INTERMEDIATE ALGEBRA FINAL EXAM REVIEW - Part A - Revised Spring 2026

Sep 30, 2026

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Intermediate Algebra Final Exam Review covers the main exam topics through worked evaluation, simplification, factoring, rationalizing, and equation/inequality solving practice. It includes variable problems with polynomial and exponent rules, expression manipulation, and rational algebra tasks such as finding undefined values and solving rational equations. The review also provides applied word problems modeled with algebraic relationships involving geometry, motion, rates, work, and mixture-style reasoning, ending with additional equation-solving sections.

LanguageEnglish

CategoryExam

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Evaluate and Simplify

Evaluate expressions for given variable values

Simplify with positive exponents

Perform Operations and Simplify

Carry out indicated operations

Apply exponent and polynomial rules

Factor and Rationalize

Factor completely

Rationalize the denominator

Solve Equations and Applications

Application problems using algebra models

Undefined values for rational equations

Solve algebraic equations

INTERMEDIATE ALGEBRA FINAL EXAM REVIEW This review represents the topics covered by the final exam. It is in no way intended to represent the quantity of any particular type of problem on the final exam. Evaluate. 1. 14 + ( y − 5)2 −12 􀁹 y for y = −2 2. 2 −5xy + y2 − 4xy3 + x6 for x = − 1 and y = 2 Simplify. All answers should contain only positive exponents. Do not leave rational exponents in your answer. Assume all variables represent nonnegative numbers 3. 4. 5. 6. 7. 8. 9. 10. (−8r7s3 )(−2rt5 )(−4 y4 )3 3 (~~ ~~xy4x2~~ ~~y8)~~ ~~ 510 􀂘 5−2 4x−2 y −3z 5 ( 2m2 n−4 )3 􀂧 4x−7 􀂷 0 􀂧 x6 y 3 􀂷−5 􀂨􀂩 9 y −2 z 􀂹􀂸 􀂘 􀂨􀂩 wz 4 􀂹􀂸 􀂧 5a6b4 􀂷 −2 􀂨 9 􀂸 􀂩 7a 􀂹 11. 12. 13. 14. 15. 16. 17. 18. 􀂧 a8b−5 􀂷 3 􀂩􀂨 5b10 a−4 􀂹􀂸(a4b−3c5 )(a−3b−3c−8)(2a3b−1)−4 14m 􀂘 7m ( 8x2 y 5 )12 􀂘 (2xy3 )32 ( x3y )32 􀂘 3x1 5 y 35 6 + 1 a 2 1 6 − a 16 x − 17 + x x − 5 + 4x Perform the indicated operations and simplify. Assume variables can represent any real number. x − 8 x2 − 5x − 24 2 y2 +17 y + 21 6 y2 − 24 19. 􀂘 20. 􀂘 x 2 + 6x + 9 x 2 −16x + 64 4 y2 − 2 y −12 3y2 +17 y − 28 INTERMEDIATE ALGEBRA FINAL EXAM REVIEW 21. 22. 23. 24. 25. 26. 27. z 2 +13z + 40 z 2 + 5z ~~ ~~ 􀁹 ~~ ~~z 2 +16z + 64 z 2 + 3z − 40 6x2 − 7x − 20 16 + 24x + 9x2 􀁹 25 − 4x2 2x2 + 3x − 5 1 1 2x − 5 − + 2x − 5 x +1 2x2 − 3x − 5 3 1 4 y − + 2 y +1 2 y −1 4 y2 −1 b 5 6 + − b2 − 25 b + 5 b 18x 􀂘 6x x2 (y + z )3 􀂘 5x23 (y + z )39 28. 29. 30. 31. 32. 33. 34. 35. |
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| 5a − 480a − 745a −612 − 5147 6 􀂘 3 2 − 98 + 8 􀂘 3 2 + 48 4 􀂘 7x8y − 3x 􀂘 7xy 6 􀂘 11x12 y + 5x 􀂘 11xy Factor completely. If the polynomial is prime, state so. 36. 15x2 + 29x +12 45. (a −5)2 −5(a −5) − 24 37. 20x2 + 7x − 6 46. x4 − r4 38. 10x2 − 37x −12 47. 9x2 − 36xy − 45y2 39. −75a2 + 85a + 20 48. 3x2 −10xy − 8y2 40. −24a2 + 66a − 45 49. 12x2 − 4xy −16y2 41. 64a2 − 32a − 60 50. 2x3 −18x2 − 6x + 54 42. −8x2 − 24xy − 32y2 51. 4x3 − 20x2 − x + 5 43. 48x2 − 72x + 27 52. 2x3 − 6x2 − 4x −12 44. 25x4 −11 53. 24z2 − 23z −12 INTERMEDIATE ALGEBRA FINAL EXAM REVIEW 54. 12x3 +16x2 − 27x − 36 55. 6x3 − 8x2 −15x − 20 56. (a + 7)2 + 5(a + 7) − 6 57. u3 + 216v3 58. y9 − 27 Rationalize the denominator. 62. 63. 59. 60. 61. 64. 65. 27 − (a +1)3 (x − 2)3 + (x + 2)3 64x2 −112x + 49 5 − 2 5 + 2 5x x + 4y Solve the following application problems. 66. A rectangular space of 390 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 11 ft. 67. A 15-ft ladder is leaning against a building. If the bottom of the ladder is 9 ft from the base of the building, how high does the ladder reach? 68. If an object is thrown upward with an initial velocity of 80 ft/sec, its height after t sec is given by h = 80t −16t2 . After how many seconds will the object hit the ground? 69. If an object is propelled upward from a height of 16 feet at an initial velocity of 64 feet per second, then its height after t seconds is given by the equation h = − 16t2 + 64t +16 , where h is in feet. After how many seconds will the object reach a height of 80 feet? 70. On a map of Nature's Wonder Hiking Trails, 1 centimeter corresponds to 5 miles. Find the length of atrail represented by a line that is 112 centimeters long on the map. Write the answer as a mixed number, if necessary. 71. A flagpole casts a shadow of 39 ft. Nearby, a 10-ft tree casts a shadow of 3 ft. What is the height of the flag pole? 72. A vehicle parked on the street that is 6 feet tall casts a shadow 24 feet long. At the same time, a house nearby casts a shadow 72 feet long. Find the height of the house. Revised Spring 2026 INTERMEDIATE ALGEBRA FINAL EXAM REVIEW 73. A painter can finish painting a house in 6 hours. Her assistant takes 8 hours to fi

FAQs

What types of problems are included in this Intermediate Algebra review?

The review includes evaluation, simplification, indicated operations, factoring completely, rationalizing denominators, and solving equations. It also contains application word problems using algebraic models.

How are the simplification answers expected to be written?

Answers should contain only positive exponents, and rational exponents should not be left in the final form. The review assumes all variables represent nonnegative numbers for the relevant sections.

What does the review ask students to do for rational equations?

For the specified rational equations, it asks students to list all numbers for which the rational equation is undefined. It then includes sections that require solving.

Is there a date or revision note associated with the review?

Yes. The document includes the note "Revised Spring 2026," indicating this is an updated version.

Sep 30, 2026

Upload by Jasmine