FC: Helpful ACT skills | ACT Skills | By Carleisha Hanns 1st period March 2nd 2012
1: Table Of Contents | page2-3: Skill 31 page4-5:Skill 32 page6-7:skill 33 page8-9: Skill 34 page10-12:Skill 34 page12-13: Skill 36 page14-15: Skill 37 page16-17: Skill 38 page18-19: Skill 39 | page20-21: Skill 40 page22-23: Skill 41 page24-25: Skill 42 page26-27: Skill 43 page28-29: Skill 44 page30-31: Skill 45 page32-33: Skill 46 page34-35: Skill 47 page36-37: Skill 49
2: Skill 31 | The Law of Exponents II | 1. If adding matching bases and matching exponents, you add coefficients. Ex: | 2. Negative exponents are the same as reciprocal Ex:
3: 3. With fraction exponents, the top number is the power, the bottom is the root. Ex:
4: Skill 32 | Slope Intercept Form | - When you see y=mx+b remember, m is the slope and b is the y-intercept. | Ex: Trex is mixing raisins and peanuts to make trail mix. Raisins have 60 calories/oz and peanuts have 150 calories/oz. Trex wants to have a total of 1200 calories. Let x= number of ounces of raisins Let y= number of ounces of peanuts Write and equation stating the total number of calories is 1200.
5: Answer: 1200 = 60x + 150y manipulate this to get equation in slope-intercept form 150y = -60x + 1200 y = (-60/150)x + (1200/150) y = (-6/15)x + (120/15) y = (-2/5)x + 8 slope is -2/5 and y-intercept is 8
6: Skill 33 | Arrangements | - In arrangements problems, first you need to make blanks for each place and then fill the places and multiply these numbers and that's the number. Also when doing teams or pairs multiply by 2. | Ex: How many license plates using one digit followed by three letters and then three digits can the state of California issue if: A. Repetition of letters and numbers is permitted? B. No repetition of letters or numbers is permitted?
7: Answer: 10*26*26*26*10*10*10 = 175,760,000
8: Skill 34 | SohCahToa | - Sin= Opposite/Hypotenuse -Soh - Cos= adjacent/Hypotenuse -Cah -Tan= Opposite/adjacent -Toa
9: Answer: You're looking for the leg. The equation would be tan58=6/x So 6/tan58 is So 3.75 f | Ex: A ladder leaning against a building makes a 58 degree angle with level ground. The distance from the foot of the ladder to the building is 6 feet. Find how far up the building the ladder will reach?
10: Skill 35 | Use the Answers | -Most ACT questions that you don't know how to solve, you can use the answers they give you. | Things you should know: -Cosecant= 1/sin -Secant= 1/cos -Cotangent= 1/tan
11: Example: 1-tan^4(x)/sec^2(x)=1-tan^2(x) | Answer: [1 - tan^4 x] / sec^2 x = (1 - tan^2 x) (1 + tan^2 x) / sec^2 x = (1 - tan^2 x) sec^2 x / sec^2 x = 1 - tan^2 x.
12: Skill 36 | Probability | -When you do probability problem you need to know the probability equation . | Probability= want/total
13: Ex: You draw one card from a 52 card deck what is the probability that it will be neither a heart nor a 7? | Answer: There are 13 hearts, including the 7 of hearts and the 7's of clubs, spades and diamonds for a total of 16. 52-16=36 36/52 =9/13
14: Skill 37 | Anything times zero is zero | -When you have equations like (x+2)(x-7)=0. All you have to do is use the answers.
15: Ex: What are the values for x that satisfy the equation (x-2)(x+5)=0? | Answer: (x-2) (x+5) x=2 x=-5
16: Skill 38 | Y= ax^2 + bx + c | - In y=ax^2+bx+c, a tells whether the u-shaped graph goes up or down, and c is y intercept. | - In y=(x-h)^2+k equations, h and k give the coordinates for the vertex. | - Vertex: the lowest and highest point of the graph.
17: Ex: Put Y = 2x^2 -24x + 40 into standard form? | Answer: Standard form is: f(x) = ax^2 + bx + c Vertex form is: f(x) = a(x - h)^2 + k y = 2x^2 - 24x + 40 y = 2(x^2 - 12x + ___) + 40 complete the square by adding 36 inside, but subtracting 72 outside y = 2(x - 6)^2 - 32 vertex: (6, - 32)
18: Skill 39 | Circles | - For circle problems you need to know, (x-h)^2+(y-k)^2=r^2 | - (h,k) is the center and r is the radius.
19: Ex: What is the center of the circle given by the equation (x-8)^2= 49 | Answer: (8,2)
20: Skill 40 | Weird Circle Factoid | - If a triangle is the diameter of a circle, and the opposite vertex is on the circle, then the triangle is right, with its right angle opposite the diameter.
21: Ex: What is a the area of a pizza with the diameter of 20 inches? | Answer: area= pi*r*r. 20/2=10 10pi
22: Skill 41 | Absolute Value | - The absolute value is represented by two bars. | -When you see absolute value bars you drop the negative. | -Don't automatically drop negatives do the math inside the bars first.
23: Ex: Simplify | 2 + 3(–4) | | Answer: | 2 + 3(–4) | = | 2 – 12 | = | –10 | = 10
24: Skill 42 | Sequences | -Arithmetic sequence is sequence of numbers where a certain number is added to each term to arrive at the next. | -Geometric sequence is a sequence of numbers where a certain number is multiplied by each term to arrive at the next.
25: Ex: What 2 numbers should be placed in the blanks so that the difference between consecutive numbers is the same? 14,_,_,47 a.11.11 b.25,36 c27,38 | Answer: 14-25= -11 25-36= -11 36-47= -11 b
26: Skill 43 | Fahrenheit/Celsius Conversions | - Formula: F= 9/5C+32 | - In problem and your are given degrees Celsius plug into formula
27: Winson reads a temperature of 34 degrees, what is the equivalent temperature on a Fahrenheit thermometer ? | Answer: F=9/5*34+32 =93.2 93
28: Skill 44 | Careless Errors | -Underline all vocab. words. | -Distribute the negatives.
29: Ex:(2x)^2 =4x^2 | Ex: -2(3x-3) = -6x+6
30: Skill 45 | Careless Errors II | - Foil (first, inner, outer, last) Ex: (x+3)(x-3)= x^2-9 | - Pemdas (Parenthesis,Exponents, Multiplication/Division ,Subtraction/Addition
31: -x with out an exponent means x^1. Ex:(x^2)(4x^5)(3x) =12x^8
32: Skill 46 | Weird Number Behavior | - Small fractions multiplied by smaller fractions make smaller fraction. Ex: (1/2)^2= 1/4 | - Larger the digit of a negative number is, the smaller it is. Ex: -318<0
33: - Subtracting a negative number is like adding. Ex: 66-(-5)=71
34: Skill 47 | Logs | - Logs in math aren't big pieces of wood, it really means writing exponents. Ex: log5 25=2 means 5^2=25
35: Ex: What is the real value of x in the equation log2 16=log4x | Answer: x= 4*4*4*4+=64
36: Skill 38 | Not so Complex Numbers | -When dealing with complex numbers treat i like a regular number. | - Always replace i^2 with -1 .
37: Ex: What is (i-2)(i-3)? | Answer: i^2-3i-2i+6= i^2-5i+6= -1-5i+6= 5-5i