Math: Content 60 questions in 60 minutes Topics – arithmetic to trigonometry Calculators are permitted but not required (cannot use TI-89 or TI-92) Questions come in two formulas: straightforward “plug and chug” calculation questions and word problems

THIS IS A THINKING AND REASONING TEST!

Math: Content Questions: 1st 20 = easy, 2nd 20 = medium, 3rd 20 = difficult Questions arranged with most (but not all) of easy problems in first twenty ?’s and most(but not all) of difficult problems in last twenty ?’s Pre Algebra – 14 Elementary Algebra – 10 Intermediate Algebra - 9 Plane Geometry – 14 Coordinate Geometry – 9 Trigonometry - 4

Math: Strategies Now, Later, Never = bank as many points as you can on easy/medium questions before tackling difficult ones Use your personal order of difficulty to decide which questions you find easiest = NOW Do tougher questions LATER, if at all. Circle the questions where you are unsure of your answer or think you should come back to it. Unless shooting for over a 30, there will be some questions you NEVER do. Use a letter of the day on these questions.

Do less problems to get more points = 40 ish, 45 ish, 50 ish Math: Strategies Do less problems to get more points = 40 ish, 45 ish, 50 ish Slow down on easy questions Use process of elimination to save time and help you to guess on harder questions

Math: Strategies Ball parking – helps you avoid careless mistakes on questions in your personal order of difficulty and make educated guesses on more difficult questions Draw a picture if one isn’t given.

Jamal sees a tree on the shore directly across a lake and wonders what the distance is across the lake to the tree. He turns 90 degrees to the right and walks in a straight line for 100 meters. Jamal turns to face the tree and finds the angle between his line of sight and his path measures 25 degrees. Which of the following is the closest distance, in meters, from Jamal’s initial position to the tree? F. 42 G. 47 H. 91 J. 213 K. 238

Using ballparking, we can eliminate answers Using ballparking, we can eliminate answers. In this problem, simply look at the picture! We want to know the distance from Jamal’s initial position to the tree. This is the leg of the right triangle. The side length 100 is opposite the larger acute angle in the right triangle, so the missing side is shorter. So, the answer can’t be J or K.

Actual solution: (Use SOHCAHTOA) tan(25) = x/100 So, x = 100tan(25) = 100(0.47) = 47.

Be careful with your calculator! Math: Strategies Plugging in – plug in values to help you solve the problem – pick 2, 5, 10 generally. Plugging in the answer Be careful with your calculator!

PLUGGING IN: (Look at #29) 29) If a = 2c and b = 6c, which of the following relationships holds between a and b for each Nonzero value of c? a = 3b a = 2b a = b a = (1/6)b a = (1/3)b

Plug in a nice value for either a, b, or c to help solve the problem. In this case, let’s pick a value for a. I’ll choose a = 10 (because this will make c a nice number). If a = 10 and a = 2c, then c = 5. Since b = 6c, b = 30. If a = 10 and b = 30, the b is triple a. The answer is b = 3a (which isn’t a choice), so divide both sides by 3. Thus, b/3 = a. So, a = (1/3)b.

Try #26 and #30 using the plugging in strategy.

Explanations for #26 and #30 Which of the following is equivalent to (x+2)0 whenever x isn’t -2? Pick any number for x other than -2. Use your calculator if you desire. Don’t forget parenthesis. See what you get. It should be 1. 30) Since you are given a range of values to plug in for F, plug in the smallest value in the range (59) and the biggest value in the range (68) and see what you get. Plugging in 59 should yield 15, and plugging in 68 should yield 20. Thus, the answer is J. This is an example of being careful with your calculator!!

PLUGGING IN THE ANSWER (PITA) 10) What is the least common denominator for adding the fractions 4/35, 1/56, and 3/16? F) 80 G) 560 H) 1,960 J) 4,480 K) 31,360

Using the strategy Since you are looking for the least common denominator, start with the smallest choice (80) and see if each denominator divides into it. Normally, we start with the middle value when we plug in the answer. HOWEVER, we aren’t going to here. WHY? The answer is G.

