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ACT MATH TEST

ACT MATH TEST. You are given 60 minutes to answer 60 questions. That’s 60 seconds or less per question. You should memorize the instructions for the Math Test before you arrive to take the test. (see handout) You don’t want to waste a single second looking at the directions on test day. .

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ACT MATH TEST

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  1. ACT MATH TEST • You are given 60 minutes to answer 60 questions. That’s 60 seconds or less per question. • You should memorize the instructions for the Math Test before you arrive to take the test. (see handout) You don’t want to waste a single second looking at the directions on test day.

  2. ACT MATH TEST • All questions are printed in the left half of the page. • The right half of the page is for “your figuring and your drawings.” USE IT!

  3. ACT MATH TEST • Five, not four, multiple choice answers. Be careful filling in the bubbles on the answer sheet. • Guess on any question you can’t answer. But, your best bet is always to try to eliminate whatever answer choices you can and then guess.

  4. ACT MATH TEST • Try to answer the easier questions first. They should take you less than 60 seconds.

  5. ACT MATH TEST • If you skip a question be sure to put a mark by it in your test booklet. It’s often suggested that you go ahead and bubble a “best guess” answer on your answer sheet. This would help keep you in order on the answer sheet and you would have a best guess in case you ran out of time and couldn’t get back to that question.

  6. ACT MATH STRATEGIES

  7. ACT MATH STRATEGY Draw a picture. • Many of the word problems become much easier when you can draw a picture of the situation. • The visual representation may remind you of properties related to the problem. • Be sure to label your drawing accurately to assist with setting up your computations. • This strategy is especially helpful with geometry problems.

  8. Let’s use this strategy on the following problem.

  9. Problem Four points, A, B, C, and D lie on a circle having a circumference of 15 units. B is 2 units counterclockwise from A. C is 5 units clockwise from A. D is 7 units clockwise from A and 8 units counterclockwise from A. What is the order of the points, starting with A and going clockwise around the circle? F. A, B, C, D G. A, B, D, C H. A, C, B, D J. A, C, D, B K. A, D, C, B

  10. Answer is J • Did drawing a picture work for you? • Did anyone use a different method to solve this problem?

  11. ACT MATH STRATEGY Eliminate two or three answer choices. • In many problems, information is provided that will make two or three of the answers impossible to be the correct answer. • Eliminate these answers and then use the additional information to choose between the remaining answer choices.

  12. Let’s use this strategy on the following problem.

  13. Problem What is the least common multiple of 70, 60, and 50? F. 60 G. 180 H. 210 J. 2,100 K. 210,000

  14. Answer is J • Which answers could you immediately eliminate? Why? • Couldn’t be 60 because of 70. • Couldn’t be 180 – not divisible by 50 evenly. • Couldn’t be 210 – not divisible by 50 or 60 evenly. • 210,000 is a multiple of all 3 numbers but it is not the least common multiple.

  15. ACT MATH STRATEGY Substitute numbers for variables. • Many problems are particularly confusing because they only contain variable expressions and few, if any, numbers. • Numbers can be substituted in for the variables to provide more information about the answer to the problem.

  16. Let’s use this strategy on the following problem.

  17. Problem The length of a rectangle is 3 times the length of a smaller rectangle. The 2 rectangles have the same width. The area of the smaller rectangle is A square units. The area of the larger rectangle is kA square units. Which of the following is the value of k? F. 1/9 G. 1/3 H. 1 J. 3 K. 9

  18. Answer is J • How did you solve this problem? Did you substitute a number? Draw a picture? • Assume area of rectangle A is 1. Width and height would each be 1 (area=w*h). Width is the same on both rectangles so could determine length of larger rectangle as 3 times the length of smaller or in this case (3)(1). • Picture would be an easy representation.

  19. ACT MATH STRATEGY Substitute answers into the problem. • Start with an answer in the middle of the choices. Substitute it into the problem. • If that answer doesn’t work, try to decide if you can eliminate the higher or lower answers. (The numbers are usually listed in numerical order.) • Continue substituting each of the remaining answers until the correct answer is found.

  20. Let’s use this strategy on the following problem.

  21. Problem For 2 consecutive integers, the result of adding the smaller integer and triple the larger integer is 79. What are the 2 integers? A. 18, 19 B. 19, 20 C. 20, 21 D. 26, 27 E. 39, 40

  22. Answer is B • Did you solve this problem by substituting in the pairs? • Did you start with the pair in the middle thereby able to eliminate higher or lower? • Did you solve another way? • Maybe you realized quickly that 3 times 20 in answer B would give you 60 + the 19 would then give you 79

  23. ACT MATH STRATEGY Determine what the question is asking. • Word problems often contain many pieces of information that could be confusing. • It is necessary to read the problem carefully to determine exactly what information the problem is asking you to find.

