 # Problem Solving Strategies

Problem Solving questions are the straightforward 5-choice multiple-choice questions that make up the bulk of the Math on the SAT (35 of 60 questions).

Arithmetic

• Simple addition, subtraction, multiplying, and dividing
• Averages, mean, median, and mode
• Percents, ratios and rates, and some probability
• Knowledge of integer properties such as primes, factors, and multiples

Algebra

• Simplifying algebraic expressions
• Solving simple algebraic equations
• Simple factoring of quadratic equations
• Working with simple roots and exponents
• Translating from English to algebra, word problems

Geometry

• Properties of parallel lines
• Properties of triangles, especially right triangles
• Properties of rectangles, squares, and circles
• Finding the volume and surface area of boxes and cylinders

Not on the Test

• Exponents and roots that are not whole, positive numbers
• Formal proofs of anything
• Trigonometry of any kind
• Any shapes or solids other than those listed in the geometry section

General Tips

• Skip harder questions until after you’ve answered questions you know.
• Math questions are arranged in order of difficulty. Easy questions have few complications, but the “obvious” answer is always wrong on hard questions.
• Since early questions are straightforward and will not contain tricks, you can really rack up some points on the basic arithmetic questions.
• Know the directions going in to the exam; don’t waste exam time reviewing them.

Calculator Use

• Use a calculator you are comfortable with. Use the same one on test day that you use for your practice.
• You don’t need a fancy calculator. A standard four-function one is fine.
• Calculators you CAN’T bring include:
• Personal Digital Assistants (PDAs) such as a Palm
• laptops or portable computers
• calculators with typewriter style keyboards
• calculators that make a great deal of noise
• calculators that have a printer
• calculators that must be plugged into an electrical outlet
• Don’t reach for your calculator until you’ve thought about the question.
• If you need to punch a lot of numbers into your calculator to answer a question, think again; you are going about it the wrong way.

Math Strategies

Working Backwards

Rather than setting up and solving an equation to find the right answer, working backwards takes advantage of the fact that all problem-solving questions give you the right answer; you just have to work out which one it is. You do this by running the answers through the equation in the question until you find the one that works.

Use working backwards when:

• You are asked to solve an equation (this is especially true when the question is in the form of a word problem).
• The answer choices are numbers.

How to work backwards:

• Step 2: Eliminate answers that are too big or too small. (If (C) is too small, everything less than (C) must also be too small, because the choices are arranged in order from smallest to largest. If (C) is too big, then everything greater than (C) must also be too big.)
• Step 3: Run the remaining answers through the question until you find the right one.

Plugging in Numbers

Plugging in numbers works with the answers, eliminating incorrect ones, and homing in on the right one. It almost always involves less messy algebra, and so it is often a lot easier than using traditional algebra.

Use plugging in when:

• You are working with percents, fractions, or ratios, and no actual values are given.

How to plug in:

• Step 1: Pick a simple number to replace the variables.
• Step 2: Plug your chosen number into the equations. The result is your target number.
• Step 3: Plug your chosen number into the answer choices, eliminating those that do not yield your target number.

To plug in numbers on percent questions, always use 100.