Math 35 Final Exam Review Calculators Not Allowed From the Chapter 2 and 3 Test: (Refer to the White Ch. 2/3 Test answer key.) Solve this literal equation for the variable requested. 4. y = mx + b (solve for m) 5. A = h (b + c) 2 (solve for b) 7. Pedro s company uses an aluminum alloy to make wheels for cars. He has 30 pounds of 75% aluminum alloy and wants to add pure aluminum to it so that the aluminum content is 80%. What is the amount of pure aluminum that must be added? % of x alloy = aluminum 8. The three angle measures in a triangle are such that the measure of the largest angle is three times the measure of the smallest angle; the middle-sized angle is 9 less than the measure of the largest angle. What are the measures of the three angles? Solve each of these inequalities. Write the solution in interval notation, and draw its graph on a number line. 9. y 4 5 < y 3 11 2 10. -1 < 1 2 q + 3 2 Solve. Write the solution in a solution set. 13. 5 4p = 1 Solve. Draw the graph of the solution, and write it in interval notation and set builder notation. 14. 6w + 15 3 15. 7 2x < 1 page 1
From the Chapter 4 and 5 Test: (Refer to the Blue Ch. 4/5 Test answer key.) 2. First write the equation 2x + 3y = -3 in slope-intercept form. Then, identify the slope and y- intercepts, and use the slope as rise run to find two other points on the line and draw the graph. Be sure to label the points on the graph. 3. Find the equation of the line that passes through (10, 1) and (-15, -9). Write the equation in slope-intercept form (y = mx + b). 4. Find the equation of the line that passes through (8, -5) and is parallel to the line y = - 3 4 x 9. Write the equation in standard form (Ax + By = C). 8. Given g(x) = 6x 5 2x 2 find a) g(-3) b) g( 3p ) 10. Solve this system by using the elimination method. 6x + 5y = 12 4x + 3y = 7 Set up a legend with two different variables, set up two equations (use a chart for assistance), solve the system of equations, and write a sentence answering the question. First % of x Solution = ammonia 12. How many liters each of a 10% ammonia solution and a 25% ammonia solution should be mixed together to create 30 liters of a 12% ammonia solution? Second From the Chapter 6 and 7 Test: (Refer to the Yellow Ch. 6/7 Test answer key.) Multiply and combine like terms. Write each answer in descending order. 9. (2x y)(4x 2 + 2xy + y 2 ) 10. (x + 3) 2 (x 3) Divide using long division. Factor this four-term polynomial. 11. (2x 3 7x 2 + 5) (2x 3) 12. 9x 3 6x 2 15x + 10 page 2
Factor each polynomial completely. If the polynomial is not factorable, write prime. 13. 3x 2 + 13x + 12 14. x 2 + 20xy + 36y 2 15. 15q 6 + 28q 3 4 16. 5r 2 20r + 20 17. 81w 4 16 18. 8m 3 + p 3 Solve each equation by factoring. 19. 3v 2 v 14 = 0 20. 4y 2 + 3y = 7y 1 Use the area of a rectangle formula to solve. Write a sentence to answer the question. 21. Dale is putting together a plaque as a tribute to Hank Aaron. The plaque contains a rectangular metal nameplate that has an area of 36 square inches. The length is 1 inch less than twice the width. What are the dimensions of the nameplate? From the Chapter 8 Test: (Refer to the White Ch. 8 Test answer key.) Write the domain of the function by first identifying the values that x cannot be. 1. f(x) = 3x 1 3x 2 + 10x + 8 Apply the indicated operation. Simplify wherever possible. 4. x 2 11x 60 x 2 17x + 30 x 2 16 3x 2 12x 6. 2x 2 x 2 4x 5 13x + 15 x 2 4x 5 8. x + 11 x 2 + 4x 5 + 2x + 5 x 2 + 5x Solve each equation. Verify each answer and write the solution in a solution set. 11. 3 x + 6 = x 2 5 x + 6 12. 1 x + 4 = 1 4 x 2 + 4x 13. Solve P = a r 1 for r page 3
14. Davina s boat can travel 12 miles per hour in still water. Going north (upriver) on the Mississippi river, she can travel 3 miles in the same amount of time that she can travel 5 miles going south. What is the rate of the current at that part of the river? Distance Rate 15. Royce and Kendrick work for a garage painting service, and together they can paint a typical garage in 2 hours. Working alone, it takes Royce 3 hours longer than Kendrick to paint a typical garage. How long does it take Royce and Kendrick to paint a typical garage when working alone? # items time rate Together From the Chapter 9 Test: (Refer to the Green Ch. 9 Test answer key.) Simplify. 1. 121x 2 2. - 180y 3 Graph the function and state its domain and range. 3. f(x) = x + 5 Evaluate. 5. 8-5/3 6. 27 8/3 27 6/3 Simplify. Write all answers with positive exponents only. For this set, assume all variables represent positive numbers. 7. 3-1,000y 15 8. ( m - 4/3 p 5/3 ) - 6 page 4
Multiply and simplify. For this set, assume all variables represent positive numbers. 10. - 5c 15c 11. 3 6w 4 3-18w 2 Simplify. Multiply and simplify. 12. - 45 + 80 14. ( 4 10 )( 1 + 2 10 ) Rationalize the denominator and simplify. For this set, assume all variables represent positive numbers. 16. 6 8y 3 17. 3 6y 3 9w 4 18. 1 5 3 + 5 Consider that i = -1. Perform the indicated operation and simplify. Write the answer in the standard complex number form, a + bi. 19. - 15-20 21. (5 + i 6 ) 2 Solve the equation. Be sure to check all answers. 24. 6 2x = x + 9 From the Chapter 10 Test: (Refer to the White Ch. 10 Test answer key.) Solve using the square root property. Write the answers in a solution set. 1. (2x 5) 2 = 49 2. (3x + 1) 2 = 24 Solve by first completing the square and then applying the square root property. 3. x 2 10x + 13 = 0 4. x 2 + 1 2 x = 3 Graph f(x) by first identifying the vertex and the axis of symmetry of the parabola. Then plot two or three sets of symmetric pairs. 5. f(x) = 2(x + 2) 2 3 6. First complete the square to write the function in vertex form. f(x) = - x 2 + 6x 4 page 5
Identify the domain and range of the functions shown above. 7. Domain: 8. Domain: Range: Range: From the Chapter 11 Test: (Refer to the Green Ch. 11 Test answer key.) Given f(x), find its inverse, f -1 (x). 1. f(x) = 2 3 x + 4 2. f(x) = 3 x 5 3. Given the graph of f(x), draw its inverse, f -1 (x). y 6 (0,3) (5,5) Write in exponential form. 4. log b (x + 1) = 1 2 (-7,-3) (-4,-2) (-2,0) -3 3 6 x Write in logarithmic form. 5. 9 5/2 = 243 Write this expression as one logarithm. -6 6. - 1 2 (log b x 6 log b y) Expand this logarithm to be the sum and/or difference of logs without any exponents or radicals. 7. log b y 5 w x Solve for x. 8. 27 x = 9 x 3 9. 25 x = 1 125 10. log 8 (5x + 2) = 5 3 page 6