A) False; there will be either two rational solutions or two irrational solutions.
B) False; there will always be two rational solutions.
C) True

Question 42

Decide whether the statement is true or false. If it is false, tell why.

-If k is a prime number, then x² = k will have two rational solutions.

A) False; the equation will have no real number solutions.
B) False; the solutions will be irrational because a prime number cannot be a perfect square.
C) True

Question 43

Decide whether the statement is true or false. If it is false, tell why.

-If k is a perfect square, then x² = k will have two integer solutions.

A) False; the equation will have two rational solutions that are not integers.
B) False; the equation will have one integer solution
C) True

Question 44

Decide whether the statement is true or false. If it is false, tell why.

-The equation x² = has two irrational solutions.

A) False; the equation has two integer solutions.
B) True
C) False; the equation has two rational solutions that are not integers.

Question 45

Decide whether the statement is true or false. If it is false, tell why.

-If k is a negative integer, then x² = k will have two irrational solutions.

A) True
B) False; the equation will have no real number solutions.
C) False; the equation will have two rational solutions.

Question 46

Decide whether the statement is true or false. If it is false, tell why.

-The equation -x² = -64 has no real solutions.

A) False; the equation has one real number solution, 8.
B) False; the equation is equivalent to x² = 64 and has two real solutions, 8 and -8.
C) True

Question 47

Decide whether the statement is true or false. If it is false, tell why.

-The equation (x + 7)² = 0 has exactly one real solution.

A) False; the equation has no real solutions.
B) True
C) False; the equation has two real solutions.

Question 48

Decide whether the statement is true or false. If it is false, tell why.

-The equation ( 8x - 3)² = -23 has two real number solutions.

A) False; the equation has no real number solutions.
B) False; the equation has one real number solution.
C) True

Question 49

Decide whether the statement is true or false. If it is false, tell why.

-The equation (x - 3)² - 48 = 0 has two irrational solutions.

A) True
B) False; the equation has exactly one real number solution.
C) False; the equation has two rational solutions.

Question 50

Complete the trinomial so that it is a perfect square.

-x² + 12x +

A) 12
B) 6
C) 144
D) 36

Question 51

Complete the trinomial so that it is a perfect square.

-k² - 10k +

A) -25
B) 5
C) 25
D) 100

Question 52

Complete the trinomial so that it is a perfect square.

- + 5m +

A)
B)
C)
D)

Question 53

Complete the trinomial so that it is a perfect square.

-x² + x +

A)
B)
C)
D) 64

Question 54

Complete the trinomial so that it is a perfect square.

-z² - z +

A)
B)
C)
D)

Question 55

Complete the trinomial so that it is a perfect square.

-x² + x +

A)
B)
C)
D)

Question 56

Solve the equation by completing the square.

-a² - 8a = 20

A) {± }
B) { -18, -2}
C) { -10, 2}
D) { 10, -2}

Question 57

Solve the equation by completing the square.

- + 4x - 1 = 0

A) { 3}
B) { 2 ± }
C) { ± 2}
D) { -2 ± }

Question 58

Solve the equation by completing the square.

-x² + 8x = 3

A) { 4 + }
B) {-1 ± }
C) {-4 ± 2 }
D) {-4 ± }

Question 59

Solve the equation by completing the square.

-z² + 18z + 60 = 0

A) { 9 + }
B) {-9 ± }
C) {-18 + }
D) { 9 ± }

Question 60

Solve the equation by completing the square.

- + 8x - 24
= 0

A) {2 ± 4}
B) {-4 ± 2 }
C) { ± 2 }
D) {-4 ± 2 }

Question 61

Solve the equation by completing the square.

- + 14x = -5

A) {-7 ± 2 }
B) {-7 ± 2 }
C) {2 ± 7}
D) {± 2 }

Question 62

Solve the equation by completing the square.

-x² + 19 = -12x

A) {-12 + }
B) { 6 ± }
C) {-6 ± }
D) { 6 + }

Question 63

Solve the equation by completing the square.

-p² + 3p - 9 = 0

A)
B)
C)
D) {-3 ± 3 }

Question 64

Solve the equation by completing the square.

- - 16m + 64 = 0

A) { 16}
B) {± 8}
C) {-8}
D) { 8}

Question 65

Solve the equation by completing the square.

- + 16k + 64 = 0

A) {± 8}
B) {-16}
C) { 8}
D) {-8}

Question 66

Solve the equation by completing the square.

- + 2x - 3 = 0

A)
B)
C)
D)

Question 67

Solve the equation by completing the square.

-6x² + 10x + 3 = 0

A)
B)
C)
D)

Question 68

Solve the equation by completing the square.

-2 - 2t + 9 = 0

A)
B)
C)
D) ?

Question 69

Solve the equation by completing the square.

-6x² + 10x = - 1

A)
B)
C)
D)

Question 70

Solve the equation by completing the square.

-(x + 1)(x - 4) = 6

A) {-2 ± }
B) {-5, 2}
C) { 5 ± }
D) {-2, 5}

Question 71

Solve the equation by completing the square.

-(x - 9)(x - 1) = 12

A) { -5 - , -5 + }
B) { 5 - 2 , 5 + 2 }
C) { -5 - 2 , -5 + 2 }
D) { 5 - , 5 + }

Question 72

Solve the equation by completing the square.

-(x + 6)(x - 3) = 3

A)
B)
C)
D)

Question 73

Solve the equation by completing the square.

- + 2x = -1

A) {-1 ± }
B)
C) {1 ± }
D) {1, 2}

Question 74

Solve the equation by completing the square.

-7 - 2x - 2 = 0

A)
B)
C)
D)

Question 75

Solve the equation by completing the square.

-z5 = 2 - 18

A)
B)
C)
D)

Question 76

Solve the equation by completing the square.

-16d² + 32d + 15 = 0

A)
B)
C)
D)

Question 77

Solve the equation by completing the square. Then (i) give the exact solutions and (ii) give the solutions rounded to the nearest thousandth.

-x² = 3 - 8x

A) (i) {-4 ± 2 } (ii) { 4.718}
B) (i) {-4 ± } (ii) { 0.359, -8.359}
C) (i) {-1 ± } (ii) { 3.359, -5.359}
D) (i) { 4 + } (ii) { 8.359}

Question 78

Solve the equation by completing the square. Then (i) give the exact solutions and (ii) give the solutions rounded to the nearest thousandth.

-( 9t + 6)² = 19

A) (i) {-6 ± } (ii) { -1.641, -10.359}
B) (i) (ii) { 0.401, -0.401}
C) (i) (ii) { 1.067}
D) (i) (ii) { -0.182, -1.151}

Question 79

Solve the equation by completing the square. Then (i) give the exact solutions and (ii) give the solutions rounded to the nearest thousandth.

-2 + 3x = 1 + 5x

A) (i) (ii) { 0.366, -1.366}
B) (i) {-1 ± } (ii) { 0.732, -2.732}
C) (i) (ii) { 1.366, -0.366}
D) (i) { 1 ± } (ii) { 2.732, -0.732}

Question 80

Solve the problem.

-A ball is thrown vertically upward from the top of a building 96 feet tall with an initial velocity of 80 feet per second. The height, s (in feet), of the ball after t seconds is givenby After how many seconds does the ball strike the ground?

A) 97 sec
B) 5 sec
C) 6 sec
D) 8 sec