ACT Math Strategies: Mastering Test Questions with Proven Tricks!

1. How do I succeed? • 34 questions right out of 60 is a 22. That is 57% • Spend time wisely on problems you can handle. FINISH the test!! • NOT PUNISHED FOR WRONG ANSWERS - GUESS - try eliminating wrong answers or use patterns. • Test moves from Easy to Hard for the most part.

2. THERE ARE SOME EASY POINTS!!

3. TRICK # 1 Underline the question!! • What is the fifth term of the arithmetic sequence 8,5,2,… A. -4 B. -1 C. 2 D. 5 E. 16 23% of our kids got it right. The majority Of the wrong answers incorrectly chose the next term or 4th term -1 Answer: A. -4

4. TRICK # 2 - Substitution: PLUG IN the number WHEN to USE: • When the problem is asking you to plug an input to find an output. • This is like plugging in an “x” value to find a “y” value. • Identify problem in y =……. Or v = …….. Or P=…..format and you are finding y or v (volume) or P (power)

5. TRICK # 2 - Substitution: PLUG IN the number • The formula for the volume • of a sphere with a radius r is If the radius is 1 ⅓, what is the volume? • 6 • 7 • 10 • 17 • 66 Finding y (V or volume) 1+ ⅓ Clear memory 2nd + 712 Ans = C or 10

6. TRICK # 2 - Substitution: PLUG IN the number • If f(x) = x3 – x2 –x, what is the value of f(-3)? • -39 • -33 • -21 • -18 • 0 f(x) notation means f(-3) tells you x = -3 FIND y or f(x) -3 Answer is B Clear memory 2nd + 712

7. Trick #3 Backsolve WHEN to USE: • This is like algebra or finding “x” value. • Substitute the answers to see if it matches the output value the problem wants • Usually start with middle number or “C” value

8. Trick #3 Backsolve – substitute an answer • The velocity, in meters per second, of an object is given by the equation V = 5/3 t + 0.05, where t is the amount of time that has passed, in seconds. After how many seconds will the object be travelling at 0.575 meters per second? • 0.28 finding x not y • 0.315 • 0.365 • 0.525 • 0.57 Use an answer not 0.575… use 0.365 5/3*0.365+.05 Too High Try .315 Answer is B

9. Trick #3 Backsolve – substitute an answer Of the participants at a conference, 1/3 are doctors; ½ are nurses; and the remaining 12 are trainers. Each participant has only one of those careers. What is the total number of participants at the conference? A.36 B.48 C.60 D.72 E.76 Doctors = ⅓ (60) = 20 Nurses = ½ (60) = 30 + trainers = 12 62 Pick 60 and backsolve

10. Trick #3 Backsolve – substitute an answer Of the participants at a conference, 1/3 are doctors; ½ are nurses; and the remaining 12 are trainers. Each participant has only one of those careers. What is the total number of participants at the conference? A.36 B.48 C.60 D.72 E.76 Doctors = ⅓ (72) = 24 Nurses = ½ (72) = 36 + trainers = 12 72 Pick 72 and backsolve D is Answer

11. Trick #4 PICKING NUMBERS • When there are variables or expressions in the answers • When it is about properties of numbers • Pick the easiest numbers to backsolve…just not 0 or 1 normally. • 2 and 3 are great choices unless asked for two even numbers or two odd numbers

12. Trick #4 PICKING NUMBERS-tables • If m is an integer, then (m-1)2 + 3 must be: • An odd integer • An even integer • An integer divisible by three • A positive integer • A negative integer (2-1)2+3 (3-1)2+3 Ans: D

13. Trick #4 PICKING NUMBERS Let r be 2 If r is an even integer and s is an odd integer, which of the following must be odd? • r (r + s) • s2 – r • 3r + 2s • (rs)2 • r/s Let s be 3 2 (2+3) = 10 even 32 – 2 = 7 odd 3(2) +2(3) = 12 even (2x3)2 = 36 even 2/3 = .667 neither B is answer

