FC: ACT Skills Scrapbook
1: Table of Contents Use the Answers . . .Page 2-3 Super Easy Algebra . . .Page 4-5 Super Easy Algebra-Algebraic Manipulation . . .Page 6-7 'Mean' Means Average . . .Page 8-9 The Six Minute Abs of Geometry: Angles. . .Page 10-11 The Six-Minute Abs of Geometry: Parallel Lines . . .Page 12-13 The Six-Minute Abs of Geometry: Triangles . . .Page 14-15 Foil . . .Page 16-17 Math Vocab . . .Page 17-18 More Math Vocab . . .Page 19-20 Multiples Vocab . . . Page 21-22 Fancy Graphing Vocab . . . Page 23-24 Green Circle, Black Diamond:Slaloming Slope I. . .Page 25-26 Green Circle, Black Diamond: Slaloming Slope II. . .Page 27-28 The Sports Page: Using Charts and Graphs. . . .Page 29-30
2: Skill 1: Use the Answers | In math there is usually no short cuts, or any that the students know of at least. Not knowing shortcuts makes students dread math, but the key to short cuts is multiple choice. If the problem is multiple choice, like the ACT will be, then there is a short cut. All you have to do is plug in each answer given to the problem and see which answer fits best.
3: Example: | Find x: 3x-4= -10 A: -2 B: -1 C:0 D: 2 E: 5 | To get the answer to this problem, I plugged in each answer given to me to which answer fit best. when doing that I found out that answer A (-2) fit the problem best. 3(-2)-4= -10
4: Skill 2 Super Easy Algebra | Algebra is a math that can confuse a lot of people, which is why you have to break is down into parts and focus. Make sure that you are paying attention to what you are suppose to do, what you are doing, and where you are moving things in your problem. Algebra can be easy, if you know what you are doing and pay attention.
5: Example: | If 6x+6=36=3x , then x=? I took 3x and subtracted it from both sides, then i took 6 and subtracted it from both sides. Once I did that and i had 3x=30 I divided both sides by 3 to get my answer. C was my answer, x=10
6: Skill 3 Super Easy Algebra - Algebraic Manipulation | Students look at algebra and think "OH NO!" because they see all of the letters and numbers together. They think that letters and numbers should not go together. Well that is true but that's all that algebra is. You have to take is slowly and pay attention.
7: Example: If I=PRT, then which of the following is an expression for R in terms of I,P and T? A: IPT B: I-PT C: I/PT D:PT/I E: 2/IPT I chose answer C for this because If you are looking for R then the only expression that would fit would be R=I/PT
8: Skill 4 "Mean" Means Average | If you are looking for the average of a few numbers in a math problem, then you will most likely be asked to find the "mean." If you are asked to find the "mean" do not freak out because they used a fancier word then average. All you have to do is add all of your numbers together and divide by how many numbers you had.
9: Example: Abida wants to find the average cost of a pint of ice cream at a local store. If the five different pints that the store sells are priced at $1.80, $2.10, $1.90, $2.80, and #3.20, what is the average price? A: $2.20 B: $2.24 C: $2.32 D: $2.36 E: $2.42 The answer would be D, $2.36 because when you add all the prices together and divide by 5, your answer is $2.36.
10: Skill 5 The Six-Minute Abs of Geometry: Angles. | On the ACT the students always see the questions that have to with angles and freak out because they don't remember how to do them from 9th grade. All you have to do is remember this: The angles in a triangle ad up to 180 degrees. The angles in a 4-sided shape add up to 360 degrees. The angles in a 5-sided shape add up to 540 degrees. The angles in a 6-sided shape add up to 720 degrees.
11: Example: If the measure of an angle is 42.5 degrees, what is the measure of its supplement? A: 47.5 degrees B: 57.5 degrees C: 132.5 degrees D:137.5 degrees E: Cannot be determined from the given information I got letter D as my answer. I took 180 degrees - 42.5 degrees to come up with my answer 137.5 degrees.
12: Skill 6 The Six-Minute Abs of Geometry: Parallel Lines | Parallel lines are another thing that students freak out on when the see it on the ACT. Well luckily we only need to know this: -Parallel lines are two lines that never touch. -If two parallel lines are crossed by another line (called a transversal), then eight angles form. -These eight angles are of two types, big or little. All bigs are equal, and all littles are equal.
13: Example: | The answer for this problem is A. You have to take angle z and subtract it from angle x, and after that you take your product and subtract it from 180 degrees.
14: Skill 7 The Six-Minute Abs of Geometry: Triangles | Another stressful part of the ACT is the triangle part. You are staring at the triangle but you can not decide what the triangle is. So just remember this: -If a triangle is isosceles, then the two angles opposite the equal sides, are also equal. -If a triangle is equilateral, then it has all equal angles of 60 degrees each.
