TSI College Level Math Practice Test

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1 TSI College Level Math Practice Test Tutorial Services Mission del Paso Campus. Factor the Following Polynomials 4 a. 6 8 b. c. 7 d. ab + a + b + 6 e. 9 f Perform the indicated operation a. ( +7y) + (4 + 7) + (y ) d. (4 6y + 9y ) (8 6y - y ) yb b. ( -4)( + 9) e. 7 9y c. (-a + 4b) f Simplify the following Epressions a. ( 7) 4 c b. 6 d Solve Each Linear Equation a. ( + ) = + c. P = L + W solve for W m 4 m b. d. 4. Solve each word problem a. Maria rode her bicycle at an average speed of 8 mph on level roads and then slowed down to 0mph on the hilly roads of the trip. The entire trip covered 98 miles. How long did the entire trip take if traveling the level roads took the same time as traveling the hilly roads? {Remember, d = r t } b. The bottom of Jim s backpack contains 0 coins in nickels and dimes. If the coins have a total value of $.8, find the number of each type of coin. c. The sum of three consecutive integers is more than twice the smallest integer. Find the integers. d. Laura invested $4,000 in two accounts: a mutual fund paying 8% annual interest and a CD paying 9% annual interest. If her annual interest was $,00 how much did she invest in each account? Saved C: Accuplacer College Level Math Assessment Page of 7

2 6. Solve the Following Quadratic Equations a. m m 6 0 b. ( + )( ) = c. 8 d Solve the following Radical Equations a. 9 b. c. 4 d. 8. Rational Epressions: Perform the indicated operation 4 a. b c. a 9 a a 6 a a 6 a 6 d. a 4a 8 a a 9. Rational Epressions: Solve the following equations a. 6 a c. 6 4 d. 0. Solve the following absolute value equations a. b. c. 7 d. 8. Eponents & Radicals: Simplify 49 a. b. 4 c. 8a b d. 6. Eponents & Radical: Perform the indicated operation a. 4 b. 6 c. 8 y y d. 8 Saved C: Accuplacer College Level Math Assessment Page of 7

3 . Imaginary Numbers (i): Perform the indicated operation a. 4 b. (4-7i) + ( + i) c. 6i( i) d. ( i)( i) 7 8 e. f. i g. (7i)(-9i) h. (6 - i)( + i) 4 i 4. Simplify the following comple fractions. a. b. c. d.. Functions: Perform the indicated operation Let f() = and let g() = a. (f + g)() b. (f g)() c. (f g)() d. f () g 6. Functions: Find the following Let f() = and let g() = + a. ( f g)( ) b. ( g f )() 7. Sequence & Series: Evaluate 6 i a. i0 b. i i c. Find the sum of the first si terms of the arithmetic sequence,, 8,, 4, 7 n S n ( a an ) d. Find the sum of the first si terms of the geometric sequence, 0, 0, 40, 80, 60 n a r S n ( ) r 8. Logarithmic & Eponential Functions: Perform the indicated operation a. Find the inverse of the given function f() = 6 + b. Find the inverse of the given function f() = 4 c. Solve: 4 = 64 d. Solve: 9 e. Solve: log ( ) 4 f. Write the equation using logarithmic notation: 49 = 7 g. Write the equation using eponential notation: log 6 4 h. Write as a single log: log 8 log 4 i. Write as a sum, difference, or multiple: j. Solve: ln () = Saved C: Accuplacer College Level Math Assessment Page of 7 log

4 9. Solve the following inequalities a. + < 8 c. < 4 < 7 b. d. - < 6 0. Graphing Linear Equations: Perform the indicated operation a. Find the slope of the line containing the following points (, ) (8, ) b. Find the equation of the line for the given points (, ) (-, 4) and graph c. Find the equation of the line through (, 8) and parallel to y = 4 d. Write the equation of the following line, vertical through (, 6) e. Write the equation of the following line, horizontal through (0, ) f. Find the and y intercepts and the slope of the following equation 6 + y = 0. Which equation is represented by this graph? a. y > b. y + c. y + d. y +. Graphing Relations, Domain & Range: For the following relation: f() = a. State if it is a function b. State the domain and range c. Graph it. Find the Verte, and the -intercepts a. y = -( ) - c. y = ( + ) + b. y = + 4 d. y = - 4. Identify the conic section and put in standard form a. Find the equation of the circle with center (-7, ) and radius 0 b. Write in standard form y 4 8y 6 Saved C: Accuplacer College Level Math Assessment Page 4 of 7

