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2012 Math What does it mean for me? 2012 Math First, find your scores for each of the three sections: Critical Reading Mathemetics Writing Skills For example, your Mathematics section might look like this… 2012 Math A score of 61 would correspond to an SAT score of 610 (actually scores ranging from 570 to 650). Note how this score compares to all other sophomores or Juniors who took this same test. 2012 Math Next, notice how you did on each strand. Where are your strengths? What weaknesses should you work on? 2012 Math Look at “Your Answers” section. What information does it contain? The correct answer to each question. √ if your answer was right. o if you omitted that question. Your answer choice if you missed it. The difficulty level of each question: e = easy m = moderate h = hard 2012 Math Let’s look at some of the math problems from this year’s PSAT: #7 # 15 # 17 # 20 # 26 # 37 2012 Math Plan 1: $20 per day plus $0.30 per mile driven Plan 2: $10 per day plus $0.35 per mile driven 7. Ramon wants to rent a car for a day and can choose from the two rental plans above. For how many miles driven would the two plans cost the same? (A) (B) (C) (D) (E) 50 100 150 200 250 Solution: Let x be the number of miles driven in a day, so Plan 1 would cost 20 + 0.3x, and Plan 2 would cost 10 + 0.35x. If the cost of the two plans is the same, then 20 + 0.3x = 10 + 0.35x Solving this equation for x gives x = 200, and the answer is D B 2012 Math D C xº A E 15. In the figure above, AB = BC, CE = CD, and x = 70. What is the measure of ⁄ ABC ? Solution: (A) 40º (B) 70º (C) 100º (D) 110º (E) 140º Since CE = CD, ΔCDE is isosceles and ⁄ CDE is 70º So ⁄ ECD is 180˚–70˚–70˚ = 40˚. Since ⁄ ECD and ⁄ ACB are vertical angles, ⁄ ACB =40˚ Since AB = BC, ΔABC is isosceles and ⁄ BAC is 40º So the measure of ⁄ ABC is 180˚–40˚–40˚ = 100˚, and the answer is C Number 2012 Math Frequency 80 x 88 y 89 15 17. The table above shows the only 90 19 five numbers that appear in a data 100 11 set containing 91 numbers. It also shows the frequency with which each number appears in the data set. If 80 is the only mode and 88 is the median, what is the greatest possible value of y? Solution: (A) (B) (C) (D) (E) 26 24 23 22 20 Since the data set has 91 numbers, the median will be the 46th number in the list. Thus, x+y = 91–(11+19+15) = 46, and the median must be 88. Since 80 is the only mode, the frequency of 80 must be greater than y, and greater than 19. Thus x must be at least 24, and y = 46–24 = 22, and the answer is D 2012 Math 20. Which of the following must be true for all values of x? I. (x + 1)2 > x2 II. (x – 2)2 > 0 III. x2 + 1 > 2x (A) (B) (C) (D) (E) I only II only I and II only II and III only I, II, and III Solution: Consider each inequality to see if it’s true: I. (x + 1)2 = x2 + 2x + 1 > x2, so 2x+1 > 0. Solving gives x > 0.5, which is not true for all values of x. II. (x – 2)2 > 0 is always true, since anything squared is always nonnegative. III. x2 + 1 > 2x is equivalent to x2 – 2x + 1 > 0, which is equivalent to (x – 1)2 , and again any expression squared is nonnegative. So statements II and III are true, and the answer is D 2012 Math 26. In ΔABC , AB = 5 and BC = 7. Which of the following CANNOT be the length of side AC ? (A) (B) (C) (D) (E) 1 3 5 7 9 Solution: By the Triangle Inequality Property, the sum of the lengths of any two sides of a triangle must be greater than the third side. If AC were equal to 1, then AB + AC = 5 + 1 = 6, which is less than BC = 7. Since AB + AC < BC, the Triangle Inequality fails to hold, and side AC cannot be equal to 1. So the answer must be A 2012 Math 37. If x and y are numbers whose average (arithmetic mean) is 1 and whose difference is 1, what is the product of x and y? Solution: Since the average of these two numbers is 1, (x + y)/2 = 1, which gives x + y = 2. Since their difference is 1, then x – y = 1. Solving the system of these two equations (by substitution or linear combination) gives x = 1.5 and y = 0.5. So the product of x and y is (1.5)(0.5) = or its fraction equivalent 3/4 0.75 , 2012 Math Final thoughts: Notice that the only math concepts being tested cover arithmetic, Algebra I , Geometry, and simple Statistics ― nothing from higher math! Notice that nothing in any of these questions required a calculator to do the math ― although technology can be used to avoid arithmetic mistakes. The more practice you have “thinking outside the box” can only mprove your problem solving abilities.