15: Example: | I got letter D as my answer to this problem. If it is an equilateral triangle then all angles are 60 degrees each, but x is outside the triangle so it equals 120 degrees.
16: Skill 8 Foil | Students always seem to confuse themselves when they use foil. But! There is a way to help cut down all the confusion and make it a little easier! When using foil just remember: First, Outer, Inner, and Last. Use the analogy that goes with foil.
17: Example: Which of the following expressions is equivalent to (2x-2)(x+5)? A: 2x^2+12x-10 B: 2x^2+12x+10 C: 2x^2-12x+10 D:2x^2+8x-10 E: 2x^2-8x+10 I can up with the answer D for this because when you foil it out, all the numbers match up to letter D's answer.
18: Skill 9 Math Vocab | Knowing the vocab will get you further then you think on the ACT. Real Number: Basically anything and everything! Constant Term: A letter in place of a number, kinda like a variable, except that it won't vary. Integer: Numbers without decimals or fractions Even/Odd: Even numbers: 2,4,6 etc... Odd numbers: 3,5,7,9 etc... Positive/Negative: Positive are greater then 0, Negative are less then 0 Consecutive Numbers: Numbers in a row: 7,8,9,10 Different Numbers: numbers that are...DIFFERENT! Prime: A number whose only factor are 1 and itself. ex:2,3,5,7,11,13,17 Units Digit: Fancy term for the "ones" digit in a number, like the 2 in 672.
19: Example: For all real numbers x, what integer values satisfy the equation 2x^2=50? A: 25 only B:5 only C:-5 only D: -5 and 5 only E: -5,5, and 25 only. | When I worked it out, letter B, 5, satisfied it for me. 2(5)^2=50.
20: Skill 10 More Math Vocab | Factors: Numbers that divide into a number evenly. Greatest Common Factor: Largest factor shared by several given numbers Prime Factors: Factors of a number that are also prime numbers.
21: Example: Which of the following is an odd number that is a factor of 140? F: 2 G:13 H:35 J:37 K:51 The answer I got to this problem was H, 35. If you take the odd number 35 and divide it by 140, you come out with 4.
22: Skill 11 Multiples Vocab | Multiples: All the numbers that are divisible by a certain number. Least Common Multiple: The lowest number that is a multiple of several numbers.
23: Example: What is the lowest number that is a multiple of 10,12, and 15? A: 1800 B:900 C:120 D:60 E:30 After working this out, my answer came out to A, 1800. If you take 1800 and divide it by each number then you get an even number each time.
24: Skill 12 Fancy Graphing Vocab | Standard (x,y) coordinate plane: A fancy term for the normal grid that you graph. Cartesian Plane: Another fancy term for the normal grid that you graph lines on. Ordered Pair: A pair of (x,y) coordinates on the normal grid. X intercept/y intercept: The value where a graph crosses the x axis or a y axis Defined/Undefined: undefined means violate math rules.
25: Example: | I came up with the answer D for this. All you had to do was think if you have a negative and positive, where would your coordinate? Or if you had a negative and a negative, or a positive and a positive.
26: Skill 13 Green Circle, Black Diamond: Slaloming Slope I | Slope is very easy if you now the formula to use. The formula for slope is: Slope = Y1-Y2 X1-X2 When having this formula all you do is plug each coordinate into the formula.
27: Example: If the slope of a line through the points (2,m) and (-2,-5) is 1/4, what is the value of m? A:2 B: 1 C:0 D:-4 E:-10 Take each answer given to you and plug it into the slope formula to see which answer gives you 1/4. The answer is D: -4.
28: Skill 14 Green Circle, Black Diamond: Slaloming Slope II | Parallel lines have equal slopes. Perpendicular lines have regular reciprocal slopes.
29: Example: In the standard (x,Y) coordinate plane, what is the slope of the line with equation 3y-9x=5? A:-2 B:-1 C:0 D:2 E:3 you have to put the problem into 3y=9x+5.Your answer will be E: 3
30: Skill 15 The Sports Page: Using Charts and Graphs
34: Live well, laugh often, love much
35: Life brings simple pleasures to us every day. It is up to us to make them wonderful memories. - Cathy Allen
37: IT'S NOT WHAT WE HAVE IN OUR LIFE, BUT WHO WE HAVE IN OUR LIFE THAT COUNTS. - J. M. Laurence
39: It's the moments I spend with you that build the memories which last a lifetime. -M Gutierrez
41: Being deeply loved by someone gives you strength; loving someone deeply gives you courage. - Lao Tzu
43: IS NOT MEASURED BY THE BREATHS WE TAKE BUT THE MOMENTS THAT TAKE OUR BREATH AWAY | LIFE
45: Families fill our lives with happiness and laughter leaving us memories to treasure today and forever after.