5 . Systems of Equations and Matrices: Perform the indicated operation y z 8 y 4 0 a. Solve the system b. Solve the system y z 0 y y z 0 c. Multiply d. Find the determinant: e. Find the inverse f. Perform the indicated operation: 6 6. Use the graph below to answer the question that follows. Which of the following equations represents line AB? A. y = + B. y = + C. y = + D. y = + 7. Use the graph below to answer the question that follows. Which of the following inequalities describes the shaded region? A. y < 4 B. C. y 4 D. y 4 Saved C: Accuplacer College Level Math Assessment Page of 7

6 8. Which of the following graphs shows the solution of y + + = 0 and y = A. B. C. D. 9. Use the diagram below to answer the question that follows. A window is rectangular with a triangular top section. What is the total area of glass needed for the window? A. 4 square feet B. 0 square feet C. 6 square feet D. 48 square feet Saved C: Accuplacer College Level Math Assessment Page 6 of 7

7 0. Use the diagram below to answer the question that follows. The drawing above represents a race track. The ends are semicircular. What is the approimate distance in meters a runner runs in 8 laps around the track? A. 60 m B m C m D. 70 m. An observatory dome is hemispherical in shape with a radius of 8 meters and is built using equal sections. Which of the following formulas describes the surface area of each section? A. B. C. D.. Use the diagram below to answer the question that follows. A ramp feet long is leaning against a raised platform which is feet above the ground. What is the distance from the ramp's contact point with the ground and the base of the platform? A. 7 feet B. 8. feet C. feet D. feet. Figure ABCDE is similar to figure FGHIJ. If AE =, FJ = 0, and BC = 40, what is GH? A. 0 B. C. 4 D If pentagon ABCDE is similar to pentagon GHIDF, and DI = 0, CD = 0, and DE = 4, what is DF? A.. B. C. 8 D. Saved C: Accuplacer College Level Math Assessment Page 7 of 7

8 . Use the diagram below to answer the question that follows. Line AB is parallel to line CD. What is the sum of the measure of angle k and the measure of angle y? A. 90 B. 00 C. 80 D Use the diagram below to answer the question that follows. If ABD is an equilateral triangle, and line BD is parallel to line CE, what is the measure of angle? A. 60 B. 90 C. 0 D Use the diagram below to answer the question that follows. A rectangular bo has dimensions feet feet feet. What is the length of the longest object that can be put in the bo, if the object can be placed in any position? A..6 feet B..9 feet C. 6. feet D.. feet Saved C: Accuplacer College Level Math Assessment Page 8 of 7

9 8. Use the pie charts below to answer the question that follows. The first pie chart represents a company's ependitures, and the second pie chart shows a breakdown of the company's advertising ependitures. What percent of the company's ependitures is spent on radio advertising? A. 6.% B..7% C. 8.0% D..0% 9. The SINE of angle B is? A a. BC AC b. AC AB c. AB BC d. AB AC C B 40. Which equation is represented by this graph? a. y > b. y > c. y d. y + 4 Saved C: Accuplacer College Level Math Assessment Page 9 of 7

10 Graphing Formulas Slope-Intercept y = m + b slope y-intercept Point-Slope y - y = m( - ) Two-Point Formula y y For finding the equation of the line {You can use this formula, when you don t Know the slope, to find the equation of the line} y y Slope-Formula m = y - y - ( ) Standard Form a + by = c of a linear equation y-intercept = c Slope = -a b b Standard Form of a + b + c = 0 or f() = a( - h) + k a quadratic equation where (h,k) is the verte Quadratic Formula = -b b - 4ac a Verte Formula = -b a Circle Formula ( - h) + (y - k) = r where (h,k) is the center and (,y) is any point on the circle Midpoint Formula y +y, Distance Formula d = ( - ) (y - y ) Saved C: Accuplacer College Level Math Assessment Page 0 of 7

