# Mathematics

### High School Algebra 1

Essential Concept 1 (ALCOS Standards #7a, 8, 9a, 9c, 18):

Students will be able to factor quadratic expressions and solve quadratic equations by factoring, taking square roots, and the quadratic formula. Students will be able to recognize that the solutions to the quadratic equation are the points that the graph of the quadratic function intersects the x-axis.

Essential Concept 2 (ALCOS Standards #9a, 9c, 28, 31a, 32, 36):

Students will be able to graph quadratic functions and identify the intercepts, maxima, and minima. Students will be able to represent various forms of transformations to the graph of a quadratic function (vertical shift, horizontal shift, and dilation).

Essential Concept 3 (ALCOS Standards #2, 10):

Students will be able to simplify algebraic expressions using properties of exponents. Students will be able to add, subtract, and multiply polynomial expressions.

### Geometry

Essential Concept 1 (ALCOS Standards #25, 28):

Students will be able to identify and describe the relationships among inscribed/circumscribed angles, radii, and chords. Examples: the length of the arc intercepted by an angle is proportional to the radius; the radian measure of the angle can be described as the constant of proportionality; determine the formula for calculating the area of a sector of a circle.

Essential Concept 2 (ALCOS Standards #18, 36):

Students will be able to use the volume of cylinders, pyramids, cones, and spheres to solve problems. Students will be able to determine the relationships between similar figures.

Essential Concept 3 (ALCOS Standards #42, 43):

Students will be able to use probabilities to make fair decisions. Students will be able to analyze decisions and strategies using probability concepts (e.g, product testing, medical testing, etc.)

### Algebraic Connections

Essential Concept 1 (ALCOS Standard #15 – Algebra II):

Students will be able to add, subtract, and multiply polynomials

Essential Concept 2 (ALCOS Standards #13, 17 – Algebra II):

Students will be able to identify the zeros of polynomials by factoring or using the Remainder Theorem and graph polynomial functions, specifically the zeros and end behavior of the polynomial.

Essential Concept 3 (ALCOS Standards #2, 22 – Alg. Conn., #7, 8, 9 – Algebra II):

Students will be able to use matrices to represent and manipulate data; add, subtract, and multiply matrices; and solve linear programming problems using systems of linear inequalities

### Algebra 2

Essential Concept 1 (ALCOS Standards #30c):

Students will be able to graph exponential and logarithmic functions, demonstrating intercepts and end behavior appropriately.

Essential Concept 2 (ALCOS Standards #12b, 31b, 36):

Students will be able to simplify exponential and logarithmic expressions, evaluate logarithmic expressions, and solve exponential and logarithmic equations using the properties of exponents and logarithms.

Essential Concept 3 (ALCOS Standards #39, 42):

Students will be able to describe possible outcomes from the sample space using terms such as union (“or”), intersection (“and”), or complement (“not”); determine if two events are independent of each other and calculate the probability of independent events occurring; and use probability concepts to make and analyze decisions.

### Algebra 2 with Trigonometry

Essential Concept 1 (ALCOS Standards #30c):

Students will be able to graph exponential and logarithmic functions, demonstrating intercepts and end behavior appropriately.

Essential Concept 2 (ALCOS Standards #12b, 31b, 36):

Students will be able to simplify exponential and logarithmic expressions, evaluate logarithmic expressions, and solve exponential and logarithmic equations using the properties of exponents and logarithms.

Essential Concept 3 (ALCOS Standards #37, 38, 39, 40):

Students will be able to define radian measure, evaluate all six trigonometric functions using the ratios of the sides of a right triangle and the coordinates on the Unit Circle, and discuss the periodicity of all six trigonometric functions, as well as the amplitude and midline of trigonometric functions.