ACT Strategies Math Modified from SparkNotes ACT strategies by S. Bothman, BHS– www.sparknotes.com

On the Math Test, a D+ Is a Pretty Good Grade On a normal test for your high school math class, if you get two-thirds of the questions right, you’ll receive something like a D-plus—not exactly a parent- impressing grade. But if you get two-thirds of the questions right on the ACT, you’ll likely end up with a Math score of 24 or 25, scoring several points higher than the average test taker. Not too shabby.

Use Your Calculator Wisely When you use your calculator on the test, it should be because you’ve thought about the question, you have a good sense of how to proceed, and you see how your calculator can help you. You should only use your calculator when you have a definite operation you want to perform. There’s no reason ever to touch a calculator when you’re dealing with variables. Calculators can certainly be helpful on some problems, but on others using a calculator might actually take more time than working the problem out by hand.

For which one of these questions would you grab a calculator? When x = 5 and y = 3, by how much does the value of 3x – 2y exceed the value of 2x – 3y ? F. 4 G. 8 H. 12 J. 20 K. 50 What is the value of x when 2x + 3 = 3x – 4 ? A. –7 B. --1 C. 1 D. 2 E. 7 Students don’t need a calculator for any problem on the ACT! However, for problem 1, students could use a calculator to plug and chug and would receive an answer of 15-6=9 and 10-9=1, which gives a difference of 8. For the second problem, a calculator would actually slow them down. The correct answer is 7

Encourage Your Inner Artist On the right-hand side of every Math Test page, you will find a column with the header “DO YOUR FIGURING HERE.” You can use this space to write formulas, graphs, drawings of triangles, or whatever else you want. Sometimes, seeing the problem visually can help you solve it. Remember, no one will see your test booklet, and only the bubble answers count. Don’t bother being neat or thorough in this scribble space.

This questions begs for a drawing… The two legs of a right triangle measure 6 and 8 inches respectively. What is the area of the circle that contains all 3 vertices of the triangle? 

A) 24Pi 
B) 25Pi 
C) 36Pi 
D) 64Pi 
E) 48Pi Students must use the pythagorean theorem to find the 3rd side. Shortcut is that a 6-8-10 triangle is a multiple of a 3-4-5 triangle avoiding the pythagorean theorem math. In order for a right triangle to be circumscribed in a circle the longest leg or hypotenuse is the diameter. Making the diameter 10, the radius 5 and, therefore, the Area is 25pi.

Avoid Partial Answers Partial answers love to prey upon eager test takers who are in a hurry to get the right answer. Instead of paying careful attention to the question, these test takers get a number, see it in the answer choices, and immediately identify it as the correct answer. ANSWER THE QUESTION THAT IS ASKED! On word problems, the last sentence of the problem usually tells you what the question is looking for. Consider rereading this last sentence once you’ve formulated your answer to make sure you did what the question asked.

Answer the question. Shannon is planning to tile a rectangular kitchen countertop that is 24 inches wide and 64 inches long. She determined that 1 tile will be needed for each 4-inch-by-4- inch region. What is the minimum number of tiles that will be needed to completely cover the countertop to its edges? 16 96 176 384 1536 Each answer choice assumes the student does something incorrectly. 4*4=16 24*64=1536 1536/(4*4) = 96 – Correct Answer 24+24+64+64 = 176 – Assumes student uses perimeter 24*64=1536 1536/(4)=384 24*64=1536

Order of Difficulty and the Math Test ACT claims that the Math Test is ordered roughly by increasing difficulty. If you find yourself spending too much time on a problem early in the test, skip it and come back to it later. Remember that all questions on the ACT are worth the same to the scoring machine, so you should set a pace that allows you to answer the early problems carefully without sacrificing speed.

Approaching Math Questions Here’s the process for answering questions: Read the question without paying attention to the answer choices. Make sure you understand what the question is asking, and have a plan for finding the answer. Answer the question as if there were no answer choices. Match your answer to the answer choices given. Fill in the appropriate bubble on the answer sheet.

Going to the Answer Choices Take the following example: A classroom contains 31 chairs, some of which have arms and some of which do not. If the room contains 5 more armchairs than chairs without arms, how many armchairs does it contain? A.10 B.13 C.16 D.18 E.21 Since the numbers ascend in value, let’s choose the one in the middle: C, 16. This is a smart strategic move because if we plug in 16 and discover that it is too small a number to satisfy the equation, we can eliminate A and B along with C. Alternatively, if 16 is too big, we can eliminate D and E along with C. If the answer choices contain variables, working backward will often be quite difficult—more difficult than working out the problem would be. If the answer choices are complicated, with hard fractions or radicals, plugging in might prove so complex that it’s a waste of time. (Video on backsolving –8:33 minutes) https://www.youtube.com/watch?v=sjVnaURzyxo

Math Questions and Time The value of timesaving strategies is obvious: less time spent on some questions allows you to devote more time to difficult problems. It is this issue of time that separates the students who ace the math section from those who merely do well. Whether or not the ability to find accurate shortcuts is an actual measure of mathematical prowess is not for us to say (though we can think of arguments on either side), but the ability to find those shortcuts absolutely matters on this test.

Shortcuts Are Really Math Intuition Every ACT math section includes a few questions that are practically begging for you to skip over them. For example, you may consider passing over questions that Are very long and wordy. Seem purposely confusing and don’t make a lot of sense even the second time you read them. Have large or complicated numbers that involve long or difficult calculations.

Lengthy/Confusing questions…guess and move on. The school owns 2 classroom sets of 30 calculators each, which students are required to have during their mathematics class. There are 2 calculators from one set and 6 calculators from the other set that are not available to for use by the students because these calculators are being repaired. For which of the following class periods, if any, are there NOT enough calculators available for each student to use a school-owned calculator without having to share? Period 2 only Period 3 only Period 4 only Periods 3 and 4 only There are enough calculators for each class period. The table with the

That doesn’t mean skip every word problem. Some are EASY!!! In a group of 50 students, 28 speak English and 37 speak Spanish. If everyone in the group speaks at least one of the two languages, how many speak both English and Spanish? 11 b. 12 c. 13 d. 14 e. 15 28+37 = 65 65-50 = 15, Therefore, there must be 15 people that speak both languages.

Strategy = Target Score If you’re looking to get a 23 or lower on the Math Test, there simply is no need to go looking for shortcuts. You can get a 23, or even a 25 or 26, without answering a large number of questions, so there’s no need to race through the test. Students looking to score a 27 or above on the Math Test, though, should not be working out every question. So you must give yourself that time by moving quickly through the earlier stages of the test. Do not sacrifice accuracy for speed.

You are ready! Now go and ROCK the ACT!!! BE PREPARED! Get a good night’s sleep prior to the test. Dress in layers; you can’t control the temperature, but you can control what you wear. Eat breakfast. Something with protein to sustain you through a long test. Read something at breakfast that you enjoy…don’t let the first thing you read that day be an essay in the English section of the ACT. Get your brain warmed up. Studies have shown that reading something enjoyable before taking an exam improves performance. Don’t stress. You have worked for many years to prepare for this test. Stressing about the test won’t make you perform better, in most cases it makes it worse. You are ready! Now go and ROCK the ACT!!!