Math 201!
Math Strategy! Prerequisite: None
Course Description
This micro-course will review the basics students should always be using as they work through the various math sections on the SAT. We will break down the ISME elements and also go over the two “non-math” approaches of Backsolving and Plug and Chug.!
Math 201
2
Problem Solving Steps
The Strategy! ! Identify:! ALWAYS begin by determining the problem type. The most important step in solving a math! problem on the SAT does NOT involve your calculator.! ! Set Up:! Write down what you know is true. If there’s a diagram, label anything you can. Determine which equation(s) you will need to do the math. ! ! Make Sure:! What is the SPECIFIC answer they are asking for? Make sure you’re not falling for one of the SAT’s tricks.! ! Execute:! Plug in the information from the problem, carefully write out ALL STEPS, and solve the problem. After you’ve got an answer, check your work, and make sure your answer makes sense.!
Math 201
3
Plug and Chug Problems
Plug and Chug Problems! ! Identify:! Look for word problems with variables in the question and in the answer choices.! ! Set Up:! PLUG: Pick simple numbers to plug in for each of the variables.! ! Make Sure:! Keep your numbers straight – write down which numbers go with which variables.! ! Execute:! CHUG: Solve the situation described in the question using your numbers. ! PLUG: Then plug the numbers into each of the answer choices. !! CHUG: Eliminate answer choices that differ from the solution you got for the question.!
Math 201
4
Backsolving Problems
Backsolving Problems! ! Identify:! Look for variables in the question and only numbers in the answer choices. ! ! Set Up:! Determine the value in the question that you want the correct answer to prove true.! ! Make Sure:! Keep your numbers straight – write down what the correct answer represents.! ! Execute:! • Pick Choice (C) to stand in for the correct answer.! • Solve the situation described in the question using Choice (C).! • If the solution doesn’t match the Set-up value you need, pick a different answer choice and try again.!
Math 201
5
Review Questions Each of the following is a factor of 90 EXCEPT (A) 5 (B) 9 (C) 12 (D) 15 (E) 30
Math 201
6
Review Questions If f(x) = –3x2 – 8, then f(–4) = (A) –56 (B) –40 (C) 8 (D) 24 (E) 40
Math 201
7
Review Questions Three consecutive integers are listed from smallest to largest. If their sum is 102, what is the second integer on the list? (A) 35 (B) 34 (C) 33 (D) 29 (E) 28
Math 201
8
Review Questions A student must answer at least 80 percent of the questions on a test correctly in order to pass his class. If the test has 30 questions on it, at least how many of the questions must the student answer correctly? (A) 18 (B) 20 (C) 21 (D) 23 (E) 24
Math 201
9
Review Questions If f(x) = 5x2 – 3x – 27, then f(5) = (A) 385 (B) 172 (C) 83 (D) 41 (E) –95
Math 201
10
Review Questions Bella’s Bakery sells only brioches, muffins and sandwiches. The shop makes 3 muffins for every sandwich and 2 brioches for every 5 muffins. If the store made 300 brioches on Tuesday, how many total items were made on Tuesday? (A) 250 (B) 500 (C) 750 (D) 900 (E) 1,300
Math 201
11
Review Questions For every house he sells, a realtor receives a commission that is equal to p% of the house’s selling price. Which of the following represents the total commission he receives, in dollars, if he sells two houses for $400,000 each? (A) 8,000p (B) 200,000p (C) 800,000p 800, 000 p 400, 000 (E) 100 + 2 p
(D)
Math 201
12
Review Questions If k is a positive even prime integer and n is a negative odd integer, which of the following CANNOT be a positive integer? (A) (B) (C) (D) (E)
k+n k–n nk kn 2k – 2n
Math 201
13
Review Questions 2m 2 + 4 If g ( m )= for all nonzero m, then what does 3m g(3) equal?
(A) (B) (C) (D) (E)
2 3 10 9 22 9 5 22 3
Math 201
14
Review Questions If a box collects d drops of water every m minutes, how many drops will it collect in h hours? (A) dmh 60h dm mh (C) 60d dh (D) 60m 60dh (E) m (B)
Math 201
15
Review Questions A convenience store is having a sale that offers a 50 cent discount on any size bottle of cola. For any given bottle, P is the price in cents, and S is the size of the bottle, in ounces. Which of the following formulas determines the price, per ounce of the cola, in cents, after the discount? (A)
50 P S
P 50 S P (C) S 50
(B)
(D) P + 50 (E)
S S 50 P
Math 201
16
Review Questions If m represents an odd integer, which of the following expressions represents an even integer? (A) 5m + 1 (B) 3m + 2 (C) 3m – 2 (D) 2m – 1 (E) m + 2
Math 201
17
Review Questions If z is an even integer less than zero, what is the greatest value of 2z – z? (A) –1 (B) –2 (C) –3 (D) –4 (E) –5
Math 201
18
Review Questions Let x ⊕ y = (x – 2y)2 for all integers x and y. What is the value of 5 ⊕ –3 ?
Math 201
19