Part I Review

Part I Review: Number and Quantity

This set mixes all three Part I chapters together with no chapter labels. Recognizing which skill a question needs is part of the difficulty here, not a given. Twenty questions test recognition across the full Number and Quantity Part. No calculator is required, though Desmos or a handheld may still help on a few.

Match the question to the tool

• Rational or irrational? Simplify the number first. A square root of a perfect square, a terminating decimal, and a fraction of integers are all rational.
• Powers of $i$: divide the exponent by $4$ and use the remainder; $i^2 = -1$ whenever it appears in a product.
• Complex division: multiply the top and bottom by the conjugate of the denominator.
• Exponents: add exponents to multiply, subtract to divide, multiply for a power of a power; a rational exponent $\frac{m}{n}$ means the $n$th root raised to the $m$ power.
• Radicals: pull out the largest perfect square, combine only like radicals, rationalize denominators, and check every radical-equation answer in the original equation.
• Vectors: add components, then apply $\sqrt{x^2 + y^2}$ last.
• Matrices: determinant is $ad - bc$; sums and scalar multiples are entry by entry; products use rows times columns and need matching inner dimensions.

Work each question, then check the one error that is easiest to make for that skill: a dropped negative sign, an extraneous root, or a subtraction done as an addition.