Portable Assisted Study Sequence (PASS) Program

Course Description

Application Math B is a standards-based course that continues to build on concepts presented in Application Math A. This course helps students develop mathematical computational and procedural skills. Concepts covered in the course include: statistics and probability, algebraic equations, geometry fundamentals, and using mathematical reasoning to solve various types of problems.

Credits: 5

State Standards

UNIT 6 — Statistics and Probability

California Mathematics Content Standards:

Statistics, Data Analysis, and Probabilities 1.0: Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings.
Statistics, Data Analysis, and Probabilities 1.0: Students display, analyze, compare, and interpret different data sets, including data sets of different sizes.
Statistics, Data Analysis, and Probabilities 1.1: Formulate survey questions; systematically collect and represent data on coordinate graphs, tables, and charts.
Statistics, Data Analysis, and Probabilities 1.1: Know various forms of displays for data sets including stem-and-leaf plot: use the forms to display a single set of data or to compare two sets of data.
Statistics, Data Analysis, and Probabilities 1.2: Organize and display single-variable data in appropriate graphs and representations (e.g., histograms, circle graphs) and explain which types of graphs are appropriate for various data sets.
Statistics, Data Analysis, and Probabilities 1.2: Represent two numerical variables on a scatter plot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables.
Statistics, Data Analysis, and Probabilities 1.3: Use fractions and percentages to compare data sets of different sizes.
Statistics, Data Analysis, and Probabilities 2.0: Students use data samples of a population and describe the characteristics and limitations of the samples.
Statistics, Data Analysis, and Probabilities 2.1: Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use the sample.
Statistics, Data Analysis, and Probabilities 2.2: Identify different ways of selecting a sample and which method makes a sample more representative for a population.
Statistics, Data Analysis, and Probabilities 2.3: Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why in which the results were displayed might have influenced the conclusions reached.
Statistics, Data Analysis, and Probability 1.0: Students compute and analyze statistical measurements for data sets.
Statistics, Data Analysis, and Probability 1.1: Compute the mean, median, and mode of data sets.
Statistics, Data Analysis, and Probability 1.1: Know why a specific measure of central tendency (mean, median, and mode) provides the most useful information in a given context.
Statistics, Data Analysis, and Probability 3.0: Students determine theoretical and experimental probabilities and use these to make predictions about events.
Statistics, Data Analysis, and Probability 3.1: Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
Statistics, Data Analysis, and Probability 3.3: Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities are reasonable; know that if the probability of an event is P, 1 – P is the probability of an event not occurring.
Statistics, Data Analysis, and Probability 3.4: Understand that the probability of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.
Statistics, Data Analysis, and Probability 3.5: Understand the difference between independent and dependent events.

Unit Objectives
Upon completion of this Unit, students will be able to:

understand that gathering, recording, and displaying data is a process used to analyze data.
understand that data can be recorded in various forms: organized lists, tables, charts, matrices and graphs and read and that interpret data.
represent two numerical variables on a scatter-plot graph, informally describe how the data points are distributed and the relationship between the two variables.
distinguish between positive and negative correlation on a scatter-plot graph.
compute the range and mean, mean and mode, and the mean of a set of data and express the data in a frequency table.
use the central tendency of a set of data (mean, median and mode) to analyze, interpret and draw conclusions from the data.
represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams).
represent probabilities as ratios, proportions, or decimals between 0 and 1, and percentages between 0 and 100, knowing that if P is the probability of an event, 1 – P is the probability of an event not occurring.
understand mutually exclusive and compound events in computing the probabilities of events.
understand the difference between an independent and dependent event when computing the probability of an event.

