Precalculus Review - Spring 018 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. Assume that variables represent nonzero real numbers. 1) (x ) x 15 1) 7 7 x 1 B) x 10 C) x 9 D) 7 x 9 ) (-x y -5 )(x -1 y) ) -8x5 y 6 B) -x y C) -8x y D) -8x y 6 ) xy 5 x y - ) 1 x 8 y 1 B) x y 8 C) 1 x 5 y 11 D) y8 x ) 1x -5 y - z xy - z - -1 ) x z 8 B) x 6 z 8 C) x6 z 8 D) x6 y 6 z 8 Use the quotient rule to simplify the expression. 5x 5) 6x 5) 6x B) x 6 C) x 6 D) x 6) 56x x x x B) 56x C) x 7x D) x 56 6) Find the product. 7) (x - 9)(x + ) 7) x - 7x - 7 B) x - 7x - 6 C) x - 6x - 6 D) x - 6x - 7 8) (x + 9)(9x + 11) 8) 18x + 10x + 10 B) 18x + 10x + 99 C) 11x + 10x + 99 D) 11x + 10x + 10 1
9) (7x - 6)(x - ) 9) 7x 6-1x - 6x + 1 B) 7x 5-0x + 1 C) 7x 5-0x + 1 D) 7x 5-1x - 6x + 1 10) (x + 1)(x - 8) 10) x - 15x - 8 B) x - 15x - 16 C) x - 16x - 8 D) x - 8x - 15 Solve the problem. 11) Write a polynomial in standard form that represents the volume of the open box. 11) x 1 - x - x x - x + 8x B) x - x + 8 C) x + x + 8x D) x - x + 8x 1) Write a polynomial in standard form that represents the area of the shaded region. 1) x + 9 x + x + x + 1-7x - B) 7x + C) x + x + D) 17x + 1 Factor the trinomial, or state that the trinomial is prime. 1) x - 6x + 8 1) (x + )(x + 1) B) (x - )(x - ) C) (x + )(x - ) D) prime 1) x + 5x - 1) (x - 8)(x + 1) B) (x + 8)(x - ) C) (x - 8)(x + ) D) prime 15) 7x + 7x + 6 15) (7x + 9)(x + ) B) (7x + 9)(7x + ) C) (7x + )(x + 9) D) prime 16) 5x - 7xy - 18y 16) y(5x + )(x - 6) B) (5x + 6y)(x - y) C) (5x + y)(x - 6y) D) prime
17) 1x + 17xy + 6y 17) (x - y)(x - y) B) (1x + y)(x + y) C) (x + y)(x + y) D) prime Multiply or divide as indicated. 5x 18) 10x + 5 6x + 18) x B) C) x 10 D) x 19) 6x - x - x - 18x - 6 19) x - 6(x + ) B) 1 6 C) 1 D) 6 0) x + 1 9x x - x + x -5x - 5 0) - 1 5 B) - x + 1 5 C) - x + 1 5(x + 1) D) x + 1 5(-x - 1) 1) x + 15x + 56 x + x - 56 x - 6 x - x - 56 1) x + 7 x - 8 B) x - 8 x + 7 C) x - 8 x - 7 D) x + 8 x - 7 Add or subtract as indicated. ) x + 1 x + + x + 7 x + x + B) 1 C) D) x + 5 x + ) ) x - 9x x - 6 + 18 x - 6 ) x + B) x - 9x + 18 x - 6 C) x - D) x - 6 ) x - 1 x + - x - 0 x - x - x - 0 ) x - x - 8 B) ( x - 5)( x + ) ( x + 5)( x - 8) C) x - x - x - 0 D) x + 5 x - 8 Solve the equation by the square root property. 5) (x - 1) = 11 5) {-10, 1} B) {-6, 5} C) {-5, 6} D) {-1, 10}
6) (x - ) = 1 6) {-10, } B) {- ± 6} C) { ± 6} D) {-, 10} 7) (5x - 6) = 1 7) -6 -, -6 + 5 5 C) {- 5, 5} D) B) - 6 5, 18 5 6 -, 6 + 5 5 Solve the equation using the quadratic formula. 8) x + 10x + 5 = 0 8) C) -5-15 -5 + 15, -10-15, -10 + 15 B) D) -5-5 -5-15,, -5 + 5-5 + 15 9) x = -10x - 1 9) C) -5 - -10 -,, -5 + -10 + B) D) -5 - -5 -, -5 +, -5 + Solve the problem. 0) A ladder that is 1 feet long is 5 feet from the base of a wall. How far up the wall does the ladder reach? ft B) 1 ft C) 19 ft D) 1 ft 0) 1) The revenue for a small company is given by the quadratic function r(t) = 9t + 1t + 50 where t is the number of years since 1998 and r(t) is in thousands of dollars. If this trend continues, find the year after 1998 in which the company's revenue will be $60 thousand. Round to the nearest whole year. 00 B) 001 C) 00 D) 00 ) The length of a rectangular storage room is feet longer than its width. If the area of the room is 88 square feet, find its dimensions. 7 feet by 10 feet B) 7 feet by 1 feet C) 8 feet by 11 feet D) 9 feet by 1 feet 1) )
