HS Math

Algebra 1

1. Solving equations and inequalities (multi-step, variables on both sides)     ex: Solve the following: 3(3m - 2) = 2(3m + 3)

2. Solving linear equations and inequalities (solve and graph)       ex: Graph y + 2x = 1 and y > 3x - 2

3. Systems of equations, (solve by graphing, substitution, and elimination, number sense with word problems)  ex: The Browns and Saints scored a combined 29 points. The Browns scored 3 more points than the Saints. How many points did they score?

4. Ratio and proportions (percentage, discount, tax, weighted averages)   ex: Luggage cost $188.00, there is a 20% discount followed by a 7% tax. How much will you pay?

5. Inverses and functions (input vs. output, domain vs. range)   ex Given f(x) = 2x + 1, find f(3) and f(x) = 5.

6. Polynomials (add, subtract, multiply, exponent rules)    ex  Simplify (4xy2)(3x2)3

7. Factoring (prime factorization, factor monomials, trinomials, grouping)   ex   Factor x2-x-6 and x2 -4

8. Quadratics (graphing, solving, real world)     ex  Solve y=x2-6x+5 by graphing.

9. Stats (sample size, counting principle  permutation and combination, compound/mutual)    ex  How many ways can 8 people finish first, second, and third? Top 3?

Algebra 2

1. Linear relations and functions (graphing and real world)   ex Find the equation of a line using point slope form that passes through (0, -2) and is perpendicular to the line 3x + 5y = 3.

2. Systems of equations (graphing, substitution, and elimination, 3 variables)  ex Solve the system of inequalities by graphing; 2x-3y>-3 and 3y>-2x-6.

3. Quadratic functions and inequalities (create, change form, highlight different aspects   ex Find the vertex, solutions and graph the following quadratic: y=-2x2+4x+3

4. Statistics (normal distribution and probability  ex Find the percentage of people with scores between 600 and 760, if the data is normally distributed with a mean of 600 and a standard deviation of 80.

5. Polynomial functions (add, subtract and divide)  ex Use the remainder theorem to show x - 2 is a factor of x3-2x2-4x+8then factor the remaining polynomial.

6. Trigonometry (right triangle, law of sines, law of cosines)  Find the exact value of sin 120 using the unit circle.

7. Exponential logarithms (switching back and forth)   ex Solve the logarithm by using the change of base formula; log357 

8. Rational expressions (add, subtract, multiply, and divide   ex Solve the following rational equation 2x/x-3  -  1/2  =   2/2x-6.

9. Radical equations (simplify, solve, add, subtract, multiply, and divide)  Solve the following x-3=4-(x+5)^½

1. Terms   Undefined term-point, line, plane;  angles and segments

2. Proofs     Two-column Formal Proofs; logical arguments

3. Lines    Lines-equations for lines, parallel and perpendicular lines

4. Transformations   Rotations, reflections and translations; vectors--magnitude and direction

5. Congruent Triangles    SSS, SAS, ASA, and AAS to show triangle congruence

6. Similarity (triangle)    Similar figures and their properties

7. Trigonometry   Sine,cosine and tangent

8. Quadrilaterals    Parallelograms, rectangles, rhombi, squares, trapezoids and isosceles trapezoids

9. Circles    Equations of circles, semicircles, arcs and sectors

10. 3-d Figures     Volume, Surface Area and Area of polygons

1. Advanced Trigonometry (with proofs)    Find the exact value of sin 75 degrees by using the sum and difference formulas

2. Conic Sections     Find the center, vertices, and focus points of x2 + 4y2 + 8x - 16y = 0

3. Functions (including logarithmic and exponential)  Given a graph, find mins, f(x) > 0, f(x) < 0,  f(x) = 0,

4. Finding zeros of  Polynomial    Solve f(x) = 2x4 + x3 - 24x2 + 20x + 16 = 0

5. Sequences (including arithmetic and geometric)   Find the17th term of 1,3,9,......

The topics include:

1. Problem solving (logic problems)

2. Set Theory (irrational, rational, real, whole numbers, venn diagrams)

3. Real numbers and properties (exponents, scientific notation, order of operations, functions, sequences)

4. Equations

5. Formulas (reworking formulas)

6. Linear equations

7. Graphs and functions (scatter plot, one-to-one, mapping, composite)

8. 2-variables or 3 variables

9. Polynomials (functions, factoring, solving, square root, quadratic formula, graphs)

10. Personal finance (pay check, income tax,  compound interest, mortgage, credit cards)

11. Geometry (angles, lines, perimeter, tessellations, polygons, area, volume, surface area, triangles)