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Dissecting the ACT MATH – PART 1 Bell Ringer – Vocabulary Censure Verb To criticize harshly To express strong disapproval Synonyms: Criticize, blame, Circuitous Adjective Indirect, taking the longest route Synonym: Roundabout, indirect, circular. Bell Ringer - Vocabulary Censure The letter from my mother contains much censure and no praise for my rehabilitation. JCPS is experiencing censure for the failing schools from the Kentucky Department of Education. Circuitous Instead of taking the highway, we took the circuitous route to reach our destination. The roundabout at the zoo and most town squares is the circuitous way to get to the other side. Agenda Bell Ringer – (10 minutes) What’s on the Math Test? Lecture and Activities (45 minutes) Summarize lesson (10 minutes) How to Succeed on Math: 1. Read the question carefully a. Answer easy questions first b. Know what they want – read the question 2. Examine diagrams or make your own 3. Solve the problem by: a. Using math skills b. Backsolving c. Picking numbers d. Guessing strategically Breaking Down Math MATH TEST Time allowed minutes Number of questions Pre-Algebra/ Elementary Algebra Intermediate Algebra / Coordinate Geometry Plane Geometry/Trigonometry Scoring 60 60 24 18 18 1-36 Breaking Down – SmartPoints Point Value 8 6 5 5 4 4 2 2 36 Point Value Mathematics Plane Geometry Variable Manipulation Proportions and Probability Coordinate Geometry Operations Patterns and Processes Number Properties Trigonometry Total Mathematics MATH TEST TAKING STRATEGIES Strategies: Picking Numbers Backsolving Using Math Skills Guessing strategically Learning appropriate strategies will allow for you to avoid algebra on 1/3 of the ACT Math questions. Picking Numbers Some questions present abstract situations (not enough information or missing pieces). Picking numbers means replacing fuzzy abstractions with concrete numbers. “x” = 3 “an even integer” = 2 Picking Numbers Make sure the numbers you pick are appropriate and easy to work with. Obey restrictions 2. Small, easily divisible by numbers in the problem 3. May have to pick more than one number, especially with: 1. a. “which of the following must be true.” b. “can never be true” Picking Numbers You can pick numbers when: 1. The question describes a relationship between numbers without giving any specific numbers. ie: Percentages or unknown numbers in terms of another unknown number 2. There are variables in the answer choices. ie: Number property questions are often this time Picking Numbers Question 1 A certain television set is discounted 20% on Monday, and then discounted another 25% on Tuesday. What is the total percent discount applied to the price of the television on Monday and Tuesday. a. 35% b. 40% When you Pick c. 45% Numbers for a percent question, pick 100! d. 50% e. 55% It is tempting to just add the percents, but Picking Numbers will show you what really happens. Picking Number Question 1 Original Cost : $100 We picked this number. Monday -> $100 - $100(0.2) or 20% = $80 Tuesday -> $80 - $80(0.25) or 25% = $60 Discount -> $100 - $60 = $40 Percent Change ->$40 / $100 * 100% = 40% Picking Numbers Question 1 A certain television set is discounted 20% on Monday, and then discounted another 25% on Tuesday. What is the total percent discount applied to the price of the television on Monday and Tuesday. a. b. c. d. e. 35% 40% 45% 50% 55% Picking Numbers Question 2 Which of the following expressions will produce an odd number for any integer a ? a. a2 b. a2 + 1 2a2 + 1 d. 3a2 + 2 e. 4a2 + 4 c. When a question asks about odd or even numbers, you’ll need to pick one of each. This question, like other common number property questions, has variables in the answer choices. Therefore, Picking Number will work well! Picking Numbers Question 2 Let’s try the integer of 1, first. a. 12 = 1 b. 12 + 1 = 1 + 1 = 2 c. 2(1)2 + 1 = 2 + 1 = 3 d. 3(1)2 + 2 = 3 + 2 = 5 e. 4(1)2 + 4 = 4 + 4 = 8 A, C, D are all odd when a = 1. Since this question asks for the expression