MATD Intermediate Algebra Review for Pretest

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1 MATD Intermediate Algebra Review for Pretest. Evaluate: a) - b) - c) (-) d) 0. Evaluate: [ - ( - )]. Evaluate: - -(-7) + (-8). Evaluate: [6 - ( - 9)]. Simplify: [x - (x - )] 6. Solve: -(x + 6) + = -6(x + ) + 0x 7. Solve: x 7 = 8. Solve for b: A = (b + c) 9. Determine the slope of the line that contains the points (-, ) and (-, -7). 0. What is the slope of the line -x + y =?. What is (a) the x-intercept and (b) the y-intercept of the line -x + y =?. Graph x - y =.. Draw the line with slope - which contains the point (,) What is the equation of the line with slope - and y-intercept?. Write the equation of a line with slope m = - and containing the point (, ). 6. Solve the system: { x - y = 6 x - y = -x + y = - 7. Solve the system: { x + y = 8. Twice the sum of a number and 7 is more than the number. Write an equation to represent this relationship. Let n represent the number. 9. Mae bought a jacket on sale at % off the regular price and paid $7.0 for it. What was the regular price of the jacket? 0. Will's salary this year is 7% greater than it was last year. If his salary this year is $7,0, what was his salary last year?

2 . A truck rental company charges a base rate of $9.9 plus an additional $0. for each mile the truck is driven. If the total charge for a truck rental was $07., how many miles was it driven? If m = total miles driven, write an equation which you could solve to answer the question. (Do not actually solve it.). The second angle of a triangle is twice as big as the first angle. The third angle is 8 more than the first angle. What are the angles?. James works two part time jobs. One pays $7/hr and the other pays $0/hr. Last week he worked a total of hours and made a total of $78. How many hours did he work at each job?. Two cars are 60 miles apart and traveling towards one another. Car B is going 0 mph slower than car A. If they pass each other after hours, how fast is each traveling?. Jay's coffee house sells two types of coffee beans. Ordinary beans cost $6.0/lb and special beans cost $8.0/lb. They want to mix the two types to create 0 lbs. of a house blend which they will sell at $6.90/lb. How much of each type should they use? 6. Harry invested a total of $0,000, part at 7% and part at 0%. How much did he invest at each rate if the total interest earned in one year was $60? 7. If you can travel miles in minutes, how long should it take to travel miles? (Assume speed is the same.) At what speed (in miles per hour) are you traveling? (Note: To convert from minutes to hours, divide by 60 minutes.) 7 x 8. If these two triangles are similar, what is the length of side x? (MATD Pretest Review - p. of 7, Last revised: August, 00)

3 9. The bar graph above shows the number of new books in several categories that were acquired by a school library in 997 and 998. a) In what category did the number of books increase the most from 997 to 998? b) In what category did the number of books decrease the most from 997 to 998? c) In what category did the number of books remain constant from 997 to 998? d) How many art books were acquired in 997? e) What was the total number of technology books acquired in 997 and 998 combined? f) What was the percentage increase in the number of technology books from 997 to 998? Number of Books Number of Library Books Acquired in 997 and Arts Fiction Other Biography Technology Subject Area 0. Simplify: (x y ) (xy ). Simplify and write your answer without negative exponents: (-x - y)(x y ). Simplify and write your answer without negative exponents: (-rs - t 0 ). Simplify and write your answer without negative exponents: m n 7 mn -. Write in scientific notation: a) 0,000,000,000 b) Write in standard notation: a). x 0 - b).7 x 0 6. Multiply and give the result in scientific notation: ( x 0 - )( x 0 ) 7. Divide and give the result in scientific notation: (. x 0) (.0 x 0 ) 8. Add: (x - x + ) + (-x + x - 6) 9. Subtract: (w + w - ) - (w - w - 7) 0. Multiply: (u - )(u + ). Multiply: (p - )(p - p + ). Multiply: (u - )(u + ). Multiply: (p - ). Divide: (x - x + 6x) (-x). Divide: (x - x + ) (x - ) (MATD Pretest Review - p. of 7, Last revised: August, 00)

4 6. Factor completely: -6r s + 8r s - 0rs 7. Factor completely: x - x + x Factor completely: k - k - 9. Factor completely: x + 8x - 0. Factor completely: 9x - 6. Factor completely: x + 0x +. Factor completely: u - 0u + 7u. Factor completely: 0x -. Solve: x - 7x + = 0. Solve: x + x = 6. Solve: x = 7x 7. Solve: x = 9 8. Solve: x = 9x + [ Use the Quadratic Formula is x = -b ± b - ac a. ]? 9. Find the length of the unknown side in the triangle shown here: ft ft 60. The length of a room is 7 feet longer than its width. The area of the rectangle is square feet. What are the dimensions of the room? What is its perimeter? 6. The length of a room is 6 feet less than three times its width. The perimeter of the rectangle is 7 feet. What are the dimensions of the room? Answers (Each answer is preceded or followed by the name of the topic that the problem is most closely associated with. If you get a wrong answer and want additional information on how to do the problem, look for this topic in the index of an elementary algebra textbook.). a) -7 b) -9 c) 0 d) Undefined (signed number arithmetic). 0 (order of operations). - (order of operations). (order of operations). 0x + 0 (like terms, distributive property) 6. x = - (linear equation in one variable) 7. x = (linear equation in one variable) 8. b = A - c (formulas) 9. m = (slope) 0. m = (slope-intercept form). (a) (-, 0) (b) (0, ) (x- and y- intercepts) (MATD Pretest Review - p. of 7, Last revised: August, 00)