11 Geometric Figures & Formulas Square Area = Perimeter = 4s Rectangle Area = w Perimeter = + w Triangle Area = bh Right triangle Pythagorean formula: Circle Area = Circumference = Diameter = r r Sphere Surface area = 4 Volume = Cube Surface area = Volume = Rectangular solid Surface area = w + h + wh Volume = wh Right circular cylinder Surface area = rh + Volume = h Saved C: Geometric Figures Microsoftword Saved C: Accuplacer College Level Math Assessment Page of 7

12 BASIC ALGEBRA RULES Order of Division Multiplication & Division Addition & Subtraction Order of Operations a (-)(+) = - b = a b = b a (-)(-) = + (+) (-) = - (-) (+) = = + 8 = 8 + = +8 = + P (innermost) E (eponents) M & D (left right) A & S (left right) a + 0 = a Addition by zero identity a + b = b + a Commutative property of addition (a + b) + c = a + (b + c) Associate property of addition a + (-a) = -a + a = 0 Inverse property of addition a 0 = 0 a = 0 Multiplication by zero identity a = a = a Multiplication by one identity a b = b a Commutative property of multiplication a a = a a = = Multiplicative inverse (reciprocal) (a b) c = a (b c) Associate property of multiplication Eponent Rules 6 ( ) 0 a = 0 a a = a 0 = undefined a = a = a b = a b ab = a b a = aa = a > < X X X = = = 4 = 8 = 9 = = = 64 = = = = = = = = = = = = 000 = = = 44 = 78 = 69 = = = 744 = = 7 Saved C: Accuplacer College Level Math Assessment Page of 7

13 ANSWER KEY. Factor the following Polynomials {p. 0 #, } & {p.8 #,,} & {p.6 EX# } Sum of Two Cubes Difference of Two Cubes ( a b )( a ab b ) ( a b )( a ab b ) a. ( 4 ) b. ( )( + ) c. ( + )( + 9) d. (a + )(b + ) e. ( - )( + ) f. ( + )( + ) a. Perform the indicated operation {p.96 #48, 49, 6, 6, 8, 8} a. 4 8y 6 d. 4 0y b. 6 e. b 6 y 4 9 c. 9 a 4ab 6b f Simplify the following Epressions { p. #, 7} &{p.7 #9, 4} a. 48 c. 4 b. - d. 4. Solve each linear equation {p.6 #8,, 6} & {p.44 #} a. {-} c. w = p b. /6 d. {-8}. Solve each word problem {p.48 E#, 4} & {p. #, } & {p.8 #49} a. distance level distance + hilly distance 98 = = b. money in nickels + money in dimes = total money (0 ) =.8 = {number of nickels} c. + ( + ) + ( + ) = + = 0 d. $4,000 at 8% and $0,000 at 9% 6. Solve the following Quadratic Equations {p.8 #, 7, 6, } a. {-6, } b. {, - + } c. {-0, } d , 7. Solve the following Radical Equations {p.6 EX#,, 4, } a. = 4 b. = -9 c. = d. = /9 Saved C: Accuplacer College Level Math Assessment Page of 7

14 ANSWER KEY 8. Rational Epressions: Perform the indicated operation {p.80 #47, 0,, 7} 0 a. b. ( )( ) c. a 4a a d. a 8 4aa ( ) 9. Rational Epressions: Solve the following equations {p.79#,,, 7} a. = 7 b. = - c. = d. = - 0. Solve the following absolute value equations {p.6 EX#, 4, 7, 8} a. {4, -0} b. The absolute value of any epression is never negative. c. {-, } d. {/4, }. Eponentials & Radicals: Simplify the following epressions {p.4 #, 49, 64, 87} a. 4 b. 7 c. ab 7 d.. Eponents & Radicals: Perform the indicated operation {p.6 #4, 8} & {p.0 #, 6} a. 0 b. c. y y d Imaginary Numbers (i): Perform the indicated operation {p.7#, 9,, 8,, 7, 4, 49} Note: to simplify imaginary eponents use the chart below. Remainder = Answer 0 = = i = - = -i Step Divide the eponent by 4 Step The remainder gives you the answer. a. i 6 b. 6 4i c. 8 + i d. 0 8 e. i f. g. 6 h Simplify the following comple fractions {purplemath.com} a. 4 b. y c. 4 t d. t. Functions: Perform the indicated operation {p. 90 E# } a. 4 b. c. - + d. all real numbers ecept 6. Functions: Find the Following {p.9 EX# 4} a. b. Saved C: Accuplacer College Level Math Assessment Page 4 of 7