) Suppose that an open box is to be made from a square sheet of cardboard by cutting out -inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 6 cubic inches, find the original dimensions of the sheet of cardboard. ) in. by in. B) 6 in. by 6 in. C) in. by in. D) 11 in. by 11 in. Use graphs to find the set. ) (-8, 0) [-, 8] ) [-, 0) B) (-8, -] C) (0, 8] D) (-8, 8] 5) (-, 8) [-, 19) 5) [-, 8) B) (-, 19) C) (-, -] D) (8, 19) 6) (-, ) [-, 19) 6) (-, -] B) (-, 19) C) (, 19) D) [-, ) Solve the linear inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 7) 7x - > 6x - 8 7) (-6, ) B) (-, -6] C) [-6, ) D) (-10, ) 5
8) -x + 6 -x + 8 8) (-, ] B) [, ) C) (-, ) D) (1, ) 9) -0x - -(x + ) 9) [1, ) B) (1, ) C) (-, 1] D) (-, 1) Use interval notation to represent all values of x satisfying the given conditions. 0) y1 = 8x -, y = 7x +, and y1 > y. 0) (, ) B) (6, ) C) [6, ) D) (-, 6] Solve the problem. 1) Claire has received scores of 85, 88, 87, and 80 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 8? 68 or greater B) 69 or greater C) 70 or greater D) 71 or greater 1) 6
) Using data from 1996-1998, the annual number of cars sold at a certain dealership can be modeled by the formula y = x + 1, where y is the number of cars, in thousands, sold x years after 1996. According to this formula, in which years will the number of cars sold exceed 15 thousand? Years after 001 B) Years after 007 C) Years after 005 D) Years after 00 ) Solve the compound inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. ) -5 < x + 6 ) [-, 9) B) (-, 9] C) [-8, ) D) (-8, ] ) -6-5x - 1 < -1 ) (-5, -] B) (, 5] C) [-5, -) D) [, 5) Solve the problem. 5) On the first four exams, your grades are 76, 78, 7, and 77. You are hoping to earn a C in the course. This will occur if the average of your five exam grades is greater than or equal to 70 and less than 80. What range of grades on the fifth exam will result in earning a C? [6, 96) B) (6, 96] C) (6, 86] D) [6, 86) 6) On the first four exams, your grades are 76, 91, 60, and 77. There is still a final exam, and it counts as two grades. You are hoping to earn a C in the course. This will occur if the average of your six exam grades is greater than or equal to 70 and less than 80. What range of grades on the final exam will result in earning a C? [58, 88) B) [6, 96] C) [58, 88] D) [6, 96) 5) 6) 7
Solve the absolute value inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 7) x - 1 < 0 7) (-, 1) B) (-1, ) C) (-1, 1) D) 8) x + < 7 8) (-, -10) (, ) B) C) (-10, ) D) [-10, ] 8
9) x + 6-5 1 9) (-, -1] [0, ) B) [-1, 1] C) (-1, 0) D) [-1, 0] 50) 7y + 1 < 7 50) (-, -6) (6, ) B) (-, -6) (0, ) C) (-6, 6) D) (-6, 0) Evaluate the piecewise function at the given value of the independent variable. 51) f(x) = x + if x < ; f() 51) 5x + if x 18 B) 17 C) 1 D) 0 5) h(x) = x - 7 x + 6 if x -6 ; h(-6) 5) x - if x = -6-8 B) undefined C) 8 D) - 5) f(x) = x - if x > -1 ; f(-) 5) -(x - ) if x -1 - B) 17 C) D) - Graph the function. 9
5) f(x) = x + 1 if x < 1 if x 1 5) B) C) D) 10
55) f(x) = x + if -8 x < -9 if x = -x + 7 if x > 55) B) C) D) 11
Based on the graph, find the range of y = f(x). if -6 x < - 56) f(x) = x if - x < 8 x if 8 x 1 56) [0, 1] B) [0, ) C) [0, 8) D) [0, 8] Find and simplify the difference quotient f(x + h) - f(x), h 0 for the given function. h 57) f(x) = x - 7 57) 6(x - 7) 0 B) + C) + -1 D) h h 58) f(x) = 9 58) 1 + 18 B) 0 C) 1 D) 9 h 59) f(x) = x 59) (x + xh + h ) h B) C) (x+h) D) 6 h + x + h 60) f(x) = 1 5x 60) 0 B) -1 x (x + h) C) 1 5x D) -1 5x (x + h) 1