UNIT 7 — Algebra

California Mathematics Content Standards:
Algebra & Functions 1.0: Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.
Algebra & Functions 1.0: Use letters, boxes, or other symbols to stand for any number in simple expressions or equations.
Algebra & Functions 1.1: Use variables and appropriate operations to write an expression, or an equation that represents a verbal description.
Algebra & Functions 1.2: Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2.
Algebra & Functions 1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.
Algebra & Functions 1.2: Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.
Algebra & Functions 1.3: Simplify numerical expressions by applying properties of rational numbers and justify the process used.
Algebra & Functions 1.4: Solve problems manually by using the correct order of operations.
Algebra & Functions 1.4: Express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs.
Algebra & Functions 1.4: Use algebraic terminology correctly.
Algebra & Functions 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
Algebra & Functions 2.2: Demonstrate an understanding that rateis a measure of one quantity per unit value of another quantity.
Algebra & Functions 2.3: Solve problems involving rates, average speed, distance, and time.
Algebra & Functions 3.0 Students graph and interpret linear and some nonlinear functions.
Algebra & Functions 3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.
Algebra & Functions 3.3 Graph linear functions, noting that the vertical change per unit of horizontal change is always the same and know that the ratio is called the slope of a graph.
Algebra & Functions 3.4 Plot the values of quantities whose ratios are always the same. Fit a line to the plot and understand that the slope of a line equals the quantities.
Algebra & Functions 4.1: Solve two-step linear equations in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
Algebra & Functions 4.2: Solve multi-step problems involving rate, average speed, distance, and time or a direct variation.
Algebra I 3.0: Students solve equations and inequalities involving absolute values.
Algebra I 4.0: Simplify expressions before solving linear equations in one variable, such as 3(2x-5) + 4(x-2) = 12.
Algebra I 5.0 Students solve multistep problems, including word problems, involving linear equations in one variable and provide justification for each step.
Algebra I 6.0: Students graph a linear equation and compute x- and y-intercepts (e.g., graph 2x + 6y = 4).
Algebra I 7.0: Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations, by using the point-slope formula.
Algebra I 8.0: Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
Algebra I 10.0: Add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
Mathematical Reasoning 1.1: Analyze problems by identifying relationships, distinguishing relevant and irrelevant information, sequencing and prioritizing information, and observing patterns.
Mathematical Reasoning 1.2: Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
Mathematical Reasoning 1.3: Determine when and how to break a problem into simpler parts.
Mathematical Reasoning 2.1: Use estimation to verify the reasonableness of calculated results,
Mathematical Reasoning 2.3: Estimate unknown quantities graphically and solve for them using logical reasoning and arithmetic and algebraic techniques.
Mathematical Reasoning 2.4: Make and test conjectures by using inductive and deductive reasoning.
Mathematical Reasoning 3.3: Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.

Unit Objectives
Upon completion of this Unit, students will be able to:

understand the concept of an abstract idea and how to use symbolism to express it.
use variables and appropriate operations to write an algebraic expression that represents a verbal description.
simplify algebraic expressions of all types, including monomials, binomials, trinomials, and polynomials using the correct order of operations.
solve multi-step equations in one variable over the set of rational numbers.
solve word problems involving rates, motion, work, direct variation, and matrices using algebraic equations and a sound problem-solving method.
evaluate an algebraic expression by substituting numeric values for the variables.
given a linear equation, substitute a numeric value for x and solve the equation for y and vice-versa.
understand the characteristics of a line, like the slope, x-intercept and y-intercept
calculate the slope of a line, given two points and given information about a line, find the equation of the line.
understand the various forms of the equations of lines: standard, point-slope and slope-intercept and how to find key information about the line from the equation.
graph linear equations.
determine if two lines are parallel by comparing slopes.
plot values of quantities whose ratios are always the same and understand that the slope of the line is the ratio.
graph and recognize the graphs of quadratic equations in both the form y = nx2 and y = ax2 + bx.
graph and recognize the graphs of cubic equations in the form y = nx3.
graph and recognize graphs that include absolute value functions.

UNIT 8 — Geometry

California Mathematics Content Standards:

Geometry 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
Geometry 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
Geometry 10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
Mathematical Reasoning 1.1 Analyze problems by identifying relationships, distinguishing relevant and irrelevant information, sequencing and prioritizing information, and observing patterns.
Mathematical Reasoning 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
Mathematical Reasoning 1.3 Determine when and how to break a problem into simpler parts.
Measurement & Geometry 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
Measurement & Geometry 2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions.
Measurement & Geometry 2.1 Measure, identify, and draw angles, lines, and polygons.
Measurement & Geometry 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
Measurement & Geometry 2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.
Measurement & Geometry 2.3 Draw quadrilaterals and triangles from given information about them.
Measurement & Geometry 3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems.
Measurement & Geometry 3.1 Identify lines that are parallel and perpendicular.
Measurement & Geometry 3.3 Know and understand the Pythagorean Theorem and its converse and use it to find the missing side of a right triangle.
Measurement & Geometry 3.4 Demonstrate an understanding of conditions that indicate two geometric figures are congruent.
Measurement & Geometry 3.5 Know the definitions of a right, an acute and an obtuse angle.
Measurement & Geometry 3.7 Know the definitions of the different triangles and identify their attributes.
Measurement & Geometry 3.8 Know the definition of different quadrilaterals.
Measurement and Geometry 1.1 Understand the concept of a constant such as ; know the formulas for the circumference and area of a circle.
Measurement and Geometry 1.2 Know common estimates of  (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.
Measurement and Geometry 1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.
Number Sense 1.2 Interpret and use ratios in different contexts to show relative sizes of two quantities, using appropriate notations.
Number Sense 1.3 Use proportions to solve problems (e.g. find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems.

