High School Program Samples

The curriculum samples shown here represent critical topics we address at each grade level.

Algebra I

  • Connecting algebra to previous learning
  • Solving linear equations, systems of linear equations (2 variables), and quadratic equations
    • Solve: 2(5x - 1) = 3x + 2
      • 2x + 3 = 14
      • 4y + 3 = 0
      • x2 - x - 1 = 0
  • Factoring
    • Factor: x2 - 8x - 20
      • a2 - 36
      • 9x2 - x - 8
      • 12abc - 8ab - 4a
  • Solving algebraic word problems
    • "30 stamps are worth a total of $8.61. Some of the stamps are worth 32¢ each and the rest are worth 23¢ each. How many of the stamps are worth 23¢ each?"

High School Geometry

  • Synthetic geometry: geometric proofs—use of axioms and primitive terms
    • "Prove vertical angles are equal."
  • Metric (coordinate) geometry—the Pythagorean theorem, the distance formula, the mid-point formula
    • "Find the diagonal of a rectangle whose length is 12 and whose width is 5."
  • Properties of geometric figures—congruence, similarity, proportionality
  • All about slope
    • "Find the slope of the line that is perpendicular to the line 3x + 2y = 8."

Algebra II

  • The relationship between logs and exponents
  • Arithmetic and geometric sequences
    • "What is the 10th term of the sequence 1, 1/2, 1/4, 1/8 ...?"
  • Combinations and permutations
    • "How many ways can 7 books be arranged on a shelf in groups of 5?"
  • Matrix operations
  • Study of complex numbers
    • "Simplify (2 + 3i)/(3 – 4i)."

Trigonometry

  • Properties of sine, cosine, and tangent and their inverses
    • "If sinA = 4/5, find cosA."
    • "Express tanB in terms of sinB and cosB."
  • Graphs of trigonometric functions
    • "Sketch ƒ(x) = 2sinx + 3 over the domain -2Π to 2Π."
  • Proving trigonometric identities
    • "Verify that secA – cosA = sinAtanA."
  • Applications in the real world
    • "A rocket is fired at sea level and climbs at a constant angle of 65° through a distance of 12,000 miles. What is the altitude of the rocket to the nearest foot?"

Pre-Calculus

  • Domain and range of a function; composition of functions
    • "What is the domain and range of the function ƒ(x) = 3/(x + 1)?"
    • "If ƒ(x) = 3x and g(x) = x + 1, find ƒ(g(x))."
  • Exponential growth
    • "Find the interest on $1,000 invested at 5% per year, compounded continuously."
  • Conic sections (circles, parabolas, ellipses, and hyperbolas)
    • "What is the center and radius of the circle whose equation is (x - 3)2 + (x – 4)2 = 9?"
  • Limits
    • "Find the limit of ƒ(x) = 1/x as x approaches infinity."