Mathematics
Core concepts
FTCE General Knowledge mathematics emphasizes arithmetic, fractions, decimals, percents, ratios and proportions, basic algebra, geometry, measurement, data, and probability. Know order of operations, exponent rules, solving linear equations and inequalities, percent change, unit conversion, perimeter and area, volume, mean/median/mode, and simple probability. Translate word problems into equations before calculating. Label units and check whether the question asks for a rate, a total, a difference, or a remaining amount.
Traps
Frequent errors include using the wrong base in percent problems, forgetting to flip an inequality when multiplying or dividing by a negative number, distributing a negative sign incorrectly, confusing radius with diameter, mixing area and perimeter formulas, and failing to convert units. In statistics, the mean is affected by outliers while the median is resistant. Probability must be between 0 and 1, and without replacement changes the denominator. Do not stop at an intermediate value; answer the question asked.
Worked example
Solve 3(x - 4) = 2x + 5. Distribute: 3x - 12 = 2x + 5. Subtract 2x: x - 12 = 5. Add 12: x = 17. Check: 3(13)=39 and 2(17)+5=39.
Rule of thumb
Write the equation, perform one operation per line, and substitute the result back into the original problem. For percent problems, use part = percent x whole and identify the whole carefully.