In the Algebra 1 course, students will study numbers and quantity, linear, quadratic, and exponential functions, statistics, and probability. Throughout the course, students will expand their knowledge of these topics as they develop problem-solving, critical thinking, and communication skills. Students will be able to graph linear and quadratic equations and interpret descriptions and graphs of functions in context. They will collaborate in groups to grow their mathematical understanding and consider challenges while developing an understanding of the world outside the classroom walls.
Students begin by practicing and generating conjectures and observations starting with work on compass and straightedge constructions which gradually builds to formal proof, engaging in a cycle of conjecture, rough draft, peer feedback, and final draft narratives. Students use transformation-based definitions of congruence and similarity, allowing them to rigorously prove the triangle congruence and similarity theorems which leads to applying these theorems to prove results about quadrilaterals, isosceles triangles, and other figures. Students derive area and volume formulas and study the effect of dilation by connecting ideas from algebra and geometry through coordinate geometry and use transformations and the Pythagorean Theorem to build equations of circles, parabolas, parallel lines, and perpendicular lines from definitions, and they link transformations to the concept of functions. Students analyze relationships between segments and angles in circles and develop the concept of radian measure for angles, which will be built upon in subsequent courses.
Algebra 2 will build on your problem-solving and reasoning skills from Geometry and Algebra 1. A heavy emphasis will be placed on designing and using functions to model real-world situations. Students will explore the dichotomy of different categories of numerical quantities such as the difference between rational and irrational numbers, and the difference between real and imaginary numbers. Students will explore new types of functions such as higher degree polynomial equations, exponential functions, logarithmic functions, and trigonometric functions in the context of their utility to model real-life situations.
Precalculus is a course designed to prepare students for calculus. Starting in Unit 2 students formalize understanding of functions and their transformations, maxima/minima, and participate in an introduction to modeling. An exploration of functions with more complex functions involves the addition, subtraction, and multiplication of polynomial functions in real-world applications and wrap up with rational functions (quotients of polynomial functions). Students continue with an examination of exponential and logarithmic functions. A transition to trigonometric functions expands students' tools to model periodic real-world situations and prepare them for the polar plane. From here with an introduction to polar coordinates and vectors leads students to an increased understanding of systems of equations and inequalities. A transition to a study of conics leads students to consider the modeling of complex real-world problems with all previously learned tools. In the final two units, an examine sequences and series which culminates in a preview of calculus.
Calculus is a course designed to prepare students for further levels of college math and applications courses. This is a four community college concurrent enrollment progression. Math 1A, Math 1B, Math 1C, and Math 1D. These are quarter classes taken at community college once the pandemic restrictions are lifted and the community college resumes in-person instruction. Now instruction will be virtual and we have created space for students in their current HS schedule to have a place to get help and additional instruction if needed. They will receive HS credit as well as college credit for the current program.
Algebra 1: Solving Systems of Equations graphically
Diego bought some raisins and walnuts to make a trail mix. Raisins cost $4 a pound and walnuts cost $8 a pound. Diego spent $15 on both ingredients. Diego bought a total of 2 pounds of raisins and walnuts combined. How many pounds of each did he buy? Explain or show how you know.
Write equations to represent each constraint. Let x be the pounds of raisins and y be the pounds of walnuts.
Here is the equation that shows Cost constraint: 4x+8y=15
Here is the equation that shows Weight constraint: x+y=2
Use graphing technology to graph the equations to show the solution of the system.
The point of intersection of two graphs has coordinates (0.25, 1.75). Since x represents pounds of raisins and y represents pounds of walnuts, it means that Diego bought 0.25 pounds of raisins and 1.75 pounds of walnuts.