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# ACT PREP

ACT PREP. . MATH. Educational Talent Search and Upward Bound Forward Service Corporation. Question 15. CORRECT ANSWER: E. 2x 5 . 3x 4 y 6. Calculator or Zoom?. 3 4 . 5 3. Calculator or Zoom?. 7 3 . 5 4. 2 5 (3 3 – 4 3 ). 7x 2 y 4. (2x 2 – 7xy 4 + 3xy). (3x – 5y 2 ) 2.

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## ACT PREP

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1. ACT PREP  MATH Educational Talent Search and Upward Bound Forward Service Corporation

2. Question 15 CORRECT ANSWER: E

3. 2x5 3x4y6 Calculator or Zoom? 34  53 Calculator or Zoom?

4. 73  54 25 (33 – 43)

5. 7x2y4 (2x2 – 7xy4 + 3xy) (3x – 5y2)2

6. Question 7 What is the value of x in the solution for the system of equations below? 2x + 5y = 20 6x – ½ y = 29 • 4 • 5 • 6 • 15 • 20 ZOOM?

7. What is the value of x in the solution for the system of equations below? 2x + 5y = 20 6x – ½ y = 29 2x + 5y = 20 6x – ½ y = 29 2x + 5y = 20 60x - 5y = 290 multiply by 10 add equations together 62x = 310 solve for x x = 5

8. What is the value of x in the solution for the system of equations below? CORRECT ANSWER: B 2x + 5y = 20 6x – ½ y = 29 solve for y 12x – y = 58 -y = 58 – 12x substitute into 1st equation y = -58 + 12x 2x + 5(-58+12x) = 20 solve for x 2x + -290 + 60x = 20 62x + -290 = 20 62x = 310 x = 5

9. 2x – 4 = 8

10. 2x – 4 < 8

11. 2x – 4 > 8

12. √576 4√1296 6√64

13. A Cos A= Sin A= Tan A= Cos C= Sin C= Tan C= 5 3 B C 4 Will you be asked for Sin B?

14. A Use Sin to find Angle A Use Cos to find Angle A 5 3 B C 4

15. A Use Sin to find Angle C Use Cos to find Angle C 13 5 B C 12

16. A Use Sin to find Angle A Use Cos to find Angle A 13 5 B C 12

17. Imaginary Numbers • i14 Calculator or zoom? • i7 • i20 • i21

18. i(2 + i) • 6i(5 – 4i) • (2 + 8i) + (-3 – 9i) • (6 – 5i) – (3 + 12i) • (2 – i)(4 + 3i)

19. Question 6 If the area of a circle is , what is the length of its circumference? • 1 • 2 •  • 2 • 3 Areacircle = r2 Circumference = 2r  = r2 1 = r2 1 = r C = 2(1) C = 2 CORRECT ANSWER: D

20. Geometry Section

21. GUESSTIMATE (cont.) A ? 4 meters B 3 meters C 12, 7, and 5 are longer than the hypotenuse – eliminate answers F, G, and H

22. GUESSTIMATE (cont.) A ? 4 meters B 3 meters C CORRECT ANSWER: K

23. EYEBALL By looking at the figure: X looks too big to be 5°- eliminate answer A X looks too small to be either 60° or 55° - eliminate answers E and D One the ACT, the diagrams are “not necessarily” drawn to scale, but usually they’re quite accurate, so you could eliminate certain answer choices by sizing things up with your eyes In the figure below, what is the value of x? • 5° • 30° • 40° • 55° • 60° x 125° 85°

24. EYEBALL (cont.) In the figure below, what is the value of x? x • 5° • 30° • 40° • 55° • 60° 125° 85° 55° 95° 180 –125 = 55 180 - 85 = 95 180 – 55 – 95 = 30 CORRECT ANSWER: B

25. Practice Questions

26. Question 1 D C • 13 • 17 • 19 • 24 • 25 4 12 A 3 B

27. CORRECT ANSWER: A 13 D C 5 4 12 A 3 B ABC is a 3-4-5 right triangle and BCD is a 5-12-13 right triangle

28. Question 2 In the figure below, line m is parallel to line n, and line t is a transversal crossing both m and n. Which of the following lists has 3 angles that are all equal in measure? • a,b,d • a,c,d • a,c,e • b,c,d • b,c,e a m n b c d e t CORRECT ANSWER: A

29. Question 3 A shirt that originally cost \$35 is on sale at 20% off. If the sales tax on shirts is 5% of the purchase price, how much would it cost to buy the shirt at its sale price? 35 (.20) = 7 CORRECT ANSWER: D 35 – 7 = 28 • \$ 7.35 • \$20.00 • \$26.60 • \$29.40 • \$29.75 28 (.05) = 1.40 28 + 1.40 = 29.40 35 (.80) = 28 28 (1.05) = 29.40

