MATH REVIEW

# MATH REVIEW

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## MATH REVIEW

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1. MATH REVIEW Getting ready for the ACT

2. ACT MATH: Broken Down • 60 Q, 60 Minutes • 23% Pre-Algebra • 17% Elementary Algebra • 15% Intermediate Algebra • 15% Coordinate Geometry • 23% Plane Geometry • 7% Trigonometry

3. Formulas • Area of a circle = π* (radius)^2 • Circumference of a circle = π *diameter • Area of a triangle = (1/2)*base*height • Area of rectangle = base*height • Area of a trapezoid = (1/2)*height*(base1 +base2) • Volume of rectangular solid = length*width*height • Pythagorean Theorem: a^2 + b^2 = c^2 (for a non-isosceles right triangle) • Perimeter of rectangle = 2(length + width)

4. Equations • Standard Form: Ax + By + C = 0 • Point-slope Form: Y- y1= m*(X - x1); m=slope, (x1, y1)=point given • Slope-intercept Form: y = mx + b; m=slope, b= y-intercept • Of a circle with center (h,k) and radius r: (x-h)^2 + (y-k)^2 = r^2 • Distance = rate*time • Slope = -(a/b); for all ax+by+c=0

5. Trigonometry • sin^2(A) + cos^2(A) = 1 • SOH: sin= opposite/hypotenuse • CAH: cosine= adjacent/hypotenuse • TOA: tangent= opposite/adjacent • sin(x)= cos(90-x) • Ratio for 30:60:90 triangles: 1:√3:2 • Ratio for 45:45:90 triangles: √2:√2:1

6. Exponents • Add: c*x^a + d*x^a = (c+d)*x^a • Subtract: c*x^a - d*x^a = (c-d)*x^a • Multiply: (c*x^a)*(d*x^b) = (cd)*x^(a+b) • Divide: (c*x^a)/(d*x^b) = (c/d)*x^(a-b) • Distribution: (cd)^a = (c^a)*(d^a) • Power of a power: c(x^a)^b= c*x^(ab)

7. Other Helpful things to know • Rule for divisibility by 3: adding the digits of a number divisible by 3 will give you a multiple of 3 (Ex: 57; 5+7=12). • Know how to set up proportions and use cross-multiplication. • There are 180° in a triangle. • Multiplying/Dividing inequalities by a negative will switch the sign from < to > or visa versa. • A larger denominator will make the fraction a smaller number/decimal.

8. Helpful Websites • www.studyguidezone.com/act_math.htm • www.flashcardexchange.com/study • www.testprepreview.com/act_practice.htm • www.sparknotes.com/math

9. Practice Questions

10. 1. Solve and simplify: (1/2) * (3/4) * (4/2) * (1/7). • A. 12/112 • B. 28/3 • C. 3/28 • D. 3/14

11. 2. Mason is ten years older than Shaun. Last year, Mason was three times as old as Shaun. How old are the two now? • A. 21, 7 • B. 17, 7 • C. 16, 6 • D. 25, 15

12. 3. Alex has 2 quarters, 3 dimes, 1 nickel, and 5 pennies in his pocket. He wants to buy a pack of gum for 20¢. The first coin he pulls out is a dime. What is the probability that he can pay for the gum with the next coin he pulls out of his pocket? • A. 2/5 • B. 5/11 • C. 4/11 • D. 1/5

13. 4. If Tom can paint a picket fence in 2 hours, and Dane can paint the same fence in 3 hours, how long would it take for the both of them to paint the same fence together? • A. 1Hr. 12 Minutes • B. 1Hr. 36 Minutes • C. 1Hr. 52 Minutes • D. 2Hrs. 5 Minutes

14. 5. Solve the following equation for x: 4x/5= 10+6x. • A. -.52 • B. 1.92 • C. 1.47 • D. -1.92

15. 6. If Bre worked 26 hours last week and earned \$150, then how much will she make for working 20 hours this week? • A. \$184.62 • B. \$115.38 • C. \$150.00 • D. \$34.62

16. 7. If B=4, then B^2(B^3-10) equals? • A. 854 • B. 1,014 • C. 864 • D. 216

17. 8. Solve: 0.35+0.45. • A. 3/4 • B. 9/10 • C. 4/7 • D. 4/5

18. 9. Factor completely: x^10*y^3 - 4x^9*y^2 - 21x^*8y. • A. xy^8(xy+7)(xy-3) • B. x^8*y(xy-7)(xy+3) • C. x^8*y(xy+7)(xy-3) • D. xy^8(xy-7)(xy+3)

19. 10. What is the square root of 108x^4*y^6*z^10? • A. 54x^2*y^3*z^3 • B. 6√3x^4*y^6*z^10 • C. 10x^2*y^(3/2)*z^(5/2) • D. 6√3x^2*y^3*z^5

20. 11. Which of the following statements is true? • A. When dividing a negative number by a positive number, the result is negative. • B. The product of one negative and one positive number is a positive number. • C. When dividing two negative numbers, the result is negative. • When adding a positive number and a negative number, the sum is always negative.

