Algebra 1B Final Review

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1 Name: Class: Date: ID: A Algebra 1B Final Review Short Answer 1. Originally a rectangle was twice as long as it was wide. When 5 m was subtracted from its length and 3 m subtracted from its width, the area of the rectangle was 55 m 2. Find the dimensions of the new rectangle. 2. A square lawn has sides of length x + 5. A square garden with sides of length x will be placed somewhere on the lawn. The rest of the lawn will be sodded. Find an expression for the area of the region that will be sodded. Write your answer in standard form. 3. Put in order from least to greatest: 3.6, 9 2, 13,31 2, Factor completely: 2x 3 + 4x 2 + 8x Ê 5. Simplify the expression: 9 ˆ Ë Á 7 6. Simplify the sum. (6u 3 + 6u 2 + 8) + (6u 3 5u + 4) 2 7. Simplify Convert to a fraction: What quantity should be added to both sides of the equation x 2 16x = 36 to complete the square? 10. Factor: x 2 x 42 1

2 Name: ID: A 11. Simplify: Ê ˆ 12. Find the product Ë Á Ê Ë Á ˆ. 13. How much water must be added to 12 grams of a 90% iodine solution to produce a 25% iodine solution? 14. Nicole sold 15 tickets to the school play and Andrew sold 24 tickets. What is the ratio of the number of tickets Nicole sold to the number of tickets Andrew sold? 15. When x pounds of force is applied to one end of a lever that is L feet long, the resulting force y on the other end is determined by the distance between the fulcrum (the lever's pivot) and the end of the lever on which the x pounds of force is exerted. The formula relating the forces is xd = yl ( d ). What formula can you use to find the length of the lever? 16. Simplify Factor 3b 8 48 completely. 18. Solve: 4 x + 2 = 2 x Simplify: 80w Factor: 15x 2 16xy+ 4y Simplify: 3a 2 (6a 2 7b 6 ) 22. The product of two consecutive positive even integers is 24. What are the integers? 23. Janet can build a fence in 8 hours. Jack can build the same fence in 5 hours. How long will it take them to build the fence if they work together? 24. The equation 16t t models the height of a soccer ball t seconds after it is kicked. When will the height of the ball reach 9 feet? 25. Simplify the expression: ( 2x 5 ) 8y 8 3x Solve the equation: 3x 2 24 = 0 2

3 Name: ID: A 27. Two cars were traveling in the same direction on the same course. The first car was traveling 65 mph and the second car was traveling 55 mph. After how long were the two cars 45 miles apart? 28. Perform the indicated operations and simplify the result. Ê ˆ Ë Á 29. Two machines can complete 5 tasks every 4 days. Let t represent the number of tasks these machines can complete in a 31-day month. Which proportion can you use to find the value of t? 30. Convert to a decimal: Solve: 16x 2 = Which of the following shows 5hj 2 45h factored completely? 33. What number is 30% of 40? 34. Find the product: (4x 6y 3 ) Factor: 49b Solve for the variable: x x + 25 = Simplify: Which is the first incorrect step in simplifying the following expression? ( 3x 2 )(4x 3 ) Given: 16x 4 Step 1: Step 2: Step 3: (9x 2 )(4x 3 ) 16x 4 36x 5 16x 4 9x A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s. a. Substitute the values into the vertical motion formula h = 16t 2 + vt + c. Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Leave in simplest radical form. 40. Simplify: ( 7x 5x 4 + 5) ( 7x 4 5 9x) 3

4 Name: ID: A 41. Solve: w + 1 = Factor: 4b b Simplify. (3k + 4)(3k 2 5k 3) 44. Factor: 3x 2 + 7x If the sides of a square are decreased by 2 cm, the area becomes 121 cm 2. Find the length of the sides of the original square. 46. Find the GCF of the terms of the polynomial. 8x x Find the missing coefficient. (3d 7)(3d 6) = 9d Which are the factors of of x 2 15x + 54? 49. What is the solution set of the quadratic equation 3y 2 + 4y + 2 = 0? 50. Put in simplest form: Solve: 5y 2 8y = The amount of apples the orchard yielded decreased from 3500 last year to 2485 this year. What was the percent of decrease in apples? 53. Find the product: (2n + 2)(2n 2) 54. What are the solutions of the quadratic equation 1 2 y 2 + 3y + 4 = 0? 55. Write in simplest form:

5 Algebra 1B Final Review Answer Section SHORT ANSWER 1. ANS: 11 m by 5 m DIF: Level B REF: A1.10.xx.CP.117A1 TOP: Area and Perimeter Puzzlers KEY: classic problem classic favorite problem solving area quadratic BLM: Comprehension NOT: ANS: 10x + 25 DIF: L3 REF: 8-4 Multiplying Special Cases OBJ: Finding the Square of a Binomial TOP: 8-4 Example 2 KEY: polynomial square of a binomial subtracting polynomials 3. ANS: 9 4, 3 1 2, 13, 3.6, 9 2 DIF: Level B REF: MALG0351 TOP: Lesson 2.7 Find square roots and compare real numbers KEY: rational order irrational BLM: Comprehension NOT: ANS: 2x(x 2 + 2x + 4) DIF: L3 REF: 8-2 Multiplying and Factoring OBJ: Factoring a Monomial from a Polynomial TOP: 8-2 Example 3 KEY: polynomial greatest common factor in a polynomial factoring out a monomial 5. ANS: DIF: L2 REF: 7-5 Division Properties of Exponents OBJ: Raising a Quotient to a Power TOP: 7-5 Example 3 KEY: raising a quotient to a power exponential expression 6. ANS: 12u 3 + 6u 2 5u + 12 DIF: L3 REF: 8-1 Adding and Subtracting Polynomials OBJ: Adding and Subtracting Polynomials TOP: 8-1 Example 3 KEY: monomial degree of a monomial polynomial adding polynomials degree of a polynomial standard form of a polynomial trinomial 1

6 7. ANS: 10 3 DIF: Level A REF: MALG1475 TOP: Lesson 11.2 Simplify Radical Expressions BLM: Knowledge NOT: ANS: or KEY: radical root integer simplify DIF: Level B REF: 7f1f2f6a-cdbb-11db-b f7 TOP: Lesson 2.1 Use Integers and Rational Numbers KEY: whole number rational number integer classifying numbers BLM: Knowledge NOT: ANS: ANS: (x 7)(x + 6) DIF: L3 REF: 8-5 Factoring Trinomials of the Type x^2 + bx + c OBJ: Factoring Trinomials TOP: 8-5 Example 3 KEY: polynomial factoring trinomials 11. ANS: 3 2 DIF: L2 REF: 10-1 Simplifying Radicals OBJ: Simplifying Radical Expressions Involving Quotients TOP: 10-1 Example 6 KEY: simplying radicals by dividing square root radical expressions fractions within a radical 12. ANS: ANS: 31.2 grams 14. ANS: 5 to 8 DIF: Level A REF: MALG0454 TOP: Lesson 3.5 Write Ratios and Proportions BLM: Knowledge NOT: KEY: ratio word 2

7 15. ANS: L = xd y + d DIF: Level B REF: MALG0585 TOP: Lesson 3.8 Rewrite Equations and Formulas KEY: solve equation solution word formula force NOT: ANS: 24 BLM: Application DIF: L2 REF: 9-3 Finding and Estimating Square Roots OBJ: Finding Square Roots TOP: 9-3 Example 1 KEY: square root 17. ANS: (a 2 + 1)(a + 1)(a 1) 18. ANS: x = 8 DIF: L2 REF: 11-5 Solving Rational Equations OBJ: Solving Proportions TOP: 11-5 Example 4 KEY: rational expression rational equation 19. ANS: 4w 5w 3 DIF: L2 REF: 10-1 Simplifying Radicals OBJ: Simplifying Radical Expressions Involving Quotients TOP: 10-1 Example 5 KEY: Division Property of Square Roots radical expressions fractions within a radical 20. ANS: (3x 2y)(5x 2y) DIF: L3 REF: 8-6 Factoring Trinomials of the Type ax^2 + bx + c OBJ: Factoring ax^2 + bx + c TOP: 8-5 Example 4 KEY: polynomial factoring trinomials 21. ANS: 18a 4 21a 2 b 6 DIF: L2 REF: 8-2 Multiplying and Factoring OBJ: Distributing a Monomial TOP: 8-2 Example 1 KEY: polynomial multiplying a monomial and a trinomial 22. ANS: 4 and 6 3

8 23. ANS: 3 1/13 hours 24. ANS: at t = second and t = 1 second 25. ANS: 48x 7 y 8 DIF: L2 REF: 7-3 Mulitplication Properties of Exponents OBJ: Multiplying Powers TOP: 7-3 Example 2 KEY: exponential expression simplifying an exponential expression multiplying powers with the same base 26. ANS: 2.83, 2.83 DIF: L3 REF: 9-7 Using the Quadratic Formula OBJ: Choosing an Appropriate Method for Solving TOP: 9-7 Example 4 KEY: solving quadratic equations 27. ANS: 4.5 hours 28. ANS: DIF: Level B REF: MALG1500 TOP: Lesson 11.2 Simplify Radical Expressions KEY: multiply distributive property radical expression simplify BLM: Application NOT: ANS: 5 4 = t 31 DIF: Level A REF: MALG0459 TOP: Lesson 3.5 Write Ratios and Proportions KEY: word proportion BLM: Comprehension NOT: ANS: 3. 3 DIF: Level B REF: 7f1f567a-cdbb-11db-b f7 TOP: Lesson 2.1 Use Integers and Rational Numbers KEY: whole number rational number integer classifying numbers BLM: Knowledge NOT:

9 31. ANS: 3 2, 3 2 DIF: L2 REF: 5-5 Quadratic Equations OBJ: Solving by Factoring and Finding Square Roots TOP: 5-5 Example 2 KEY: square root 32. ANS: 5h(j + 3)(j 3) 33. ANS: 12 DIF: Level A REF: MALG0511 TOP: Lesson 3.7 Solve Percent Problems KEY: percent BLM: Knowledge NOT: ANS: 16x 2 48xy y 6 DIF: L3 REF: 8-4 Multiplying Special Cases OBJ: Finding the Square of a Binomial TOP: 8-4 Example 1 KEY: polynomial square of a binomial 35. ANS: (7b + 9)(7b 9) DIF: L3 REF: 8-7 Factoring Special Cases OBJ: Factoring the Difference of Squares TOP: 8-7 Example 4 KEY: polynomial factoring trinomials difference of squares 36. ANS: 1, 11 DIF: L2 REF: 5-7 Completing the Square OBJ: Solving Equations by Completing the Square TOP: 5-7 Example 1 KEY: perfect square trinomial 37. ANS: 10 2 DIF: Level B REF: MALG1495 TOP: Lesson 11.2 Simplify Radical Expressions BLM: Application NOT: ANS: Step 1 KEY: add radical 5

10 39. ANS: 0 = 16t t + 101; 8 s DIF: L2 REF: 9-7 Using the Quadratic Formula OBJ: Using the Quadratic Formula TOP: 9-7 Example 3 KEY: quadratic formula solving quadratic equations word problem problem solving multi-part question 40. ANS: 2x 4 + 2x + 10 DIF: L2 REF: 8-1 Adding and Subtracting Polynomials OBJ: Adding and Subtracting Polynomials TOP: 8-1 Example 4 KEY: monomial degree of a monomial polynomial degree of a polynomial subtracting polynomials standard form of a polynomial trinomial 41. ANS: 99 DIF: L2 REF: 10-4 Solving Radical Equations OBJ: Solving Radical Equations TOP: 10-4 Example 1 KEY: radical radical equation solving equations 42. ANS: (2b + 9) 2 DIF: L3 REF: 8-7 Factoring Special Cases OBJ: Factoring Perfect-Square Trinomials TOP: 8-7 Example 2 KEY: polynomial factoring trinomials perfect-square trinomial 43. ANS: 9k 3 3k 2 29k 12 DIF: L2 REF: 8-3 Multiplying Binomials OBJ: Multiplying a Trinomial and a Binomial TOP: 8-3 Example 4 KEY: polynomial multiplying a binomial and a trinomial 44. ANS: (3x 2)(x + 3) DIF: L2 REF: 8-8 Factoring by Grouping OBJ: Factoring Trinomials by Grouping TOP: 8-8 Example 3 KEY: polynomial factoring trinomials factoring by grouping 45. ANS: 13 cm DIF: Level B REF: A1.10.xx.CP.108A1 TOP: Area and Perimeter Puzzlers KEY: classic problem classic favorite problem solving area quadratic BLM: Comprehension NOT:

11 46. ANS: 8x 3 DIF: L2 REF: 8-2 Multiplying and Factoring OBJ: Factoring a Monomial from a Polynomial TOP: 8-2 Example 2 KEY: polynomial greatest common factor in a polynomial factoring out a monomial 47. ANS: 39 DIF: L2 REF: 8-3 Multiplying Binomials OBJ: Multiplying Two Binomials TOP: 8-3 Example 2 KEY: polynomial FOIL 48. ANS: x 9, x ANS: no real solution 50. ANS: 7 DIF: L2 REF: 10-3 Operations With Radical Expressions OBJ: Simplifying Sums and Differences TOP: 10-3 Example 2 KEY: like radicals combining like radicals radical expressions 51. ANS: 1.82, 0.22 DIF: L2 REF: 9-7 Using the Quadratic Formula OBJ: Using the Quadratic Formula TOP: 9-7 Example 2 KEY: quadratic formula solving quadratic equations 52. ANS: 29% DIF: Level B REF: MALG0547 TOP: Lesson 3.7 Solve Percent Problems KEY: word evaluate divide percent difference BLM: Analysis NOT: ANS: 4n 2 4 DIF: L3 REF: 8-4 Multiplying Special Cases OBJ: Difference of Squares TOP: 8-4 Example 4 KEY: polynomial difference of squares 54. ANS: y = 4 or y = 2 7

12 55. ANS: DIF: L3 REF: 10-3 Operations With Radical Expressions OBJ: Simplifying Products and Quotients TOP: 10-3 Example 5 KEY: radical expressions rationalize conjugates 8

Algebra 2 Summer Math Answer Section

Algebra 2 Summer Math Answer Section 1. ANS: A PTS: 1 DIF: Level B REF: MALG0064 STA: SC.HSCS.MTH.00.AL1.A1.I.C.4 TOP: Lesson 1.1 Evaluate Expressions KEY: word volume cube area solid 2. ANS: C PTS: 1