Download MATH REVIEW

MATH REVIEW
Getting ready for the ACT
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
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)
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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
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
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)
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.
Helpful Websites
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www.studyguidezone.com/act_math.htm
www.flashcardexchange.com/study
www.testprepreview.com/act_practice.htm
www.sparknotes.com/math
Practice Questions
1. Solve and simplify:
(1/2) * (3/4) * (4/2) *
(1/7).
A. 12/112
B. 28/3
C. 3/28
D. 3/14
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
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
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
5. Solve the following
equation for x: 4x/5=
10+6x.
A. -.52
B. 1.92
C. 1.47
D. -1.92
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
7. If B=4, then B^2(B^3-10)
equals?
A. 854
B. 1,014
C. 864
D. 216
8. Solve: 0.35+0.45.
A. 3/4
B. 9/10
C. 4/7
D. 4/5
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)
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
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.
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
13. Find the slope in the equation: 2x6y=10.
A. 2
B. 3
C. (1/3)
D. -2
14. 15 is 40% of what number?
A. 37.5
B. 21
C. 35.5
D. 40
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
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
17. Solve for x: 10^2 + x^2 =
26^2
A. 16
B. 24
C. 20
D. 12
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
19. Approximate: √80 + √50.
A. 10
B. 11
C. 12
D. 16
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
21. If Ryan’s car uses 25 gallons of gas to
drive 350 miles, how many gallons does
it take to drive 630 miles?
A. 42
B. 43
C. 45
D. 48
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
23. Simplify: √x(x^2)^3.
A. x^3
B. x^(13/2)
C. x^6
D. x^(15/2)
24. Solve for x: 16^{2x+(1/2)}=
64^(x+5)
A. 4/3
B. 5
C. 7
D. 14
25. All of the following are whole numbers
EXCEPT:
A. 0
B. -3
C. 6
D. 7
26. Find the answer to a^2*ba*b^2+2a^2*b
if a=4 and b=2.
A. -48
B. 96
C. 80
D. 112
27. Solve 6x+2y=26
3x+18y=-21
A. (5, -8/17)
B. (-17/8, 5)
C. (5, -17/8)
D. (-5, 8/17)
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
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.
30. What is the complement
of an eighty degree angle?
A. 80°
B. 100°
C. 10°
D. 260°
31. If p=2a and 4a=5t,
then p equals?
A. t/2
B. t
C. 2t
D. 5t/2
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%
33. Divide x^2 by x^6.
A. x^4
B. x^(1/3)
C. x^-4
D. x^(-1/3)
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.
35. If 6 is 24% of a number, then
what is 60% of the same number?
A. 10
B. 15
C. 24
D. 30
Answer Key
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1. B
2. C
3. A
4. A
5. D
6. B
7. C
8. D
9. B
10. D
11. A
12. D
13. C
14. A
15. C
16. D
17. B
18. C
19. D
20. A
21. C
22. D
23. B
24. D
25. B
26. C
27.A
28.C
29. A
30. C
31. D
32. C
33.C
34. B
35. B