#### Great Gifts for Math Lovers 2023

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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."

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