15 The linked image cannot be displayed. The file may have been moved, renamed, or deleted. Verify that the link points to the correct file and location. 7. Sequence & Series: Evaluate {p. E#} & {p.9 E# } & {p. EX#4} 6 i a. = 0 4 i0 Answer Key 6 = ( ) = 7 0 b. i i 4 = = = 6 n c. S n ( a an ) = ( ) ( ) d. S n a( r r n 6 ) ( ) ( 6) = S 6 8. Logarithmic & Eponential Functions: Perform the indicated operation{p.07 #7,, 4,, 6, 8, 40, 46, 4, 68} To find the inverse Step Replace f() with y Step Interchange and y Step Solve the equation for y ( 4) a. f ( ) b. f ( ) 6 f. log 7 49 g. 4 c. { } d. {-} e. 7 6 h. log i. log log ( ) j. e 9. Solve the following inequalities {p.6 E#} & {p. 69 EX#,, } 9 a. b. 9 c. d. 0. Graphing Linear Equations {p. #,} & {p.0 #9, 4, 4} a. 9 b. y c. 4 y = 4 d. = e. y = f. -intercept (, 0) y-intercept (0, 6) slope = 6 Saved C: Accuplacer College Level Math Assessment Page of 7

16 . C. y + {Taken from internet Site Purple Math.com } Answer Key. Graphing Relations: Find the Domain and Range {purplemath.com } a. yes b. Domain [/, ) & Range [0, ) c.. Find the verte, and the intercepts {p.87 #6,,, } a. verte (, -) there are no -intercepts b. verte (-, -9) and the -intercepts are = - and = c. verte (-, ) there are no -intercepts d. verte (, -6) and the -intercepts are = and = - 4. Identify the conic section and put in standard form {p.86 EX# 7, 8} a. ( h) ( y k) r ( 7) ( y ) 00 b. You must complete the square, to get the equation in standard form. ( ) ( y 4) 6. Systems of Equations and Matrices: Perform the indicated operation {p.44 # 7,,} & Aims Ditto y z 8 y 4 0 a. answer is {, } b. y z 0 answer is {6, -, 4} y y z c. Multiply The Answer is = 4 0 d. Find the determinant 7 ad bc = (7) ()(-) = + = 6 e. Find the inverse of The Answer is = A 7. C 8. C 9. B f. Perform the indicated operation 6 The Answer is = -8 4 Saved C: Accuplacer College Level Math Assessment Page 6 of 7

17 Answer Key 0. C. Step Step Find the perimeter of the rectangle Find the circumference of the circle P = L + W C = d P = (00) + (0) C =.4(0) P = C = 7. D. C. D 4. C. C 6. C P = 400 Step (400 8 laps) + (7 8 laps) = 446 Note: When finding the perimeter of composite figures you must delete the side they share from one of the equations, it you don t you ll end up counting that side twice, and your answer will be wrong. That s why, 00 was deleted from the perimeter of the rectangle. The rectangle and the circle share that side, so it was deleted from one of the formulas. 7. B Step This is an unusual problem to solve because you are dealing with the concept of -dimensions, which usually isn t covered in great detail until you reach calculus II or III. Since, we are trying to squeeze the object into the bo, we are trying to find the longest diagonal line within the bo. So, to solve this problem you need to use the following formula: D +y +z You can also write your formula this way D = l w h D +y +z D = () () (.) D D. D =.9 feet 8. A. Step You have to find 8% of %, so make % your base. 8% of is what? 8 a 00 a = 6. A 9. D. SINE = opposite hypotenuse The answer is SINE = AC AB opposite hypotenuse C Adjacent B 40. B. {do not pick choice C the inequality sign is incorrect} Problems taken from Math 00 Tetbook Intermediate Algebra by K. Elayn Martin-Gay99, & Purplemath.com, and THEA Test Saved C: Accuplacer College Level Math Assessment Page 7 of 7

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