14. Trick #4 PICKING NUMBERS-tables • Which of the following statements describes the total of the first n terms of the sequence below? 1,3,5,7,9,…. A. The total is always equal to 25 regardless of n. B. The total is always 2n. C. The total is always 3n. D. The total is always equal to n2. E. There is no consistent pattern for the total. n total 1 term 2 terms 3 terms 12=1 22=4 32=9 D is Answer

15. Trick 5 - USE THE CALCULATOR • Be able to square root and use exponents • Be able to use absolute value in an equation • Trace, Tables & set table, Zoom in/out, Calc Key • Find greatest common factor & least common multiple • Solve simultaneous equations with app • Find roots by graphing or root finder app

16. MATH→NUM for absolute value 14 TI-84+ACT = Success!

17. Graph it: y=x2 – 15 the x axis is y=0 2 X-intercepts show 2 solutions 6 TI-84+ACT = Success!

18. Graph it – the x intercepts will make factors or roots = 0 X=3 is a zero (x-3) will make a zero with 3 (5x+2) will make a zero with -.4 X=-.4 is a zero Ans=A 13 TI-84+ACT = Success!

19. Systems of equations: Graph 7 TI-84+ACT = Success!

20. Systems of equations: Graph • What is the solution set for 5x-7 = 5(x+2) A. {2} B. {7} C. no solution D. all positive numbers E. all real numbers Parallel lines have no solution

21. 2ndCALC Key FASTER to TRACE 9 TI-84+ACT = Success!

22. MATH→NUM for gcd or lcm 12 TI-84+ACT = Success!

23. An APP that would need to be added to the calculators • APPS:PlySmlt2 • Can be used to find solutions and roots of polynomials in lieu of graphing • Can be used to solve systems of equations in standard form

24. Systems standard form APPS:PlySmlt2 Substitute or Eliminate Faster 11 TI-84+ACT = Success!

25. Systems APPS:PlySmlt2 Substitute or Eliminate Faster 8 TI-84+ACT = Success!

26. Trick #6 Guessing is GOOD…BUT • Don’t randomly choose letters, NEVER randomly choose strangest answer or the never works or none of these (E, K) • Eliminate weird answers and guess • Look for a pattern and choose most similar OR STICK WITH YOUR LETTER OF THE DAY B, C or D

27. A better Guess • 2y3∙ 3xy2 ∙ 6xy2 is equivalent to : • 11x2y7 • 11x2y12 • 36x2y7 • 36xy12 • 36x2y12 Why not A or B? 2 ∙ 3 ∙ 6 = 36

28. A patterned guess is the next bestthing to an educated guess!!! What would you guess? • F.  2 • G.  6 • H. 14 • J. 21 • K. 42 In math, value matters Two 1 digit answers and 3 two digits Why not 21? Answer is K

29. A patterned guess is the next bestthing to an educated guess!!! Your turn….What would you guess? • A.$  44.44 • B.$109.08 • C.$118.80 • D.$408.04 • E.$444.40 Answer probably has a four in it and probably be in the hundreds. Answer is D! Sweet!

30. REVIEW TOPICS • Slope, parallel slopes, perpendicular slopes, standard and mx+b • X and Y intercepts • FOIL and Factoring • Vocabulary of roots of a function and solutions of a function • Percentages • Probability & Combinations (tree diagram) • Angles and intersecting lines and parallel lines • Pythagorean Theorem and distance formula • Area of circles, triangles, rectangles, trapezoids • Open or closed inequalities • Mean and average

31. REVIEW General Techniques • Underline the question!!! • Based on answers what can I do to get the question right • Make a table • Use graphing calculator to find X-intercepts or y-intercepts • Backsolve • Pick numbers • Elimination of possibilities • By looking at drawing • By type of problem (You might need a π or √ )