Number Sense, Concepts, and Operations
Core content
Number sense on this exam is mostly about flexibility: moving among fractions, decimals, percents, and scientific notation; applying integer and exponent rules; and choosing efficient strategies for proportional reasoning. Candidates should be able to classify numbers (natural, whole, integer, rational, irrational), use the number line to compare and order, apply order of operations, find GCF and LCM, and solve multi-step percent and rate problems. Also know properties of operations and how they justify regrouping or rewriting expressions.
Traps
Common wrong answers come from treating (-3)^2 as -9; the correct value is 9 because the parentheses include the negative. By contrast, -3^2 = -9 because exponentiation precedes negation. Other traps include dropping a negative sign when subtracting integers and assuming a percent increase followed by the same percent decrease returns to the original value. In percent-change problems, divide the change by the original amount, not the new amount. When dividing by a fraction, multiply by its reciprocal. Watch units in rate problems and check whether a question asks for a part, a whole, or a percent.
Worked example
Evaluate -3^2 + (-2)^3 / 4. Exponentiate first: -3^2 = -9 and (-2)^3 = -8. Then divide: -8 / 4 = -2. Finally add: -9 + (-2) = -11. A common error is 9 - 2 = 7, which misreads the first term.
Rule of thumb
For percent change, use (new - original) / original times 100%; the original value is always the denominator.