30. Question 4 What is the slope of the line x = 2y +3? CORRECT ANSWER: A y = mx + b

31. Question 5 In the figure below, A, C, and D are collinear. If the measure of A is 30 and the measure ofBCD is 120, what is the measure of B? • 30 • 60 • 90 • 120 • 150 B A C D

32. In the figure below, A, C, and D are collinear. If the measure of A is 30 and the measure of BCD is 120, what is the measure of B? CORRECT ANSWER: C B 180 – 30 – 60 = 90 90 30 60 120 A C D 180 – 120 = 60

33. Question 8 Regular calculator or ZOOM? CORRECT ANSWER: C

34. Question 9 For all y, 26y – (-10y) – 3y(-y+3) = ? • 10y • -3y2 + 25y • 3y2 + 7y • 3y2 + 25y • 3y2 + 27y 26y – (-10y) – 3y(-y+3) 26y +10y +3y2 – 9y 3y2 +27y CORRECT ANSWER: E

35. Question 10 C • 65 • 70 • 75 • 80 • 85 D 100 30 A B

36. C D • 65 • 70 • 75 • 80 • 85 80° 100 50 50 30 A B 180 – 30 – 50 = 100 180 – 100= 80 m BDC = 80 CORRECT ANSWER: D

37. Question 11 In the figure below, S is a right angle, RS is 3 units long, and ST is 4 units long. If the measure of R is x, then sin x = ? T 4 x R 3 S

38. In the figure below, S is a right angle, RS is 3 units long, and ST is 4 units long. If the measure of R is x, then sin x = ? T a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 5 = c 5 4 x CORRECT ANSWER: C R 3 S RST is a 3-4-5 right triangle

39. Question 12 In the figure below, the lengths of DE, EF, and FG are given, in units. What is the area, in square units, of triangle DEG? G 10 D 12 E 7 F

40. In the figure below, the lengths of DE, EF, and FG are given, in units. What is the area, in square units, of triangle DEG? G 10 D 12 E 7 F AreaTriangle = ½ base x height = ½ (12) (10) = 60 CORRECT ANSWER: C

41. Question 13 A 6 •  • 2 • 6 • 12 • 36 O 60 B

42. Circumference = 2r C = 26 C = 12 degrees = arc 60(12) = 360 x 720 = 360 x 2 = x A 6 O 60 CORRECT ANSWER: B B

43. Question 14 A 13 C 12 B

44. a2 + b2 = c2 122 + b2 = 132 144 + b2 = 169 b2 = 25 b = 5 CORRECT ANSWER: A A 13 5 C 12 B

45. Question 16 What is the cost in dollars to carpet a room x yards long and y yards wide if the carpet costs two dollars per square foot? x yards = 3x feet y yards = 3y feet • xy • 2xy • 3xy • 6xy • 18xy Arearectangle= length x width = 3x(3y) = 9xy square feet Total Cost = area x price = 9xy (2) = 18xy CORRECT ANSWER: E

46. Question 17 In the figure below, the largest possible circle is cut out of a square piece of tin. The area of the remaining piece of tin is approximately (in square inches) 2 inches • 0.14 • 0.75 • 0.86 • 1.0 • 3.14

47. Question 17 In the figure below, the largest possible circle is cut out of a square piece of tin. The area of the remaining piece of tin is approximately (in square inches) 2 inches Areacircle = r2 • 0.14 • 0.75 • 0.86 • 1.0 • 3.14  12 =  = 3.14 1 Areasquare = s2 22 = 4 Areapiece = Areasquare - Areacircle 4 – 3.14 = 0.86 CORRECT ANSWER: C

48. Question 18 Which of the following is equal to 3.14 x 106? Regular calculator or ZOOM or NEITHER? • 314 • 3140 • 31,400 • 314,000 • 3,140,000 3.1400000000 3140000.0000 CORRECT ANSWER: E

49. Question 19 Find the last number in the series: 8, 4, 12, 6, 18, 9,? 84 8-4=4 or 82=4 412 4+8=12 or 4x3=12 126 12-6=6 or 122 = 6 6 18 6+12=18 or 6x3=18 189 18-9=9 or 182 = 9 • 19 • 20 • 22 • 24 • 27 9x3=27 CORRECT ANSWER: E

50. Question 20 Lyndsey receives grades of 91, 88, 86, and 78 on four tests. What grade must she receive on her fifth test to have an average test score of 85? • 82 • 83 • 84 • 85 • 86 Let x = the fifth test score (91 + 88 + 86 + 78 + x )  5 = 85 343 + x = 425 x = 82 CORRECT ANSWER: A

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