Overview: Using the Test Itself
Everyday math homework emphasizes solving the same type of problems over and over again, and following specific steps to solve them. By contrast, the SAT, ACT, and other standardized math tests give a range of answers to problems. Determining the correct answer is a matter of speed and accuracy. On many questions, one of the alternative answers is correct. and the other alternatives serve as a distraction. Since the tests are timed, it is important to go from problem to problem, work quickly and accurately, and use the time that is available.
Draw a Diagram or Picture
Standardized tests often have separate answer sheets. Therefore, students have a place to draw a quick sketch of the problem on scratch paper in order to clarify what is being asked. Sometimes that strategy will be all that is needed to determine the correct alternative from among the many possible answers. If it is a strategy that is used often in solving problems, it might be helpful on the test. For example, if the question were “What is the least integer greater than -3.2?” and the alternatives were a) -3.3 b) 0 c) -3.0 d) 3.1 e)1.8, drawing a number line would help to find the answer and eliminate the alternatives.
Substitute and Solve
In order to eliminate alternatives, try substituting some of the answers given in the problem stem to see if they make sense. Then math problems can be solved without using complicated formulas that take time and extra steps. Sometimes alternatives can be eliminated by thinking logically about the problem. If there are 60 students total taking Algebra 1, and there are 8 more girls than boys in the class, how many boys are there in the class? The alternative “30” can be eliminated, because then the class would be evenly divided. The alternative “34” can be eliminated , as there would be more boys than girls.
Use Properties and Postulates
Careful attention to math properties and postulates sometimes makes the answer stand out from the rest. For example, the Distributive Property can be used to solve a long, complicated fraction such as 12(16-8) -8 (16-8)/4 by simplifying it to (12-8)(16-8)/4 or 4(16-8)/4, cancelling out the 4/4, and giving the answer as 16-8 =8.
Make It Real
There are two reasons to make it real. First, unless the test directions say differently, all answers will be in real numbers, not imaginary or complex numbers. Second, sometimes the problem is easier to see when small numbers, such as 2 for x and 5 for y are substituted. In that case, an algebra problem can be turned quickly into simple arithmetic.
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