FC: Must Have ACT Skills | Travis Swails 1st Period September 24, 2012
1: Table of Contents | Page 2-3 4-5 6-7 8-9 10-11 12-13 14-15 16-17 18-19 20-21 22-23 24-25 26-27 28-29 30-31 | Use the Answers Super Easy Algebra Super Easy Algebra-Algebraic Manipulation Mean "Means" Average Six Minute Abs of Geometry:Angles Six Minute Abs of Geometry:Parallel Lines Six Minute Abs of Geometry:Triangles FOIL Math Vocab More Math Vocab Multiples Vocab Fancy Graphing Vocab Green Circle, Black Diamond Slaloming Slope 1 Green Circle,Black Diamond Slaloming Slope II The Sports Page: Using Charts and Graphs
2: Using the Answers | Most often we lose time on a test trying to work the problem out. If we use this quick and easy skill, you can save yourself a lot of time. This skill is simply taking the answers given and put them in the equation given to find your answer. | Most often we lose time on a test trying to work the problem out. If we use this quick and easy skill, you can save yourself a lot of time. This skill is simply taking the answers given and put them in the equation given to find your answer.
3: Example:The lengths of the sides of the triangle are 3 consecutive even integers. If the perimeter of the triangle is 36 cm, what is the length, in cm, of the shortest side? A) 7 B) 8 C) 10 D) 12 E) 14 | Try each one as the shortest side. 7 is not even. 8+10+12 does not = 36 10+12+14=36 12+14+16 does not= 36 14+16+18 does not= 36 | Your answer would be C because it is the only answer that works after using this method.
4: Super Easy Algebra | Use simple algebra to solve the problem | Lets try one problem!!!
5: If 2x + 3 = 8x - 5, then x =? | Lets use simple algebra to solve the answer. | 2x+3= 8X-5 -2x 3=6x-5 +5 8=6x 8/6= 4/3 = 1.33 = X | Your answer is 1.33 because you have solved the problem as far as it can go. After you - your x, you have to add or subtract your whole numbers. This should leave you with #=#x? Divide both by your X, and thats your answer
6: Super Easy Algebra-Algebraic Manipulation | 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". | Lets try a problem to help!
7: If 3x+4y= 12 what is y in terms of x? 1) Subtract 3x from both sides 2)You will have 4y= 12-3x Divide everything by 4 and get y=3-3/4x
8: Mean Means Average | When you see mean on the ACT ,use Average = Sum/Number of items
9: A student earned 40,37,44, and 42 on four 50 point quizzes. What must the student score on the fifth to have a 42 average for 5 quizzes? | Average = Sum/number of items 210= 40+37+44+42+x 210= 163+x 47=x
10: Six Minute Abs of Geometry: Angles | When you see vertical angles, a linear pair, or a triangle calculate the measures of all angles.
11: In the figure , if b=100 what is the value of c? | When it gives you one angle in a linear pair, find the other angle. | 180-140= 40. Now we have three of the four angles that must add up to 360. So the fourth one must be. 360-100-40-77= 143 degrees. Answer: 143 degrees.
12: Six Minute Abs of Geometry: 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 the small ones too
13: In the figure shown ^MNO below, line a is parallel to line b. Which of the following is congruent to Angle ONM? | In the pair of parallel lines crossed by segment MN, several angles are formed, and angle ONM is a smaller-looking angle and is equal to all other small. ZMN are bigger looking angles and are equal to each other , but not to angle ONM. Your answer Angle XMN
14: Six Minute Abs of Geometry: Triangles | When you see a triangle with two equal sides, mark the two opposite as equal, and when all sides are equal, mark all angles 60 degrees
15: IF MN=MO in the figure below, which of the following cannot be true. N=a degrees M= a degrees, and O = c degrees | First mark the diagram Since two angles are equal in this triangle, that means that the other two can be also. So b+c therefore b=c. B=c cannot be correct, and all other answers are correct. | Correct answer = B
16: FOIL | When you see an expression like (2x - 5)(5X-4) multiply the first number and letter into the second parenthesis, and then collect matching terms
17: For all x (2x-5)(5X-4) =? Remember multiply first, 2x to 5x, then to 4. 5 to 5x and to 4. Then gather matching terms. 2x(5x-4)= 10x^2 - 8X -5(5x-4)=-25x+20 10x^2- 8x + (-25x) +20 10x^2-33x+20 That is your final answer.
18: Math Vocab | This tip is hard to explain, but anytime you see a math vocab underline it. That is basically what is being said.
19: Basic Words include: Real number, constant term, integer, even/odd,positive,negative,consecutive numbers,different numbers, prime, and units digit | Example | For all real numbers x, how many values of x are odd prime numbers less than 20. | You would underline odd, prime, real numbers. | List primes less than 20: 2,3,5,7,9,11,13,17,19 all are odd except 2,so there are 7 odd prime less than 20.
20: More Math Vocab | Don't be scared by big words in a problem, just think what they mean and solve.
21: Some words may be Factors, Greatest Common Factor, and Prime Factors | Example, How many different, real number, prime factors does 120 have? | To answer you will factor out 120, and find the prime numbers. The only numbers are 2,3,5. There are only 3 prime factors.
22: Multiples Vocab | To find the "least common multiple", or "lowest common denominator", Use the Answers. Take the vocab that they give you in the question and use it to your advantage
23: Example: What is the least common multiple of 30,40,and 50? | Just use the answers in that are given. Divide each number by 30,40,and 50. 600 is the lowest number that is divisible. 1200 works also, but we are looking for the lowest possible answer.
24: Fancy Graphing Vocab | Don't be intimidated by words like: Standard Plane,Cartesian Plane, ordered pair, intercepts, or defined and undefined. Use these words to answer the question instead of wasting time trying to solve.
25: Example: | What is the x intercept of the line that contains the points (-2,3) and (4,1) in the standard coordinate plane? | Instead of doing the algebraic process, sketch a graph of some sort. This problem is really just seeing if you know vocabulary or not. | Correct Answer: H
26: Green Circle, Black Diamond: Slaloming Slope I: | To find slope, or rate of change, use the equation y2-y1/x2-x1.
27: Example: | If the slope of a line through the points (-2,5) and (3,b) is -1 what is the value of b? | 5-b/-2-3= 5-b/-5 =-1 So now that you have this, you can go back to the first step we ever did and use the answers. Your correct answer in this problem is 0 | We used the slope formula to solve for 5-b/-5=-1
28: Green Circle, Black Diamond: Slaloming Slope II | An equation of a line is y=mx+b. Where m represents the slope. Parallel Lines are the same, and perpendicular are negative reciprocals.
29: Example: | In the standard coordinate plane, what is the slope of the line with the equation 3x-5y=-12? | How to Solve: Subtract 3x from both sides. -5y= -3x-12. Divide both sides by -5. y=3/5x+12/5 is your final answer
30: The Sports Page: Using Graphs and Charts | The key to solving problems like this is to read the material that is given to you in the table and the "note" if one is present.
31: Example: | If a slip of paper is chosen from the box what is the percent that it will be wedding crashers? | You must take the number of slips that have wedding crashers on it, and divide by the total amount of slips. In this case would be 4/31 which gives you approximately 13%.