Math

44 questions across two 35-minute modules. Calculator allowed on every question (built-in Desmos plus any personal calculator). About 75% multiple choice and 25% student-produced response (free-entry). Four content domains cover the same algebra-through-trig surface, with question difficulty escalating from Module 1 into the harder Module 2.

The four math domains

Algebra

Linear equations & inequalities

• Solve ax + b = c, isolate variables, distribute carefully.
• Inequalities flip when multiplied/divided by a negative.
• Word problems: translate "is" → =, "more than" → +, "less than" → –, "of" → ×.

Systems of linear equations

• Solve by substitution or elimination. Desmos can do it visually — graph both lines, intersection is the solution.
• "No solution" → parallel lines (same slope, different intercepts).
• "Infinite solutions" → same line (multiples of each other).

Linear functions

• Slope-intercept form: y = mx + b. m = slope, b = y-intercept.
• Point-slope form: y − y₁ = m(x − x₁).
• Slope between two points: (y₂ − y₁) / (x₂ − x₁).
• Parallel lines have the same slope; perpendicular lines have slopes whose product is −1.

Advanced math

Quadratics

• Forms: standard ax² + bx + c, vertex a(x − h)² + k, factored a(x − r₁)(x − r₂).
• Vertex: x = −b / (2a); the parabola opens up if a > 0, down if a < 0.
• Roots: quadratic formula x = (−b ± √(b² − 4ac)) / (2a).
• Discriminant b² − 4ac: positive → two real roots; zero → one root; negative → no real roots.
• Sum of roots = −b/a; product = c/a.

Polynomials & rationals

• A polynomial of degree n has at most n real roots.
• If P(r) = 0, then (x − r) is a factor.
• Rational expressions: factor numerator and denominator, cancel common factors, watch for restrictions where denominator = 0.

Exponential & radical

• Rules: aᵐ · aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ.
• Radicals as fractional exponents: √a = a^(1/2), ⁿ√a = a^(1/n).
• Exponential growth: y = a · bˣ. Growth if b > 1, decay if 0 < b < 1.
• "Doubles every 3 years" → y = a · 2^(t/3).

Function notation

• f(x + 2) = shift graph left 2; f(x) + 2 = shift graph up 2.
• −f(x) reflects across the x-axis; f(−x) reflects across the y-axis.
• Composition: (f ∘ g)(x) = f(g(x)).

Problem-solving & data analysis

Ratios, rates, percentages

• Percent change: (new − old) / old × 100%.
• Successive percent changes don't add — multiply: a 20% increase then a 10% decrease = 1.20 × 0.90 = 1.08 → +8%.
• Unit conversions: cross-multiply or chain conversion factors so units cancel.

Statistics

• Mean: sum ÷ count. Median: middle value when sorted. Mode: most frequent.
• Range: max − min. Standard deviation: measures spread; doesn't depend on outliers' position relative to median.
• Adding a constant to every value shifts mean & median by that constant; standard deviation unchanged.
• Multiplying every value by a constant multiplies mean, median, and SD by that constant.

Probability

• P(event) = favorable / total.
• Independent events: P(A and B) = P(A) × P(B).
• Mutually exclusive events: P(A or B) = P(A) + P(B).
• Read two-way tables carefully: "given that X" means divide by the row/column total for X.

Geometry & trigonometry

Lines & angles

• Vertical angles are equal; angles on a straight line sum to 180°.
• Parallel lines cut by a transversal: corresponding angles equal, alternate interior angles equal.

Triangles

• Interior angles sum to 180°.
• Right triangle: a² + b² = c² (Pythagorean theorem).
• Common right triangles: 3-4-5, 5-12-13, 8-15-17, and their scaled versions.
• Special right triangles: 45-45-90 sides in ratio 1 : 1 : √2; 30-60-90 sides in ratio 1 : √3 : 2.
• Similar triangles: corresponding sides in proportion; corresponding angles equal.

Circles

• Area: πr². Circumference: 2πr.
• Arc length and sector area scale with the central angle: arc = 2πr · (θ / 360°).
• Circle equation: (x − h)² + (y − k)² = r² with center (h, k) and radius r.
• Convert from general form by completing the square.

Volume

Reference sheet on screen has these — memorize anyway:

• Box: l · w · h. Cube: s³.
• Cylinder: πr²h. Cone: (1/3) πr²h. Sphere: (4/3) πr³.
• Pyramid (rectangular base): (1/3) · l · w · h.

Right-triangle trig

• SOH-CAH-TOA: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj.
• For complementary angles: sin(θ) = cos(90° − θ).
• Radians: π rad = 180°.

Section strategy

• Pace. 35 minutes ÷ 22 questions ≈ 95 seconds each. Easier in Module 1; harder in Module 2 (especially the latter half).
• Use Desmos aggressively. Graph everything: systems → intersection point; quadratic roots → x-intercepts; inequality regions → shaded area. Faster and less error-prone than algebra by hand.
• Plug in answer choices when the algebra is messy and the choices are simple numbers. Usually start with B or C.
• Pick numbers for problems with variables in the answer choices. Pick easy ones (n = 2, n = 10), compute, match to a choice.
• Free-response (student-produced). Type the number exactly; fractions allowed (e.g. 3/4); decimals allowed; negative numbers allowed. No commas, no units, no $.
• Always answer. No penalty for wrong; a guess on a question you skipped has positive expected value.