# 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
- x
^{2}- x - 1 = 0

- Solve: 2(5x - 1) = 3x + 2
- Factoring
- Factor: x
^{2}- 8x - 20- a
^{2}- 36 - 9x
^{2}- x - 8 - 12abc - 8ab - 4a

- a

- Factor: x
- 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}...?"

- "What is the 10th term of the sequence 1,
- 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?"

- "What is the center and radius of the circle whose equation is (x - 3)
- Limits
- "Find the limit of ƒ(x) = 1/x as x approaches infinity."