Unit Objectives
Upon completion of this Unit, students will be able to:

recognize and identify the descriptions of some basic geometric shapes.
understand the basic elements of geometry involving points, lines, curves, angles, triangles, and planes.
construct two-dimensional geometric shapes.
demonstrate an understanding of the conditions that indicate that two geometric figures are congruent and what congruence means about their relationships between the sides and angles of the two figures.
demonstrate an understanding of the conditions that indicate that two geometric figures are similar and what similarity means about their relationships between the sides and angles of the two figures.
solve problems involving the Pythagorean Theorem.
understand and apply the concepts of ratios and proportions and solve algebraic equations involving proportions.
use ratios and proportions to find missing sides in similar triangles.
find the perimeter and area of parallelograms, rectangles, squares, triangles, trapezoids, and circles.
compute the surface area and volume of prisms, rectangular solids, and cylinders.

UNIT 9 — Problem Solving

California Mathematics Content Standards:
Algebra 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
Geometry 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
Geometry 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
Geometry 10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
Geometry 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
Mathematical Reasoning 1.1 Analyze problems by identifying relationships, distinguishing relevant and irrelevant information, sequencing and prioritizing information, and observing patterns.
Mathematical Reasoning 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
Mathematical Reasoning 1.3 Determine when and how to break a problem into simpler parts.
Mathematical Reasoning 2.8 Make precise calculations and check the validity of the results from the context of the problem.
Mathematical Reasoning 3.1 Evaluate the reasonableness of the solution in the context of the original situation.
Mathematical Reasoning 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
Mathematical Reasoning 3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
Number Sense 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

Unit Objectives
Upon completion of this Unit, students will be able to:

explore general problem-solving strategies and approaches to word problems of a variety of types.
review general word problem-solving techniques, using algebraic equations.
solve word problems involving consecutive integers, money, ages of individuals, mixtures, percentage, uniform motion (distance, speed, and time), probability, geometry, fractals, estimation, area of irregular two-dimensional figures, and the volume of irregular three-dimensional figures.

UNIT 10 — More Problem Solving Applications

California Mathematics Content Standards:
All standards from the California State Mathematics Framework are listed in each of the Units below:
Algebra 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
Algebra 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4).
Algebra 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
Algebra 15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
Geometry 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
Geometry 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
Geometry 22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
Mathematical Reasoning 1.1 Analyze problems by identifying relationships, distinguishing relevant and irrelevant information, sequencing and prioritizing information, and observing patterns.
Mathematical Reasoning 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
Mathematical Reasoning 1.3 Determine when and how to break a problem into simpler parts.
Mathematical Reasoning 2.8 Make precise calculations and check the validity of the results from the context of the problem.
Mathematical Reasoning 3.1 Evaluate the reasonableness of the solution in the context of the original situation.
Mathematical Reasoning 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
Mathematical Reasoning 3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
Number Sense 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
Number Sense 1.6 Calculate the percentage of increases and decreases of a quantity.
Number Sense 1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

Unit Objectives
Upon completion of this Unit, students will be able to:

review and understand the math concepts and solve problems from Units 6-9 of this course.
solve word problems involving digits in whole numbers, percentage increase and decrease, money using simple and compound interest, and finance.
understand the possible solutions to systems of linear equations.
solve systems of linear equations using a graphs, the substitution method, and the elimination method.
solve various word problems using systems of linear equations.
graph two-dimensional geometric figures on a coordinate graph.
find the lengths and areas of two-dimensional geometric figures on a coordinate graph.

understand translations and reflections of two-dimensional geometric figures on a coordinate graph.