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ACT Math Prep: Practice Questions and Tips

Maximize your ACT Math score with this comprehensive test prep guide. Includes 60 questions from Pre-Algebra, Elementary Algebra, Intermediate Algebra, Coordinate Geometry, Plane Geometry, and Trigonometry. Learn valuable strategies and tips for pacing, problem-solving, and checking your answers. No calculator required, but you can use one if you prefer.

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ACT Math Prep: Practice Questions and Tips

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

  2. Content 14 questions dealing with Pre-Algebra  10 questions from Elementary Algebra  9 questions based on Intermediate Algebra  9 questions from Coordinate Geometry  14 questions from Plane Geometry  4 Trigonometry questions The questions assume knowledge of basic formulas and computational skills but do not require memorization of complex formulas or extensive computation

  3. Pace Yourself • 60 questions 60 minutes Don’t waste time on any one problem, spend your dftime doing as many problems as you can The questions are arranged in order of difficulty RELAX: answering only half of the questions right onwill give you a score of 20 on the Math Section

  4. Pace Yourself Go Through The Test Twice • Take 45 minutes to go through the test • Answer the questions that you know how to do • Guess on the questions you know you’ll never get • Mark the harder questions that you’ll come back to later • Spend the last 15 minutes going over the test again Answer the questions you skipped • Make sure you have answered every question • Spend any remaining time checking your work

  5. Calculators ALL PROBLEMS ON THE ACT CAN BE SOLVED WITHOUT USING A CALCULATOR • You may use a four-function, scientific, or graphing calculator on the Math test • Calculators, such as TI-89 and TI-92 are NOT permitted (see page 4 in the ACT prep booklet) • Bring a calculator that you know how to use – bringing a more powerful calculator that you do not know how to use isn’t going to help you

  6. Understand the Problem • Read the problem carefully • Pay attention to what the question asks you to find • Watch for unnecessary information • Label the figures with numbers or letters • Draw a picture

  7. Solving the Problem • There’s more than one way to solve these problems • It’s a timed test – find a quick and reliable way to solve the problem • Do your work in your test booklet • Be careful using your calculator – it’s easy to push the wrong button • Don’t get involved in long, complicated, or tricky calculations

  8. Check Your Answer • Make sure you answered the question that was asked • Each of the wrong answers represents a common mistake that you might have made • If your answer isn’t one of the choices, reread the question and check your work

  9. When You Get Stuck

  10. BACKSOLVE Take advantage of the multiple-choice format and try each answer until you find the one that works. WARNING: Doing it this way will take more time. The greatest common divisor of 84, 90, and 66 (that is, the largest exact divisor of all three numbers) is: • 6 • 12 • 18 • 36 • 90 84 = 2٠2٠3٠7 90 = 2٠3٠3٠5 66 = 2٠3٠11 2٠3 = 6 90 does not go into 84 – eliminate answer E 36 does not go into 84 – eliminate answer D 18 does not go into 84 – eliminate answer C 12 does not go into 90 – eliminate answer B 6 must be the correct answer and it checks CORRECT ANSWER: A

  11. BACKSOLVE (cont) • F. 0 • G. 2 • 4 • J. 8 • K. 10

  12. BACKSOLVE (cont) • F. 0 • G. 2 • 4 • J. 8 • K. 10 Correct Answer:J

  13. GUESSTIMATE If you can estimate the correct answer, then you should be able to eliminate at least one or two answer choices. What is 2% of 60? 60 x 0.02 = 1.2 • 120 • 12 • 1.2 • 0.12 • 0.012 120 is greater than 60 – eliminate answer A 12 is too large – eliminate answer B CORRECT ANSWER: C 0.012 is too small – eliminate answer E

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

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

  16. 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°

  17. 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

  18. EYEBALL (cont.) By looking at the figure: A looks larger than 99°– eliminate answer F A looks smaller than 240° – eliminate answer K Lola is making the circle graph below showing the number of students at each grade level in her high school. What should be the measure of A? F. 99° G. 120° H. 133° J. 167° K. 240° 240 freshmen A 200 sophomores 130 seniors 150 juniors

  19. EYEBALL (cont.) Total number of students = 720 Total number of freshmen = 240 Total number of degrees in a circle = 360° CORRECT ANSWER: G

  20. PICK NUMBERS Some problems are hard because they’re general or abstract, so replace variables with specific numbers If kx + k = 0, and k>1, then x = ? Pick a value for k that is greater than 1 • 0 • -1 • 1 • -k • k Let k = 2 kx + k = 0 2x + 2 = 0 2x = -2 x = -1 Let k = 5 kx + x = 0 5x + 5 = 0 5x = -5 x = -1

  21. PICK NUMBERS (cont.) If kx + k = 0, and k>1, then x = ? • 0 • -1 • 1 • -k • k kx + k = 0 k(x+1) = 0 k= 0 OR x+1 = 0 k= 0 OR x = -1 CORRECT ANSWER:B

  22. PICK NUMBERS (cont.) For all a  0, what is the slope of the line segment connecting (a,b) and (-a,b) in the usual (x,y) coordinate plane?

  23. PICK NUMBERS (cont.) For all a  0, what is the slope of the line segment connecting (a,b) and (-a,b) in the usual (x,y) coordinate plane? CORRECT ANSWER: F

  24. Practice Questions

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

  26. 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

  27. 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

  28. 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

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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. Question 8 CORRECT ANSWER: C

  37. 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

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

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

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

  45. 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

  46. Question 14 A 13 C 12 B

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

  48. Question 15 CORRECT ANSWER: E

  49. 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

  50. 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

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