PLUGGING IN THE ANSWER #2 5) What is the largest value of x for which there exists a real value of y such that x2 + y2 = 256? 16 128 240 256 512

PLUGGING IN THE ANSWER #2 Use the choices. I generally like to start with the middle choice. If x = 240, then we have 2402 + y2 = 256. This equals 57600 + y2 = 256.So, y2 = -57344. So, y is not a real number. Thus, 240 was too big of a choice for x. So, we should use a smaller choice. Next, use either 16 or 128. If x = 128 and we follow the same procedure, we again get y2 equal to a negative, which we know isn’t possible. If x = 16, we get y2 equal to 0, which means y = 0. The answer is A.

BE CAREFUL WITH YOUR CALCULATOR!! |5(-4) + 3(6)| = ? F) -2 G) 2 H) 10 J) 19 K) 38

|5(-4) + 3(6)| = ? F) -2 G) 2 H) 10 J) 19 K) 38 Since the given expression is in absolute value bars, you need the absolute value command on your calculator. Hit MATH, go over to NUM, and choose abs. |5(-4) + 3(6)| = ? F) -2 G) 2 H) 10 J) 19 K) 38

Try question #12 on your calculator.

Be careful on this one. Make sure BOTH the numerator and denominator are in parenthesis. Otherwise, your calculator won’t understand your problem correctly. Then, if the answer isn’t a whole number (like here), turn your answer into a fraction on your calculator. Hit MATH and choose option #1 and hit enter. On the main screen, hit enter again.

If a geometry question is given WITHOUT a picture, draw one!! 25) The sides of one triangle are 12 inches, 14 inches, and 15 inches long, respectively. In a second triangle similar to the first, the shortest side is 8 inches long. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?

15 8 x 12 14 This picture tells us that 8/12 = x/15. (If you don’t remember how to solve an equation like this, plug in the answers.) Multiply both sides by 15 and we get x = 10.

Word Problems: The Basic Approach Know the question. Read the whole problem before calculating anything, and underline the actual question. Let the answers help. Look for clues on how to solve and ways to use POE Break the problem into bite-sized pieces. Watch out for trick phrasing.

KNOW THE QUESTION #37 A data set has 15 elements. The 15 elements in a second data set are obtained by multiplying each element in the first data set by 10. The 15 elements in third data set are obtained by decreasing each element of the second data set by 20. The median of the third data set is 50. What is the median of the first data set?

LET THE ANSWERS HELP #37 In this problem, I’m not sure the answers do you a lot of good, unless you utilize a PITA strategy. However, either PITA or ballparking can be beneficial if you are given a diagram or a problem that immediately allows you to rule out some answers.

BITE SIZED PIECES #37 Part 1: A data set has 15 elements. Part 2: The 15 elements in a second data set are obtained by multiplying each element in the first data set by 10. Part 3: The 15 elements in third data set are obtained by decreasing each element of the second data set by 20. RESULT: The median of the third data set is 50. What is the median of the first data set?

SOLUTION #37 Since we are talking about the median, only the middle piece of data matters. Doing any operation to a data set keeps the data in the same order. Let the first data set have median “x”. In set 2, this piece becomes 10x. In set 3, the piece becomes 10x – 20, which is also known as 50. If 10x – 20 = 50, 10x = 70, so x = 7.

KNOW THE QUESTION #40 Each edge of a cube is 4 inches long. Each edge of a second cube is triple the length of each edge of the first cube. The volume of the second cube is how many cubic inches bigger than the volume of the first cube?

LET THE ANSWERS HELP #40 If you recognize that the volume of the first cube is 4 x 4 x 4 = 64, and you recognize that answers G and H and answers J and K are 64 units apart, you can actually rule out H and K as possibilities. This is because H and K are distractors and are provided if you don’t read the question carefully.

BITE SIZED PIECES #40 #1) The first cube has volume 4 x 4 x 4 = 64. #2) The second cube has edges that are triple in length of the first cube. So, the second cube is 12 x 12 x 12 = 1728. #3) The difference in their volumes is 1728 – 64 = 1664.

Math: Strategies SLOW DOWN! Accuracy is more important than speed. You don’t get points for showing your work – use it when you need to. Watch out for careless mistakes. Be careful of the trap answers – just because you came up with a number that is a choice doesn’t mean you got that right answer.