by Jenny Paden, jenny.paden@fpsmail

1. by Jenny Paden, jenny.paden@fpsmail.org

2. 1A the sum of 9 and r 9 increased by r Give two ways to write each algebra expression in words. 9 + r

3. 1B Lou drives at 65 mi/h. Write an expression for the number of miles that Lou drives in t hours. 65t

4. 1C Evaluate each expression for a = 4, b =7, and c = 2. ac Substitute 4 for a and 2 for c. ac = 4 ·2 = 8 Simplify.

5. 2A Add. –5 + (–7) –5 + (–7) = 5 + 7 When the signs are the same, find the sum of the absolute values. 5 + 7 = 12 Both numbers are negative, so the sum is negative. –12

6. 2B Add. x + (–68) for x = 52 First substitute 52 for x. x + (–68)= 52 + (–68) When the signs of the numbers are different, find the difference of the absolute values. 68 – 52 Use the sign of the number with the greater absolute value. –16 The sum is negative.

7. 2C 1 2 –3 To subtract add . When the signs of the numbers are the same, find the sum of the absolute values: = 4. 1 2 3 1 2 1 2 3 + Subtract. 4 Both numbers are positive so, the sum is positive.

8. 3A Find the value of each expression. The quotient of two numbers with the same sign is positive. 12

9. 3B Find the value of each expression. –6x for x = 7 –6x = –6(7) First substitute 7 for x. The product of two numbers with different signs is negative. = –42

10. 3C and have the same sign, so the quotient is positive. Divide. Copy Change Flip Multiply the numerators and multiply the denominators.

11. 4A Simplify • (-2)3 = • -8 • -72 = • -49

12. 4B 2 9 2 9 2 9 2 9 2 9   Use as a factor 2 times. 4 81 = Evaluate the expression.

13. 4C Write each number as a power of the given base. 81; base –3 (–3)(–3)(–3)(–3) The product of four –3’s is 81. (–3)4

14. 5A A. = 4 B. = –3 Find each square root. Think: What number squared equals 16? 42 = 16 Positive square root positive 4. Think: What is the opposite of the square root of 9? 32 = 9 Negative square root negative 3.

15. 5B Write all classifications that apply to each Real number. –32 32 can be written as a fraction and a decimal. 32 1 –32 = – = –32.0 rational number, integer, terminating decimal

16. 5C = 3.16227766… Write all classifications that apply to each real number. The digits continue with no pattern. irrational number

17. 6A Simplify each expression. 15 – 2 · 3 + 1 15 – 2 · 3 + 1 There are no grouping symbols. 15 – 6 + 1 Multiply. Subtract and add from left to right. 10

18. 6B Simplify each expression. 12 – 32 + 10 ÷ 2 12 – 32 + 10 ÷ 2 There are no grouping symbols. Evaluate powers. The exponent applies only to the 3. 12 – 9 + 10 ÷ 2 12 – 9 + 5 Divide. Subtract and add from left to right. 8

19. 6C Evaluate the expression for the given value of x. (x · 22) ÷ (2 + 6) for x = 6 (x· 22) ÷ (2 + 6) (6 · 22) ÷ (2 + 6) First substitute 6 for x. (6 · 4) ÷ (2 + 6) Square two. Perform the operations inside the parentheses. (24) ÷ (8) 3 Divide.

20. 7A Write the product using the Distributive Property. Then simplify. 9(52) 9(50 + 2) Rewrite 52 as 50 + 2. 9(50) + 9(2) Use the Distributive Property. 450 + 18 Multiply. 468 Add.

21. 7B Simplify the expression by combining like terms. 72p – 25p 72p –25p 72p and 25p are like terms. 47p Subtract the coefficients.

22. 7C Simplify the expression by combining like terms. 0.5m + 2.5n 0.5m + 2.5n 0.5m and 2.5n are not like terms. 0.5m + 2.5n Do not combine the terms.

23. 8A •F •E •G •H Name the quadrant in which each point lies. A. E Quadrant ll B. F no quadrant (y-axis)

24. 8B •F •E •G •H The ordered pair of each point G (4, 1) (-1, -1) H

25. 8C A cable company charges $50 to set up a movie channel and $3.00 per movie watched. Write a rule for the company’s fee. Write ordered pairs for the fee when a person watches 1, 2, 3, or 4 movies. y = 50 + 3x (1, 53), (2, 56), (3, 59), (4, 62)

26. 9A Solve the equation. Check your answer. y – 8 = 24 + 8+ 8 Since 8 is subtracted from y, add 8 to both sides to undo the subtraction. y = 32

27. 9B 5 7 7 7 = z– Since is subtracted from z, add to both sides to undo the subtraction. 16 16 16 16 3 + + 4 7 7 = z 16 16 Solve the equation. Check your answer.