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 61) (x - 7)(x + ) > 0 61) (-, -7) (, ) B) (-, ) C) (-, -) (7, ) D) (-, 7) 6) (x + 7)(x - ) 0 6) (-, -7] [, ) B) [-7, ] C) (-, -7) (, ) D) (-7, ) 1
6) x - x - 1 0 6) (-, -] B) (-, -] [6, ) C) [6, ) D) [-, 6] 6) x + 11x + 0 0 6) [-6, -5] B) (-, -6] C) (-, -6] [-5, ) D) [-5, ) 1
65) (x + 5)(x + )(x - ) > 0 65) (-, -) B) (-5, -) (, ) C) (-, -5) (-, ) D) (, ) 66) 18x < 17x + 1 66) -, - 1 18 (1, ) B) (-, -1) 1 18, C) -1, 1 18 D) - 1 18, 1 15
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 67) x - x + 1 < 0 67) (-, -1) B) (-, -1) or (, ) C) (, ) D) (-1, ) 68) -x + x - 0 68) (, ] B) (-, ) or [, ) C) (-, ] D) [, ] 69) 15 - x 6x + 1 0 69) [5, ) B) - 1 6, 5 C) -, - 1 6 or [5, ) D) -, - 1 6 or [5, ) 16
(x + 7)(x - 5) 70) 0 70) x - 1 [-7, 1] [5, ) B) [-7, 1) [5, ) C) (-, -7] [5, ) D) (-, -7] (1, 5] 17
Graph the function by making a table of coordinates. 71) f(x) = x 71) B) C) D) 18
7) f(x) = 1 x 7) B) C) D) Write the equation in its equivalent exponential form. 7) log 5 5 = 7) 5 = 5 B) 55 = C) 5 = 5 D) 5 = 5 7) log b 6 = 7) 6 = b B) 6 b = C) b = 6 D) b = 6 19
Write the equation in its equivalent logarithmic form. 75) 6 = 16 75) log 6 16 = B) log 6 = 16 C) log 16 6 = D) log 16 = 6 76) 7 = x 76) log x 7 = B) log 7 x = C) log 7 = x D) log x = 7 Evaluate the expression without using a calculator. 77) log 5 15 77) 1 B) 15 C) D) 1 78) log 10 10,000 78) 1 10000 B) 0 C) D) - 79) log 11 11 79) 11 B) 1 C) 1 11 D) 1 80) log 1 80) - 1 B) 1 C) - 1 D) 1 Convert the angle in degrees to radians. Express answer as a multiple of. 81) 0 81) 6 radians B) 5 radians C) 7 radians D) 8 radians 8) - 150 8) - 5 6 radians B) - radians C) - 6 7 radians D) - 5 radians Convert the angle in radians to degrees. 8) - 8) -5 B) -5 C) - D) -1 8) 19 8) 6 10 B) 570 C) 110 D) 85 0
Use the Pythagorean Theorem to find the length of the missing side.then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. 85) Find sin. 85) 1 5 B) 1 5 C) 1 1 D) 5 1 1 86) Find cos. 86) 7 10 19 7 B) 19 10 C) 10 19 19 D) 7 19 19 87) Find tan. 7 87) 5 7 7 B) 7 5 C) 7 5 D) 5 7 1
Use the given triangles to evaluate the expression. Rationalize all denominators. 88) tan 0 88) 1 B) C) D) 89) cot 6 89) B) C) D) 1 90) tan 90) B) C) D) 91) tan 5 - sin 60 91) - 6 B) - C) - D) - 6 9) cot - cos 6 9) - 6 B) - 6 C) D) - 6 is an acute angle and sin and cos are given. Use identities to find the indicated value. 9) sin = 5 7 6, cos =. Find tan. 9) 7 5 6 5 B) 7 5 C) 5 6 1 D) 7 6 1 9) sin = - 11 6, cos = 5. Find cot. 9) 6-6 11 11 B) 6 5 C) 11 5 D) -5 11 11
is an acute angle and sin is given. Use the Pythagorean identity sin + cos = 1 to find cos. 95) sin = 1 95) 15 B) C) 15 15 D) 15 15 Complete the identity. 1 96) sec x - sec x =? 96) 1 + cot x B) - tan x C) sin x tan x D) sec x csc x 97) sin x cos x + cos x sin x =? 97) 1 + cot x B) sin x tan x C) - tan x D) sec x csc x 98) sin x + sin x cot x =? 98) sin x + 1 B) cot x + 1 C) cot x - 1 D) 1 Find the exact value by using a sum or difference identity. 99) cos (5 + 60 ) 99) - ( - 1) B) ( + 1) C) ( - 1) D) - ( + 1) Find the exact value of the expression. 100) cos 18 sin 9 - cos sin 9 18 100) 1 B) C) 1 D) 1