High School Diploma Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in High School Diploma, not a summary of it.

1. 1

   Algebra I

   5 topics

   • Expressions, Equations, and Inequalities
     • Simplifying and evaluating expressions
     • Solving linear equations and inequalities
     • Literal equations and formulas
   • Linear Functions
     • Slope and rate of change
     • Slope-intercept and point-slope forms
     • Graphing and interpreting lines
   • Systems of Equations
     • Solving by graphing, substitution, and elimination
     • Systems of inequalities
   • Exponents and Polynomials
     • Laws of exponents
     • Adding, subtracting, and multiplying polynomials
     • Factoring techniques
   • Quadratic Functions
     • Graphing parabolas
     • Solving by factoring and the quadratic formula
2. 2

   Geometry

   6 topics

   • Foundations and Logic
     • Points, lines, planes, and angles
     • Deductive reasoning and proofs
   • Triangles and Congruence
     • Triangle properties and classification
     • Congruence postulates and theorems
   • Similarity and Right Triangles
     • Similar polygons and ratios
     • Pythagorean theorem
     • Right triangle trigonometry
   • Polygons and Circles
     • Properties of quadrilaterals
     • Arcs, chords, and tangents
   • Area, Surface Area, and Volume
     • Two-dimensional area formulas
     • Solids: surface area and volume
   • Transformations and Coordinate Geometry
     • Translations, reflections, rotations, dilations
     • Distance and midpoint formulas
3. 3

   Algebra II

   5 topics

   • Functions and Their Graphs
     • Function notation and transformations
     • Domain, range, and inverse functions
   • Polynomial and Rational Functions
     • Higher-degree polynomials and roots
     • Rational expressions and equations
   • Exponential and Logarithmic Functions
     • Exponential growth and decay
     • Properties of logarithms
     • Solving exponential and log equations
   • Complex Numbers and Quadratics
     • Imaginary and complex numbers
     • Completing the square and the discriminant
   • Sequences and Series
     • Arithmetic and geometric sequences
     • Summation notation
4. 4

   Statistics and Probability

   4 topics

   • Descriptive Statistics
     • Measures of center and spread
     • Data displays and distributions
   • Probability
     • Sample spaces and events
     • Conditional probability and independence
     • Permutations and combinations
   • Data Collection and Inference
     • Sampling methods and bias
     • Experiments and observational studies
   • Bivariate Data
     • Scatterplots and correlation
     • Linear regression and prediction
5. 5

   Precalculus and Trigonometry

   4 topics

   • Trigonometric Functions
     • Unit circle and radian measure
     • Graphs of sine, cosine, and tangent
   • Trigonometric Identities and Equations
     • Pythagorean and angle identities
     • Solving trigonometric equations
   • Analytic Geometry
     • Conic sections
     • Polar coordinates and vectors
   • Introduction to Limits
     • Concept of a limit
     • Continuity and end behavior

Mathematics flashcards for High School Diploma

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. What is the distributive property, and give an example expanding 3(x + 4)?

   a(b + c) = ab + ac. So 3(x + 4) = 3x + 12.

2. What does it mean to solve an inequality, and what operation reverses the inequality sign?

   To find all values that make it true. Multiplying or dividing both sides by a negative number reverses the inequality sign.

3. What is the slope-intercept form of a linear function, and what does each symbol represent?

   y = mx + b, where m is the slope (rate of change) and b is the y-intercept (value of y when x = 0).

4. What is the slope formula given two points (x1, y1) and (x2, y2)?

   m = (y2 − y1) / (x2 − x1).

5. How do the slopes of parallel lines and perpendicular lines compare?

   Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (their product is −1).

6. What are the three methods for solving a system of linear equations, and what does the number of solutions indicate geometrically?

   Graphing, substitution, and elimination. One solution = lines intersect; no solution = parallel lines; infinitely many = same line.

7. State the product rule and the quotient rule for exponents.

   Product: a^m · a^n = a^(m+n). Quotient: a^m / a^n = a^(m−n).

8. What do a negative exponent and a zero exponent equal?

   a^(−n) = 1/a^n (for a ≠ 0), and a^0 = 1 (for a ≠ 0).

9. What is the degree of a polynomial, and what is a binomial?

   The degree is the highest exponent on the variable. A binomial is a polynomial with exactly two terms.

10. State the quadratic formula for ax² + bx + c = 0.

    x = [−b ± √(b² − 4ac)] / (2a).

11. What does the discriminant b² − 4ac tell you about a quadratic's roots?

    Positive = two real roots; zero = one repeated real root; negative = two complex (non-real) roots.

12. What is the vertex form of a quadratic, and what is the vertex?

    y = a(x − h)² + k, where the vertex is (h, k) and x = h is the axis of symmetry.

13. In logic, what is the converse, inverse, and contrapositive of 'If p then q'?

    Converse: if q then p. Inverse: if not p then not q. Contrapositive: if not q then not p (logically equivalent to the original).

14. What is the difference between an axiom (postulate) and a theorem?

    An axiom/postulate is accepted as true without proof; a theorem is a statement proven true using axioms, definitions, and logic.

15. State the Triangle Sum Theorem and the Exterior Angle Theorem.

    The interior angles of a triangle sum to 180°. An exterior angle equals the sum of the two non-adjacent interior angles.

16. Name the triangle congruence shortcuts (postulates/theorems).

    SSS, SAS, ASA, AAS, and HL (Hypotenuse-Leg, for right triangles). Note: SSA and AAA do not prove congruence.

17. What is the difference between congruent and similar figures?

    Congruent figures have the same shape and size (corresponding parts equal). Similar figures have the same shape but proportional sides and equal corresponding angles.

18. State the Pythagorean Theorem and what type of triangle it applies to.

    a² + b² = c², where c is the hypotenuse, applying only to right triangles.

19. Give the side ratios for 45-45-90 and 30-60-90 special right triangles.

    45-45-90: legs in ratio 1 : 1 : √2 (hypotenuse). 30-60-90: sides in ratio 1 : √3 : 2 (opposite 30°, 60°, 90°).

20. What is the sum of the interior angles of a convex polygon with n sides?

    (n − 2) × 180°.

21. State the relationship between an inscribed angle and its intercepted arc in a circle.

    An inscribed angle equals half the measure of its intercepted arc (central angle).

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