2. Educational Talent Search and Upward Bound Forward Service Corporation 

3. CORRECT ANSWER: E Question 15

4. 2x 5  3x 4 y 6 Calculator or Zoom? 3 4  5353 Calculator or Zoom?

5. 7 3  5454 2 5 (3 3 – 4 3 )

6. 7x 2 y 4 (2x 2 – 7xy 4 + 3xy) (3x – 5y 2 ) 2

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

8. 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 multiply by 10 solve for x x = 5 2x + 5y = 20 60x - 5y = 290 add equations together 62x = 310

9. What is the value of x in the solution for the system of equations below? 2x + 5y = 20 6x – ½ y = 29 12x – y = 58 -y = 58 – 12x y = -58 + 12x 2x + 5(-58+12x) = 20 solve for y substitute into 1 st equation solve for x2x + -290 + 60x = 20 62x + -290 = 20 62x = 310 x = 5 CORRECT ANSWER: B

10. 2x – 4 = 8

11. 2x – 4 < 8

12. 2x – 4 > 8

13. √576 4 √1296 6 √64

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

15. A BC 3 4 5 Use Sin to find Angle A Use Cos to find Angle A

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

17. A BC 5 12 13 Use Sin to find Angle A Use Cos to find Angle A

18. Imaginary Numbers 1.i 14 Calculator or zoom? 2.i 7 3.i 20 1.i 21

19. 1.i(2 + i) 2.6i(5 – 4i) 3.(2 + 8i) + (-3 – 9i) 4.(6 – 5i) – (3 + 12i) 5.(2 – i)(4 + 3i)

20. If the area of a circle is , what is the length of its circumference? Area circle =  r 2 Circumference = 2  r  =  r 2 1 = r 2 1 = r C = 2  (1) C = 2  A.1 B.2 C.  D.2  E.3  CORRECT ANSWER: D Question 6

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

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

24. EYEBALL 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? 125° 85° x A.5° B.30° C.40° D.55° E.60° 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

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

27. C A D B 4 12 3 A.13 B.17 C.19 D.24 E.25 Question 1

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

29. 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? t a mnmn b c d e A.  a,  b,  d B.  a,  c,  d C.  a,  c,  e D.  b,  c,  d E.  b,  c,  e CORRECT ANSWER: A Question 2

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

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

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? A B C D A. 30  B. 60  C. 90  D.120  E.150  Question 5

33. 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? A B C D 30120 180 – 120 = 60  60 180 – 30 – 60 = 90  90 CORRECT ANSWER: C

34. Question 8 Regular calculator or ZOOM?

35. For all y, 26y – (-10y) – 3y(-y+3) = ? A.10y B.-3y 2 + 25y C.3y 2 + 7y D.3y 2 + 25y E.3y 2 + 27y 26y – (-10y) – 3y(-y+3) 26y +10y +3y 2 – 9y 3y 2 +27y CORRECT ANSWER: E Question 9

36. A B 30  100  D C A.65  B.70  C.75  D.80  E.85  Question 10

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

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 = ? x R 3 S 4 T Question 11

39. 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 = ? a 2 + b 2 = c 2 3 2 + 4 2 = c 2 9 + 16 = c 2 25 = c 2 5 = c x R 3 S 4 T 5 RST is a 3-4-5 right triangle CORRECT ANSWER: C

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? D 12 E 7 F G 10 Question 12

41. 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? D 12 E 7 F G 10 Area Triangle = ½ base x height = ½ (12) (10) = 60 CORRECT ANSWER: C

42. O 6 A 60  B A.  B.2  C.6  D.12  E.36  Question 13

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

44. A C12 B 13 Question 14

45. A C12 B 13 a 2 + b 2 = c 2 12 2 + b 2 = 13 2 144 + b 2 = 169 b 2 = 25 b = 5 5 CORRECT ANSWER: A

46. CORRECT ANSWER: E 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? A.xy B.2xy C.3xy D.6xy E.18xy y yards = 3y feet x yards = 3x feet Area rectangle = length x width = 3x(3y) = 9xy square feet Total Cost = area x price = 9xy (2) = 18xy

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) A.0.14 B.0.75 C.0.86 D.1.0 E.3.14 2 inches

48. CORRECT ANSWER: C 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) A.0.14 B.0.75 C.0.86 D.1.0 E.3.14 2 inches Area circle =  r 2  1 2 =  = 3.14 Area square = s 2 2 2 = 4 Area piece = Area square - Area circle 4 – 3.14 = 0.86 1

49. CORRECT ANSWER: E Question 18 Which of the following is equal to 3.14 x 10 6 ? A.314 B.3140 C.31,400 D.314,000 E.3,140,000 3.1400000000 3140000.0000 Regular calculator or ZOOM or NEITHER?

50. CORRECT ANSWER: E Question 19 Find the last number in the series: 8, 4, 12, 6, 18, 9,? A.19 B.20 C.22 D.24 E.27 8  4 8-4=4or8  2=4 4  124+8=12 or 4x3=12 12  612-6=6 or 12  2 = 6 6  186+12=18 or 6x3=18 18  918-9=9 or 18  2 = 9 9x3=27

51. CORRECT ANSWER: A 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? A.82 B.83 C.84 D.85 E.86 Let x = the fifth test score (91 + 88 + 86 + 78 + x )  5 = 85 343 + x = 425 x = 82

52. CORRECT ANSWER: C Question 21 One angle,  A, has 3 times the measure of its supplement,  B. What is the degree measure of  A? A.112 ½° B.120° C.135° D.150° E.157 ½° Let x = the measure of  B then 3x = the measure of  A x + 3x = 180° 4x = 180° x = 45°  B = 45°  A = 135°

53. CORRECT ANSWER: D Question 22 A bag contains 4 red jelly beans, 5 green jelly beans, and 3 white jelly beans. If a jelly bean is selected at random from the bag, what is the probability that the jelly bean selected is green? Probability of drawing a green jelly bean

54. CORRECT ANSWER: C Question 23 For all positive values of a, b, and c with a c, which of the following MUST be true? I. a+b>c II. 2a>c III. a+c>b A.I only B.II only C.I and II only D.II and III only E.I, II, and III I.a and b are both greater than c, so their sum will also be – TRUE III. If c=2, a=4, and b=10, then a+c<b - FALSE II. a>c, so 2a>c – TRUE c < a < b

55. CORRECT ANSWER: C Question 24 B A 1 C

56. Question 25 B E C D A

57. B 20-x E x C 4 D 6 A CORRECT ANSWER: E 10 20

58. Things to Remember on the Math ACT Don’t read the directions Bring a calculator that you know how to use Read the question carefully Pay attention to what the question asks you to find Watch for unnecessary information Draw a picture Pace yourself (60 questions/60 minutes)

59. Things to Remember on the Math ACT Do the easy questions first, then try the hard ones Show some work and circle your answers in your test booklet Don’t waste too much time on one problem Eliminate wrong answers before guessing Answer every question Check your work Work for the whole 60 minutes