5 (graphing linear equation in one variable - using intercepts, point and slope. y = - x + (slope-intercept form). y - () = -(x - ) (point-slope form); y = -x + (slope-intercept form) 67. (solve a system of two line. eq. in two vbles) 6. (x, y) = (8, 0) 7. (x, y) = (, -) 8. (n + 7) = n + (expressions, operations, word problems) 9. Let x = regular price. x - 0.x = $7.0. x = $8 (percentage decrease) 0. Let x = Will's salary last year. x +.07x = $7,0 x = $,000. (percentage increase) ( & - set up and solve linear equations in one variable, sum of angle of a triangle). Let m = miles driven. $07. = $9.9 + $0.m. m = 0 miles. Let x = size of first angle, x = size of second angle, x + 8 = size of third angle x + x + (x + 8 ) = 80, first = 0., second = 8, third = 8. (-6 may be done by setting up and solving a single linear equation in one variable, or a system of two linear equations in two variables). Two Variables: If x = hours worked at first job and y = hours worked at second job. x + y = This gives system: { 7x + 0y = 78 hours at $7/hr and 8 hours at $0/hr One variable: 7x + 0( - x) = 78. Two Variables: Let x = rate of car A, y = rate of car B. y = x - 0 This gives system:{ x + y = 60 car A is going 6 mph, car B is going mph One variable: x + (x - 0) = 60. (MATD Pretest Review - p. of 7, Last revised: August, 00)

6 . Two Variables: Let x = amount of ordinary beans, y = amount of special beans. x + y = 0 We get the system: { $6.0x + $8.0y = 0($6.90) 0 lbs of ordinary beans and 0 pounds of special beans One variable: $6.0x + $8.0(0 - x) = 0($6.90) 6. Two Variables: Let x = amount invested at 7% and y = amount invested at 0%. x + y = $0,000 We get the system: { 0.07x + 0.0y = $60 $,000 at 7% and $8000 at 0% One variable: 0.07x + 0.0($0,000 - x) = $60 7. (Set up and solve proportion) miles minutes = miles x minutes It will take 7 minutes (or hours, minutes, or.9 hours) Speed is /7 miles/minute or.86 mph. 8. (Similar triangles, set up and solve proportion) = 7 x, x = 9 = 8 9. (Reading bar graphs) a. Technology b. Biography c. Fiction d. e. 6 f. 60% 0. (laws of exponents) (x y ) (xy ) = (8x y 6 )(xy ) = x y 8 - (negative exponents). y x. r s 6. m n. (scientific notation) a). x 0 b) 7.6 x 0 -. (scientific notation) a) b) 70,000,000, (scientific notation) 6.. x x (addition/subtraction of polynomials) 8. x + x w + w (multiplication of polynomials) 0. 0u - u -. 6p - 7p + p (special product). u p - p + (MATD Pretest Review - p. 6 of 7, Last revised: August, 00)

7 -. (division of polynomials). -x + x -. x - + x rs(r - rs + ) (factoring out GCF) 7. (x + )(x - ) (factoring by grouping) 8. (k - 6)(k + ) (factoring trinomials) 9. (x - )(x + ) (factoring trinomials) 0. (x + )(x - ) (factoring, diff of sq). (x + ) (factoring, pfct sq trinomials). u(u - ) (factoring out GCF, pfct sq trinomials). (x + )(x - ) (factoring out GCF, diff of sq). x =, x = (Solve quad eq. by factoring). x + x - = 0, x =, - 6. x - 7x = 0, x = 7, x = 0 (Solve quad eq. by factoring) (Solve quad eq. by factoring) 7. x = ± (using square root principle to solve quadratic equation) 8. x - 9x - = 0, x = -(-9) ± (-9) - ()(-) () = 9 ± 0 (solve quadratic equation by using square root principle) 9. + x =, x = Unknown side is ft. (Pythagorean Thm., solve quadratic equation by using square root principle) 60. Let x = width of room, x + 7 = length of room. x(x + 7) =. Dimensions: 9 ft x 6 ft. Perimeter = (9) + (6) = 0 ft. (Formulas for area and perimeter of rectangle, solving quadratic equation.) 6. Let x = width of room, x - 6 = length of room. (x - 6) + x = 7. Dimensions: 0. ft x. ft. (Formulas for perimeter of rectangle, solving linear equation in one variable.) (MATD Pretest Review - p. 7 of 7, Last revised: August, 00)

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