21. 12. Evaluate: (3x^2*y^3*z)(5x^3*y*z^3) • A. 15x^-1*y^2*z^-2 • B. 15x^6*y^3*z^3 • C. 8x^5*y^4*z^4 • D. 15x^5*y^4*z^4

22. 13. Find the slope in the equation: 2x-6y=10. • A. 2 • B. 3 • C. (1/3) • D. -2

23. 14. 15 is 40% of what number? • A. 37.5 • B. 21 • C. 35.5 • D. 40

24. 15. If Zach paid an average of \$10 per steak for four steaks, one of which was more expensive than any of the others, how much was the most expensive steak? (1) The amount paid for the most expensive steak was \$13 more than the least expensive steak.(2) Zach paid an average of \$7 per steak for three of the steaks. • A. \$10.00 • B. \$12.50 • C. \$19.00 • D. \$20.00

25. 16. Which answer correctly identifies this number in scientific notation: 0.0000063? • A. 6.3 X 10^6 • B. 6.3 X 10^-5 • C. .63 X 10^-7 • D. 6.3 X 10^-6

26. 17. Solve for x: 10^2 + x^2 = 26^2 • A. 16 • B. 24 • C. 20 • D. 12

27. 18. Find the median in this group of values: 8.2, 11.3, 9.7, 7.4, 14.3, 4.1, 19.6, 12.8, 11.4, 8.6 • A. 9.7 • B. 10.0 • C. 10.5 • D. 11.3

28. 19. Approximate: √80 + √50. • A. 10 • B. 11 • C. 12 • D. 16

29. 20. Two kids are evenly balanced on a seesaw, weighing 40 and 60 pounds. If the lighter kid is 9 feet from the middle, how far is the heavier kid from the middle? • A. 6 feet • B. 7 feet • C. 8 feet • D. 9 feet

30. 21. If Ryan’s car uses 25 gallons of gas to drive 350 miles, how many gallons doesit take to drive 630 miles? • A. 42 • B. 43 • C. 45 • D. 48

31. 22. Evaluate: |2(3x-15)-3(20x-22)| - |4(x-12)-2(2x+6)| • A. -82x+96 • B. 26x+24 • C. -82x-24 • D. 26x-24

32. 23. Simplify: √x(x^2)^3. • A. x^3 • B. x^(13/2) • C. x^6 • D. x^(15/2)

33. 24. Solve for x: 16^{2x+(1/2)}= 64^(x+5) • A. 4/3 • B. 5 • C. 7 • D. 14

34. 25. All of the following are whole numbers EXCEPT: • A. 0 • B. -3 • C. 6 • D. 7

35. 26. Find the answer to a^2*b-a*b^2+2a^2*bif a=4 and b=2. • A. -48 • B. 96 • C. 80 • D. 112

36. 27. Solve 6x+2y=26 3x+18y=-21 • A. (5, -8/17) • B. (-17/8, 5) • C. (5, -17/8) • D. (-5, 8/17)

37. 28. If a circle has a radius of 6, then what is the circumference? • A. 18.85 • B. 18.0 • C. 37.70 • D. 36.0

38. 29. What is the area of a triangle with sides of 5, 12, and 13? • A. 30 • B. 65/2 • C. 60 • D. Cannot be determined.

39. 30. What is the complement of an eighty degree angle? • A. 80° • B. 100° • C. 10° • D. 260°

40. 31. If p=2a and 4a=5t, then p equals? • A. t/2 • B. t • C. 2t • D. 5t/2

41. 32. Katie wants to buy a webcam regularly priced for \$35. She buys it for \$10. What was the percent discount she got on the webcam? • A. 2.86% • B. 25.00% • C. 28.57% • D. 35.00%

42. 33. Divide x^2 by x^6. • A. x^4 • B. x^(1/3) • C. x^-4 • D. x^(-1/3)

43. 34. Steph wants to make some biscuits and gravy. The biscuits need 3 1/2 cups of flour, and the gravy 7/4 cups of flour. She has 5 cups of flour. Does she have enough for her batch, or if not, how much more does she need? • A. She has enough. • B. She needs 1/4 cup more. • C. She needs 3/2 cups more. • D. She needs 3 cups more.

44. 35. If 6 is 24% of a number, then what is 60% of the same number? • A. 10 • B. 15 • C. 24 • D. 30

45. Answer Key • 1. B 19. D • 2. C 20. A • 3. A 21. C • 4. A 22. D • 5. D 23. B • 6. B 24. D • 7. C 25. B • 8. D 26. C • 9. B 27.A • 10. D 28.C • 11. A 29. A • 12. D 30. C • 13. C 31. D • 14. A 32. C • 15. C 33.C • 16. D 34. B • 17. B 35. B • 18. C