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ACT Scrapbook

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ACT Scrapbook - Page Text Content


FC: ACT Scrapbook By:Daniel Trent, 1st period October 3, 2012

1: Table of Contents | Use the answers ---------------------------- 2 Super Easy Algebra ------------------------ 4 Algebraic Manipulation ----------- 6 "Mean" Means Average -------------------- 8 The six minute abs of Geometry: Angles ------------------------------ 10 Parrallel Lines --------------------- 12 Triangles ---------------------------- 14 Foil ------------------------------------------ 16 Math Vocab -------------------------------- 18 More Math Vocab ------------------------- 20 Multiples Vocab --------------------------- 22 Fancy Graphing Vocab ------------------- 24 Slaloming Slope I ------------------------- 26 Slaloming Slope II ------------------------ 28 Using Charts and Graphs ---------------- 30

2: When you see variables in the question and numbers in the answer, "use the answers." Convert fractions, Pi, or square roots to decimals. | "USE THE ANSWERS" | In other words... | If the question gives you unknowns, such as x, and there are numbers in the answers, use the answers to determine what the unknown equals.

3: This question looks difficult, but its actually quite simple if you use your answers. You are looking for the smallest of 3 consecutive even integers that add up to 36. All you have to do is find the number that, along with the next 2 even integers that follow it, adds up to 36. In this case, it's C. 10+12+14=36.

4: SUPER EASY ALGEBRA | When you see "then x=?" complete the algebra or just "use the answers." | If 2x+3-4=0, then x=? All you have to do is solve for x. 2x-1=0 2x=1 x=1/2

5: In other words... | When a question asks "then x=?", just get x alone, and do the algebra.

6: ALGEBRAIC MANIPULATION | In other words... | "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." | When a question asks "what is y in terms of x and z," it is just asking you to get y alone on one side and solve for it.

7: What is y in terms of x and z when x=4y-5z+4? Just solve for y. -4y=-x-5z+4 y=1/4x+5/4-1

8: "MEAN" MEANS AVERAGE | When you see the word "mean" or "average" on the ACT, use: | Average = sum number of items

9: In other words... | A mean is just an average of the numbers listed. Divide the sum of the items by the number of items listed. | Tom measured the height of 3 of his friends. Jim was 6 feet tall. Roger was also 6 feet tall. Jessica was only 5 feet tall. What is the average height of Tom's friends? Average = 17 3 Average = 5.6 feet tall.

10: ANGLES | In other words... | When you see vertical angles, a linear pair, or a triangle, calculate the measure of all angles. | When vertical angles, linear pairs, or triangles are present, simply use the measures of the angles to calculate the answer. Vertical angles are equal, linear pairs and triangles add up to 180.

11: In the triangle ABC, angle ABC has a measure of 35 degrees. Angle CAB has a measure of 65 degrees. What is the measure of angle BCA? | All you have to do is add 35 and 65, then subtract the sum from 180. Then you will have the measure of angle BCA because a triangle has to add up to 180 degrees.

12: PARALLEL LINES | 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 ones are equal. | In other words | When two parallel lines are intersected by another line, eight angles are formed. Every big angle is equal to the others, and all the smaller angles are equal to one another.

13: 180-37.5=142.5 Since linear pairs add up to 180, x has to equal 142.5.

14: TRIANGLES | 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 60 degrees. | The side of the triangle AB has a length of 5. The side of the triangle CB also has a length of 5. Angle BCA has a measure of 70 degrees. What is the measure of angle ABC? | Since AB and CB both have a length of 5, they angles BAC and ACB are equal. combined, they have a total measure of 140 degrees. That means that angle ABC has a measure of 40 degrees because 180-140=40.

15: In other words... When two sides of a triangle are equal, the adjacent angles are also equal.

16: FOIL | When you see an expression like (2x-5) (5x-4), multiply the first number and letter into the second parenthesis, then multiply the second number and letter into the second parenthesis, and then collect matching terms. | In other words... When you see two binomials, multiply the first number of the first parenthesis with the first number of the second parenthesis, then the second. Do the same with the second number in the first parenthesis.

17: (5x+7) (3x-4)=0 15x-20x+21x-28=0 16x-28 16x=28 x=7/4 | Simply work the problem out like the skill says to. Once everything is multiplied out, just solve for x.

18: For all real numbers y, find the integer value that would satisfy the equation 40y=2000. | All this problem is asking you to do is solve for y. Therefore, divide 2000 by 40, and you will find what y is. y=50 if you divide correctly.

19: MATH VOCAB | Anytime you see a math vocab word, underline it. Examples of math vocab words include: Real Number Constant Term Integer Even/Odd Consecutive numbers Prime Units Digit | Underline all math vocab terms in a question. | In other words...

20: In other words... Never be intimidated by words you don't know. Learn as many vocab terms as possible.

21: MORE MATH VOCAB | Don't be intimidated by fancy vocabulary terms, such as factors, Greatest Common Factor, and Prime Factors. | What is the Greatest Common Factor of 20 and 40? | 20=1,2,4,5,10,20 40=1,2,4,5,8,10,20,40 GCF=20 | To find the Greatest Common Factor of two numbers, first list their factors, or the numbers that they can be divided by. List one number's factors above the other one. Find the largest number that is common in both lists. That is their Greatest Common Factor.

22: MULTIPLE VOCAB | To find the "least common multiple" or the "lowest common denominator," "Use the Answers!". | Find the least common multiple of 2 and 10. | 2- 2,4,6,8,10,12,14,16,18... 10- 10,20,30,40,50,60,70... least common multiple=10 | Simply list the multiples of each number, and choose the smallest number that they have in common. Alternatively, you can just divide the answer choices by each number until you find the smallest number that can be divided by all numbers.

23: In other words... in order to find the least common multiple or the lowest common denominator, simply divide each answer choice by the given numbers and choose the smallest number that can be divided by all the givens.

24: FANCY GRAPHING VOCAB | don't be intimidated by fancy graphing terms like standard coordinate plane, Cartesian plane, ordered pair, or x-intercept. | In other words... Know what those terms mean so that you will know what a question is asking of you.

25: What is the x-intercept of the line that contains the points (-2,3) and (4,1) in the standard (x,y) coordinate plane? | So, all you need to do is write out the equation of the line of the two given points. x+3y=7 Then find the x intercept by removing the y. xintercept=7

26: SLALOM I | To find the slope, or "rate of change" of a line, use slope = y1-y2 X1-x2 | Find the slope of the line that intersects (0,1) and (2,3).

27: In other words.,. | Use the formula, slope = y1-y2 X1-x2 to find the slope of a line. | What is the slope of a line that runs through the points (1,2) and (3,4)? | Just use the formula. (x2,y2); (x1,y1). So... slope = 4-2 = 2 3-1 2 slope = 1

28: SLALOM II | An equation of a line in the form of y=mx+b is called slope intercept form. m= the slope. parallel lines - equal slopes perpendicular lines - negative reciprocal of each others slope | In other words... | The slope intercept form is y=mx+b, where m=slope and b=y-intercept.

29: Write the equation of the line 2x+5y=50 in slope intercept form. 5y=-2x+50 y=-2/5x + 10

30: USING CHARTS AND GRAPHS | The key to charts and graphs is to read the intro material and the "note," if there is one. Expect an average, percent, and/or a probability question about the data.

31: In other words... | Be sure to read the intro material before a graph, so that you have a better understanding of the graph. | This question asks that you find the percent of students that chose Wedding Crashers. Simply divide the number of those that picked that movie, 4, and divide it by the total number of votes, 31. The answer is 13%, B.

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