28. 9C Solve the equation. Check your answer. 4.2 = t +1.8 –1.8– 1.8 Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition. 2.4= t

29. 10A n = 2.8 6 Solve the equation. Since n is divided by 6, multiply both sides by 6 to undo the division. n = 16.8

30. 10B Solve the equation. Check your answer. 9y = 108 Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = 12

31. 10C 5 6 5 6 6 5 6 5 The reciprocal of is . Since w is multiplied by , multiply both sides by . Solve the equation. 5 w= 20 6 w = 24

32. 11A + 2 + 2 5t = –30 5 5 Solve 5t – 2 = –32. 5t – 2 = –32 First t is multiplied by 5. Then 2 is subtracted. Work backward: Add 2 to both sides. 5t = –30 Since t is multiplied by 5, divide both sides by 5 to undo the multiplication. t = –6

33. 11B + 4 + 4 7x = 7 7 7 Solve –4 + 7x = 3. –4 + 7x = 3 First x is multiplied by 7. Then –4 is added. Work backward: Add 4 to both sides. 7x = 7 Since x is multiplied by 7, divide both sides by 7 to undo the multiplication. x = 1

34. 11C – 3 – 3 Solve 2a + 3 – 8a = 8 2a + 3 – 8a = 8 2a – 8a + 3 = 8 Use the Commutative Property of Addition. –6a+ 3 = 8 Combine like terms. Since 3 is added to –6a, subtract 3 from both sides to undo the addition. –6a = 5 Since a is multiplied by –6, divide both sides by –6 to undo the multiplication.

35. 12A –3b –3b – 2 – 2 Solve 4b + 2 = 3b 4b + 2 = 3b To collect the variable terms on one side, subtract 3b from both sides. b + 2 = 0 b = –2

36. 12B –0.3y –0.3y +0.3 + 0.3 Solve 0.5 + 0.3y = 0.7y – 0.3 To collect the variable terms on one side, subtract 0.3y from both sides. 0.5 + 0.3y = 0.7y – 0.3 0.5 = 0.4y – 0.3 Since 0.3 is subtracted from 0.4y, add 0.3 to both sides to undo the subtraction. 0.8 = 0.4y Since y is multiplied by 0.4, divide both sides by 0.4 to undo the multiplication. 2 = y

37. 12C –2x –2x – 6 – 6 Solve 3x + 15 – 9 = 2(x + 2) Distribute 2 to the expression in parentheses. 3x + 15 – 9 = 2(x + 2) 3x + 15 – 9 = 2(x) + 2(2) 3x + 15 – 9 = 2x + 4 3x + 6 = 2x + 4 Combine like terms. To collect the variable terms on one side, subtract 2x from both sides. x + 6= 4 Since 6 is added to x, subtract 6 from both sides to undo the addition. x = –2

38. 13A The ratio of the number of bones in a human’s ears to the number of bones in the skull is 3:11. There are 22 bones in the skull. How many bones are in the ears? Write a ratio comparing bones in ears to bones in skull. Write a proportion. Let x be the number of bones in ears. Since x is divided by 22, multiply both sides of the equation by 22. There are 6 bones in the ears.

39. 13B Raulf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is about 3.47 flips/s.

40. 13C The ratio of games lost to games won for a baseball team is 2:3. The team has won 18 games. How many games did the team lose? Write a ratio comparing games lost to games won. Write a proportion. Let x be the number of games lost. Since x is divided by 18, multiply both sides of the equation by 18. The team lost 12 games.

41. 14A 3(m) = 5(9) 3m = 45 m = 15 Solve the proportion. Use cross products. Divide both sides by 3.

42. 14B 6(7) = 2(y – 3) 42 = 2y – 6 +6 +6 48 = 2y 24 = y Solve the proportion. Use cross products. Add 6 to both sides. Divide both sides by 2.

43. 14C In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there? 162

44. 15A The length of XY is 2.8 in. Find the value of x in the diagram if ABCD ~ WXYZ. ABCD ~ WXYZ Use cross products. Since x is multiplied by 5, divide both sides by 5 to undo the multiplication. x = 2.8

45. 15B A flagpole casts a shadow that is 75 ft long at the same time a 6-foot-tall man casts a shadow that is 9 ft long. Write and solve a proportion to find the height of the flag pole. Since h is multiplied by 9, divide both sides by 9 to undo the multiplication. The flagpole is 50 feet tall.

46. 15C A forest ranger who is 150 cm tall casts a shadow 45 cm long. At the same time, a nearby tree casts a shadow 195 cm long. Write and solve a proportion to find the height of the tree. 45x = 29250 Since x is multiplied by 45, divide both sides by 45 to undo the multiplication. x = 650 The tree is 650 centimeters tall.

47. 16A Find 30% of 80 Method 1 Use a proportion. Use the percent proportion. Let x represent the part. 100x = 2400 Find the cross products. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. x = 24

48. 16B What percent of 45 is 35? Round your answer to the nearest tenth. Method 1 Use a proportion. Use the percent proportion. Let x represent the percent. 45x = 3500 Find the cross products. Since x is multiplied by 45, divide both sides by 45 to undo the multiplication. x ≈ 77.8

49. 16C 38% of what number is 85? Round your answer to the nearest tenth. Method 1 Use a proportion. Use the percent proportion. Let x represent the whole. 38x = 8500 Find the cross products. Since x is multiplied by 38, divide both sides by 38 to undo the multiplication. x = 223.7

50. 17A Mr. Cortez earns a base salary of $26,000 plus a sales commission of 5%. His total sales for one year were $300,000. Find his total pay for the year. total pay = base salary + commission = base + % of total sales = 26,000 + 5% of 300,000 = 26,000 + (0.05)(300,000) = 26,000 + 15,000 = 41,000 Mr. Cortez’s total pay was $41,000.