S: ACT SCRAPBOOK
BC: A Good Beginning Makes a Good Ending
FC: ACT Scrapbook
1: Table of Contents Page 2-3: Use the Answers Page 4-5: Super Easy Algebra Page 6-7: Algebraic Manipulation Page 8-9: Means Average Page 10-11: Angles Page 12-13: Parallel Lines Page 14-15: Triangles Page 16-17: FOIL Page 18-19: Math Vocab Page 20-21: More Math Vocab Page 22-23: Multiples Vocab Page 24-25: Fancy Graphing Page 26-27: Green Circle, Black 1 Diamond: Slaloming Slope I Page 28-29: Green Circle, Black 1 Diamond: Slaloming Slope II Page 30-31: The Sports Page: Using 1 Charts and Graphs
2: When you see variables or unknowns in the question and numbers in the answer choices, "Use the Answers." Converts fractions, , or to decimals. | If 3x -4 = -10, then x = ? A) -2 B) -1 C) 0 D) 2 E) 5 The answer is, A, because when you plug -2 in for x, you get -10 on both sides. | Just plug an answer in for x until it works out correctly.
3: Skill 1: Use the Answers
4: Skill 2: Super Easy Algebra
5: When you see "then x = ?" complete the algebra or just "Use the answers." | If 6x + 6 = 36 + 3x, then x = ? A) 3 B) 9 C)10 D)33 E)9/5 The answer is C) 10, because when you plug 10 in for x you get 66 on both sides.
6: Super Easy Algebra- Algebraic Manipulation | "What is x in terms of y and z" is just a fancy way of saying "solve for y" or "use algebra to get y alone."
8: "Mean" Means Average | When you see the word "mean" or "average" on the ACT, use average = sum number of items
9: So far, a student has earned the following scores on four 50-point quizzes during this marking period: 40,37,44,and 42. What score must the student earn on the fifth quiz to earn an average quiz score of 42 for the 5 quizzes? F) 42 G) 45 H) 47 J) 49 K) The student cannot earn an average of 42 | The answer is H, because if you add 40,37,44,42, and 47 together you get 210, then you must divide 210 by the number of total quizzes which is five. You will then get 42, which is the average the student was achieving for.
10: The Six-Minute Abs of Geometry: Angles | If the measure of an angle is 42.5, what is the measure of its supplement? A) 47.5 B) 57.5 C) 132.5 D) 137.5 E) Cannot be determined from the given data | D is the answer because, you take 42.5 and subtract that number from 180 degrees to get the answer 137.5.
11: When you see vertical angles, a linear pair, or a triangle, calculate the measures of all angles.
12: The Six-Minute Abs of Geometry: Parallel Lines | In the figure to the right, r || s. If 1 = 37.5, what is the value of 6? A) 42.5 B) 100 C) 137.5 D) 142.5 E) 180 | The answer is D because if you subtract 37.5 from 180 you get 142.5.
13: 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.
14: The Six-Minute Abs of Geometry: 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.
16: When you see an expression like (2x - 5)(5x-4), multiply the first number and letter into the second parenthesis, multiply the second number and letter into the second parenthesis, and then collect matching terms.
17: Foil | 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 | The answer is D
18: Math Vocab | Anytime you see a math vocab term, underline it. | Positive/Negative - Positive numbers are greater than 0. Negative numbers are less than 0. Consecutive numbers - Numbers in a row: 7, 8, 9, 10. Different numbers - Numbers that are.....ummm.....different. Prime - A number whose only factors are 1 and itself. The numbers 2, 3, 5, 7, 11, 13, 17,...are prime. Units digit - Just a fancy term for the "ones" digit in a number, like the 2 in 672.
19: 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 | The answer is B, because when you plug in the answers for x it is the only one that equals 50. | Constant Term - This word really throws some kids, but it just means a letter in place of a number, kinda like a variable, except that it won't vary. Integer - Numbers without decimals or fractions: -3, -2, -1, 0, 1, 2, 3, ... Even/Odd - Even numbers: 2, 4, 6, 8...; odd numbers: 1, 3, 5, 7, ... The number 0 is considered even.
20: More Math Vocab | Which of the following lists the factors of 60? A) 1, 10, 20, 30, and 60 B) 2, 4, 6, 10, 12, 20, 30, and 60 C) 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 D) 1, 2, 3, 4, 5, 6, and 10 E) 60, 120, 180, and 240 | The answer is C, because when you look at the answers all are the correct factors of 60.
21: Don't be intimidated by fancy vocabulary words. | Greatest Common Factor - The largest factor shared by several given numbers. Prime Factors - The factors of a number that are also prime numbers.
22: Multiples Vocab | What is the lowest number that is a multiple of 10, 12, and 15? A) 1800 B) 900 C) 120 D) 60 E) 30 | The answer is D, because 60 is the lowest answer that 10, 12, and 15 all fit into evenly.
23: To find the "least common multiple" or "lowest common denominator," "Use the Answers!" | Multiples - All the numbers that are divisible by a certain number. Least Common Multiple - The lowest number that is a multiple of several numbers.
24: Don't be intimidated by fancy graphing terms. | Standard (x,y) coordinate plane - A fancy term for the normal grid that you graph lines on. Cartesian Plane - Another fancy term for the normal grid that you graph lines on. Ordered Pair - A fancy term for a pair of (x,y) coordinates on the normal grid. x intercept/y intercept - The value where a graph crosses the x axis or y axis.
25: Fancy Graphing Vocab | What is the x intercept of the line that contains the points (-2,3) and (4,1) in the standard (x,y) coordinate plane? A) (1/2, 0) B) (0, 1/2) C) (7,0) D) (0,7) E) (7,1/2) | C is the correct answer.
26: Green Circle, Black Diamond: Slaloming Slope I | If the slope of a line through the points (-2,5) and (3,b) is -1, what is the value of b? A) -2 B) -1 C) 0 D) 1 E) 2 | The answer is C, because when you plug the numbers in for Y1 and y2 and X1 and x2 and solve, you get the answer 0.
27: To find the slope or "rate of change" of a line, use Slope = Y1 - Y2 X1 - X2
28: Green Circle, Black Diamond: Slaloming Slope II
29: An equation of a line in the form y = mx + b is called slope-intercept form, where m represents the slope of a line. Parallel lines have equal slopes, like 2/3 and 2/3. Perpendicular lines have negative reciprocal slopes, like 2/3 and -3/2.
30: The Sports Page: Using Charts and Graphs
31: 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, and/or probability question about the data. | The ans | The answer is C.