  24. Let’s use this strategy on the following problem.

  25. Problem Lines p and n lie in the standard (x,y) coordinate plane. An equation for line p is y = 0.12x + 3,000. The slope of line n is 0.1 greater than the slope of line p. What is the slope of line n? F. 000.012 G. 000.02 H. 000.22 J. 001.2 K. 300

  26. Answer is H • What is the question asking? • Do you know what the slope of line p is? (0.12) • Do you know what the slope of line n is? (0.1 > than slope of line p) (0.12 + 0.1…0.22)

  27. Remember…Strategies are just that. • They do not replace math skills. • They are meant to support your understanding of math. • Good strategies can help you put your knowledge of math and the ACT format to the best possible use and help you achieve your target score.

  28. Let’s try a few more problems.

  29. Problem Kaya ran 1-2/5 miles on Monday and 2-1/3 miles on Tuesday. What was the total distance, in miles, Kaya ran during those 2 days? A. 3-2/15 B. 3-3/8 C. 3-2/5 D. 3-7/15 E. 3-11/15

  30. Answer is E • Total distance = sum of 1-2/5 and 2-1/3 • To add mixed numbers, each fraction must have a common denominator • 3 and 5 do not have any common factors other than 1 so the least common denominator is 3(5), or 15 • To convert 2/5, multiply by 3/3 = 6/15 • To convert 1/3, multiply by 5/5 = 5/15 • 1-6/15 + 2-5/15 = 1+2 and 6/15+5/15 = 3-11/15

  31. Problem (3x3)(2x2y)(4x2y) is equivalent to: F. 9x7y2 G. 9x12y2 H. 24x7y2 J. 24x12y K. 24x12y2

  32. Answer is H • Multiply the constants (3)(2)(4) • When have common base, use the base and add the exponents. • Combine the x terms (x3x2x2 – x3+2+2 – x7) • Combine the y terms (yy – y1y1 – y1+1 – y2) • Result is 24x7y2 If you didn’t get the correct answer, do you see where you made your mistake?

  33. Problem If a rectangle measures 54 meters by 72 meters, what is the length, in meters, of the diagonal of the rectangle? F. 48 G. 63 H. 90 J. 126 K. 252

  34. Answer is H • Did you draw a picture? • Could use the Pythagorean theorem because the sides of the rectangle are the legs of a right triangle • Diagonal of the rectangle is the hypotenuse of the right triangle • Then h2 = 722 + 542 then h = 80 72 meters h 54 meters

  35. Problem If a = b + 2, then (b – a)4 = ? F. -16 G. -8 H. 1 J. 8 K. 16

  36. Answer is K • To find (b - a)4 given a = b+2, you could solve the equation for b - a. • Subtract a and 2 from both sides • You get -2 = b – a • Substitute -2 for b – a in (b – a)4 • (-2)4 or 16

  37. Problem Points B and C lie on AD as shown below. The length of AD is 30 units; AC is 16 units long; and BD is 20 units long. How many units long, if it can be determined, is BC? F. 4 G. 6 H. 10 J. 14 K. cannot be determined from the given information A D C B

  38. Answer is G • Did you use the line drawing to determine your answer? • If AD is 30 units and BD is 20 units then AB is 10 units • If AC is 16 units then AC – AB is 6 units

  39. Problem A cord 24 inches long is 5 inches from the center of a circle, as shown below. What is the radius of the circle, to the nearest tenth of an inch? A. 29.0 B. 24.5 C. 16.9 D. 13.0 E. 10.9 r 5 24

  40. Answer is D • Use the right triangle shown on the diagram • Half the length of the cord is 12 inches (the length of one leg) • The other leg is 5 inches long • The hypotenuse is r inches long • This is a right triangle because the distance between a point and line must be measured perpendicular to the line. • Pythagorean theorem r2 = 122 + 52 then r2 = 169 • r = 13 inches

  41. Problem The larger of two numbers exceeds twice the smaller number by 8. The sum of twice the larger and 3 times the smaller number is 65. If x is the smaller number, which equation below determines the correct value of x? F. 3(2x + 8) + 2x = 65 G. 3(2x - 8) + 2x = 65 H. (4x + 8) + 3x = 65 J. 2(2x + 8) + 3x = 65 K. 2(2x - 8) + 3x = 65

  42. Answer is J • One strategy is to find equations. • In the first part of the problem let y be the larger number and get the equation y = 2x + 8. • The second part of the problem says 2y + 3x = 65. • Substitute 2x + 8 for y in the second equation. • 2(2x + 8) + 3x = 65

  43. To get better at taking the test… • TAKE PRACTICE TESTS • TAKE PRACTICE TESTS • TAKE PRACTICE TESTS

  44. Resources • ACT website • http://www.actstudent.org/ • Louisville Free Public Library • http://www.lfpl.org/MyLibraryU/act.htm • The Real ACT Prep Guide • SparkNotes • http://www.sparknotes.com/testprep/act/

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