that is odd for any value of a, try another number for these three choices. Picking Numbers Question 2 Let’s try the integer of 2 for the remaining three options. a. 22 = 4 c. 2(2)2 + 1 = 2(4) + 1 = 8 + 1 = 9 d. 3(2)2 + 2 = 3(4) + 2 = 12 + 2 = 14 Only C is odd for both a = 1 and a = 2, so it must be correct. Picking Numbers Question 2 Which of the following expressions will produce an odd number for any integer a ? a. a2 b. a2 + 1 2a2 + 1 d. 3a2 + 2 e. 4a2 + 4 c. Picking Numbers - WARNING 1 is usually not a great number to pick because it tends to make several answer choices the same (ie: if A is n and B is n2, both will be 1 if n is 1). In this problem, the only relevant characteristics of the numbers to pick are that one is even and one is odd, so it doesn’t matter if 1 is picked since students have to pick another, even number. Backsolving Since the ACT is a multiple-choice test, you know the correct answer is right there! When you backsolve, you let the ACT pick numbers for you. Backsolving For most questions, you’ll start in the middle. If a question asks for the smallest possible value start with the answer options of C or H: Answers are arranged from least to highest or vice versa If the result is too small, go to the next highest If a question asks for the largest possible value: Start with the smallest or largest possible answer. Backsolving You can backsolve when: THERE ARE NUMBERS IN THE ANSWER CHOICES! ie: Word problems Algebraic equation Questions too difficult to set up Questions that will take too long to solve Backsolving Question 1 Of the participants at a certain conference, 1/3 are anthropologists, 1/2 are biologists, and the remaining 12 participants are chemists. Each participant specializes in only one field. What is the total number of participants at the conference? 36 There are #’s in the 48 answers so we can backsolve! 60 72 76 Start in the middle so you can see whether you need to move up or down. a. b. c. d. e. Backsolving Question 1 Of the participants at a certain conference, 1/3 are anthropologists, 1/2 are biologists, and the remaining 12 participants are chemists. Each participant specializes in only one field. What is the total number of participants at the C 60 conference? a. b. c. d. e. 36 48 60 72 76 60/3 = 20 anthropologist 60/2 = 30 biologists 60 – 20 – 30 = 10 chemist 60 is not enough because we are looking for 12 chemists. So we need to move down an answer choice. Backsolving Question 1 Of the participants at a certain conference, 1/3 are anthropologists, 1/2 are biologists, and the remaining 12 participants are chemists. Each participant specializes in only one field. What is the total number of participants at the D 72 conference? a. b. c. d. e. 36 48 60 72 76 72/3 = 24 anthropologist 72/2 = 36 biologists 72– 24 – 36 = 12 chemist The correct answer choice is D 72 total participants. Backsolving Question 1 Of the participants at a certain conference, 1/3 are anthropologists, 1/2 are biologists, and the remaining 12 participants are chemists. Each participant specializes in only one field. What is the total number of participants at the conference? a. b. c. d. e. 36 48 60 72 76 Backsolving Question 2 What is the value of x if x + 1 _ x + 2 = 0? x–3 x–4 a. -2 b. -1 0 d. 1 e. 2 c. You can avoid complicated algebra by backsolving. Backsolving Question 2 What is the value of x if x + 1 _ x + 2 = 0? x–3 x–4 a. -2 b. -1 0 d. 1 e. 2 c. Let’s start with the middle number which is 0 0 + 1 _ 0 + 2 = 1 _ 2 = -1 + 1 0 – 3 0– 4 = -3 -4 3 2 This DOES NOT equal zero, but it is hard to see whether a bigger or small number is necessary. If you are not sure which number to choose – just choose the number that looks the easiest. Backsolving Question 2 What is the value of x if x + 1 _ x + 2 = 0? x–3 x–4 a. -2 b. -1 0 d. 1 e. 2 c. Let’s try the easiest number which is 1 1+1_1+2=2_3= 1 – 3 1– 4 = -2 -3 = -1 – (-1) = 0 Using the easiest integer, 1 is the correct option! Backsolving Question 2 What is the value of x if x + 1 _ x + 2 = 0? x–3 x–4 a. -2 b. -1 0 d. 1 e. 2 c.