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# ACT Scrapbook - Chris Stamper

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FC: PORTFOLIO | Chris Stamper

1: Table of Contents: | Table of Contents - Page 1 -Skill 1: Use the Answers - Pages 2-3 -Skill 2: Super Easy Algebra - Pages 4-5 -Skill 3: SEA--Algebraic Manipulation - Pages 6-7 -Skill 4: "Mean" means Average - Pages 8-9 -Skill 5: The Six-Minute Abs of Geometry: Angles - Pages 10-11 -Skill 6: | Six-Minute Abs of Geometry: Parallel Lines - Pages 12-13 -Skill 7: Six-Minute Abs of Geometry: Triangles - Pages 14-15 -Skill 8: FOIL - Pages 16-17 -Skill 9: Math Vocab - Pages 18-19 -Skill 10: More Math Vocab - Pages 20-21 -Skill 11: Multiples Vocal - Pages 22-23 -Skill 12: Fancy Graphing Vocab 24-25 -Skill 13: Green Circle, Black Diamond: Slaloming Slope - Pages 26-27 -Skill 14: GC, BD: Slaloming Slope Part II - Pages 28-29 -Skill 15: Sport Page: Using Charts and Graphs - Pages 30-31

2: SKILL 1: USE THE ANSWERS Normally you would solve problems the hard way, no shortcuts. That is not so on the ACT. On this, you must use the answers. This is especially easy when there are fractions, pi, or square roots in the questions or answers. "Use the Answers" works best when there are variables and unknowns in the questions and numbers in the answer choices. | MATH MANTRA #1: When you see variables or unknowns in the question and numbers in the answers, "Use the Answers." Convert fractions, pi, or square roots to decimals.

3: I really don't know of a job where this is really useful.

4: SKILL 2: SUPER EASY ALGEBRA 2x+3=8x-5 Use algebra to get x alone. 2x+3+5=8x-5+5 2x+8-2x=8x-2x 8=6x 8/6 = 6x/6 8/6 = 4/3 = x 4/3 = 1.33 = x | Math Mantra #2: When you see "X=?" complete the algebra or just "Use the Answers"

5: Subtract 2x from both sides, and add 5 to both. You will get 8=6x. Divide by 6. You will get 4/3=x. So, x=4/3. | Not sure how this is useful in a job.

6: SKILL 3: Super Easy Algebra - Algebraic Manipulation Generally, the answer choices in these will have variables as well as numbers. Whatever letter is after the "What is" is the variable you are solving for. 3x+4y=12 3x-3x+4y=14-3x 4y=12-3x Divide both sides by 4. y = 3-3/4x | Math Mantra #3: "What is y in terms of x and z" is just a fancy way of saying "solve for y" or "use algebra to get y alone."

7: Also not sure of a job where this could be useful.

8: SKILL 4: "Mean" means Average Average = Sum/Number of items Median is the middle number in a list of numbers Mode is the number that appears most often. 5,7,9,9,11,12,12,15,15,15,15 The median in this list would be 12; the mode would be 15. When you see a median or mode, just rewrite the data as a list in order, | Math Mantra #4: When you see the word "mean" or "average" on the ACT, use: Average = Sum/Number of items

9: I believe this is useful in a job in sports somehow.

10: SKILL 5: Six Minute Abs of Geometry - Angles 1) Vertical angles are equal 2) The angles in a linear pair add up to 180 degrees (If you are given M then n=180-m, m and n are supplements, meaning they add up to 180. 3) The angles in a triangle add up to 180. 4-sided figure, 360. 5-sided, 540. 6-sided, 720. | Math Mantra #5 - When you see vertical angles, linear pairs, or a triangle, calculate the measures of all angles. | This skill is most useful in construction, when deciding what angles to use on building a house.

12: Skill 6: Six Minute Abs of Geometry - Parallel Lines Parallel Lines - Lines that never touch If two parallel likes are crossed by another line (called a transversal), then eight angles form Two angle types - Big and little. All bigs are equal, all littles are equal Congruent - Equal | Math Mantra #6 - When you see two parallel lines that are crossed by another line, eight angles are formed, and all the bigger-looking angles are equal, and all the smaller-looking angles are equal. | Parallel lines are generally used in planning and construction. A common set of parallel lines are railroad tracks.

14: Skill 7: Six Minute Abs of Geometry - Triangles Isosceles triangle - Two equal sides; angles opposite the sides are also equal. Equilateral - All sides equal; angles of 60 degrees. | Math Mantra #7 - When you see a triangle with two equal sides, mark the two opposite angles as equal, and when all sides of a triangle are equal, mark all angles as 60. | This is useful in designing buildings, generally the roof, or perhaps the rest of the building if there is an odd design plan.

