Mathematics
The ORELA Mathematics (NT304) domain samples the content a secondary mathematics teacher in Oregon must command: number systems and operations, algebra and functions, geometry and measurement, trigonometry, calculus, and probability and statistics. Items are multiple-choice and reward both procedural fluency and the reasoning behind a method, so an answer you can justify structurally is safer than one you reached by pattern-matching.
Rules that decide answers
- Number: know which sets are closed under which operations, integer and rational exponent equivalence, and proportional reasoning via unit rates rather than cross-multiplying blindly.
- Algebra: equivalent forms drive most solutions; the domain of a function is restricted by denominators and even-index radicals; multiplying or dividing an inequality by a negative reverses the sign.
- Geometry: under a similarity ratio k, lengths scale by k, areas by k², volumes by k³.
- Trigonometry: work in radians unless degrees are stated; quadrant determines sign on the unit circle; the SSA case admits zero, one, or two triangles.
- Calculus: a derivative is an instantaneous rate of change and a definite integral is accumulated change; the Fundamental Theorem links the two.
- Statistics: the mean responds to outliers while the median resists them; standard deviation carries the same units as the data.
Worked example
A cylindrical tank has radius 3 m and height 10 m. A similar tank has height 25 m. The similarity ratio is k = 25/10 = 2.5, so volumes scale by k³ = 15.625. Original volume = π(3²)(10) = 90π m³, giving 90π × 15.625 = 1406.25π ≈ 4418 m³. The reasoning matters: only the linear dimension is given, so the volume factor is the cube, not k or k².
Traps that cost marks
- Using the area factor k² when the question asks for volume.
- Squaring both sides of an equation and accepting every result; test candidates in the original to discard extraneous roots.
- Evaluating trigonometric expressions with the calculator in the wrong angle mode.
- Reporting standard deviation in squared units, or claiming the median shifts when one extreme value is added.
- Misreading a "which is NOT" stem as "which is."