# High School Program Samples

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

### Algebra

• 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 \$8.66. 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
• "Find the slope of the line that is perpendicular to the line 3x + 2y = 8."

• 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 centre 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."