16: Skill 8: FOIL First, Outside, Inside, Last (3x+2)(2x-4): Multiply 3x by 2x. Multiply 3x by -4. Multiply 2 by 2x. Multiply 2 by -4. You will get 6x^2-12x+4x-8. Combine like terms. You will get 6x^2-8x-8. | Math Mantra #8 - When you see an expression like (2x-5)(5x-4), multiply the first letter and number into the second parenthesis, multiply the second number into the matching parenthesis, and collect the like terms. | I see no real world application for FOIL, honestly.

17: Multiply 2x by 5x. Multiply 2x by -4. Multiply -5 by 5x. Multiply -5 by -4. You will have 10x^2-8x-25x+20. Collect like terms. You will have 10x^2-33x+20.

18: Skill 9: Math Vocab -Real number: Any number -Constant term: Letter in place of a number, like a variable, expect it won't vary -Integer: Numbers without decimals or fractions -Even numbers: 2,4,6,8... 0 is considered an even number -Odd numbers: 1,3,5,7,9... -Positive/Negative: Positive numbers are greater than 0, negative less than 0 -Consecutive numbers: Numbers in a row; 7,8,9,10... -Different numbers: Numbers that are different -Prime number: A number whose only factors are 1 and itself. 2,3,5,7,11... 1 is NOT considered a prime number, and 2 is the only even one -Units digit: Fancy terms for the "ones" digit in a number, like the 2 in 672 | Math Mantra #9 - Anytime you see a math vocab word, underline it. | I really only see a use for this skill in jobs like a mathematician.

19: Find out the prime numbers. They are 2,3,5,7,11,13,17,19,23... You need to know the odd ones less than 20. Those are 3,5,7,11,13,17, and 19. There are 7 odd prime numbers less than 20.

20: Skill 10: More Math Vocab -Factoring: Numbers that divide into a number evenly, without a remainder. -Greatest common factor: The largest factor shared by several given numbers. (48 and 32. GCF is 16, being the largest number that can smoothly go into both.) -Prime factors: The factors of a number that also happen to be prime numbers. | Math Mantra #10 - Don't be intimidated by fancy vocabulary words. | Once again, I only see this skill being useful as a mathematician or something similar.

21: Factor it out. Then, find the amount of factors that are also prime numbers. | There are only three prime numbers in that: 2, 3, and 5. Therefore, the answer is H. | This is a factoring tree, another way of factoring. This one goes down right to the prime numbers.

22: Skill 11: Multiples Vocab -Multiples: All the numbers that are divisible by a certain number (multiples of 3: 3,6,9,12,15,18,21,24,27...) -Least common multiple: The lowest number that is a multiple of several numbers (LCM of 10,15, and 20?) | Math Mantra #11 - To find the "least common multiple" or "lowest common denominator," "Use the Answers!" | I sadly do not see a major use for this in real life.

23: Simply divide the numbers into all of the potential answers. If all three divide evenly into it, then that is one of the multiples. The smallest one happens to be 600.

24: Skill 12: Fancy Graphing Vocab -Standard (x,y) coordinate plane: a fancy term for the normal grid that you graph lines on -Cartesian plane: another fancy term for the grid -Ordered pair: a fancy term for the (x,y) coordinates on a grid -x-intercept/y-intercept: value a graph crosses the x/y axis -Defined/Undefined: Undefined is where the expression violates math rules. So, defined does not. (Square root of -25 is undefined) | Math Mantra #12 - Don't be intimidated by fancy terms. | Unless you do a lot of graphing, this is not going to be that useful in life.

25: For the ACT, it is usually easier to sketch a diagram. If you do that, you will find that (7,0), or H, is the answer.

26: Skill 13: Green Circle, Black Diamond: Slalom Slope 1 -Slope = y1-y2/x1-x2 -Slope of a line measures steepness; larger slope, steeper line -Slope is also called rate or rate of change -Positive slope if it raises from left to right -Negative if it falls from left to right | Math Mantra #13 - To find the slope or "rate of change" of a line, use y1-y2/x1-x2 | I believe this is useful when planning anything that has to do with slopes.

28: Skill 14: Slaloming Slope 2 -Parallel lines have equal slopes -Perpendicular slopes have negative reciprocal slopes -A line expressed in the form of y=mx+b has a slope of m -That form is slope-intercept form -Ax+By=C is standard form -Use algebra to convert that to slope-intercept | Math Mantra #14 - An equation in the form of y=mx+b is called slope-intercept form, where m represents the slope of the line. Parallel lines have the exact same slope, like 2/3 and 2/3. Perpendicular lines have negative reciprocal slopes, such as 2/3 and -3/2 | Unless you are a mathematician, I don't see how this is useful, honestly.

30: Skill 15: Using Charts and Graphs | Math Mantra #15 - The key to charts and graphs is to read the intro material and the "note" if there is one, and to expect an average, percent, or probability question about the data. | This is extremely useful in many jobs, such as creating a graph or chart for sales, or as a reference.

31: To solve this problem, add up the total amount of votes. There should be 31. Divide the number of votes for Wedding Crashers by the total votes. You should get .129, or 13%.

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• By: Chris S.
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