AP CALCULUS AB PART A
MA.12.V3APCalculusA.Bnet4copy
AP Calculus AB Part A is the first part of a full academic year of work in calculus and related topics, comparable to courses in colleges and universities. Students must have a thorough knowledge of college preparatory mathematics including algebra, axiomatic geometry, trigonometry, and analytic geometry. Topics include: Functions, Graphs, Limits, Derivatives and Integrals. Conceptual understanding of the essential concepts of calculus is emphasized in theory and practice. Professional mathematics organizations have strongly endorsed the use of graphing calculators in mathematics instruction, and consequently these calculators are also used throughout the course and required for a portion of the AP exam. Due to the rigorous nature of this course, students who are considering taking AP Calculus should seek the advice of their current mathematics teacher.
Enduring Understanding
The student will understand:
- Students should develop a deeper understanding of very small and very large numbers and a variety of ways to represent them.
- Representations should be used to model and interpret physical, social, and mathematical phenomena
- Mathematical thinking should be communicated coherently and clearly to teachers, peers, and others
- Students should be able to judge the meaning, utility, and reasonableness of the results of symbol manipulation, including those carried out by technology.
- Functions should be analyzed by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
- Students should be able to use the language of mathematics to express mathematical ideas incisively.
Content Topics
Unit 1
Prerequisites for Calculus
Unit 2
Limits and Continuity
Unit 3
Derivatives
Unit 4
Applications of Derivatives
Standards Alignment:
Anchor A
M11.A.1.1 Represent and/or use fractions as decimals and percents—change percent to fraction, change fraction to decimal, etc. (Item may ask for 2 of any of these 3.)
M11.A.1.1.1 Find the square root of an integer using either a calculator or estimation Integer may or may not be a perfect square. Answer may be a range of values.)
M11.A.1.1.2 Express numbers and/or simplify expressions using scientific notation.
M11.A.1.1.3 Simplify square roots (e.g., the square root of 24).
M11.A.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.
M11.A.1.2.1 Find the Greatest Common Factor (GCF) for sets of monomials and/or factor polynomial expressions using the greatest common monomial factor.
M11.A.1.3 Estimate the value of an irrational number.
M11.A.1.3.1 Locate and identify irrational numbers at the approximate location on a number line.
M11.A.1.3.2 Compare and/or order any real numbers (rational and irrational may be mixed).
M11.A.2.1 Apply ratio and/or proportion in problem-solving situations.
M11.A.2.1.1 Solve problems using operations with rational numbers including rates and percents.
M11.A.2.1.2 Solve problems using direct and inverse proportions.
M11.A.2.1.3 Identify and/or use proportional relationships in problem solving settings.
M11.A.2.2. Use exponents, roots and/or absolute value to solve problems.
M11.A.2.2.1 Simplify/evaluate expressions involving positive and negative exponents, roots and/or absolute value.
M11.A.2.2.2 Simplify/evaluate expressions involving multiplying with exponents, powers of powers, and powers of products.
M11.A.3.1 Apply the order of operations in computation and problem-solving situations.
M11.A.3.1.1 Simplify expressions using the order of operations to solve problems.
M11.A.3.2 Use estimation strategies in problem-solving situations.
M11.A.3.2.1 Use estimation to solve problems.
Anchor B
M11.B.2.1 Use and/or compare measurements of angles.
M11.B.2.1.1 Measure and/or compare angles in degrees.
M11.B.2.2 Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface area, and/or volume.
M11.B.2.2.1 Calculate surface area of prisms, cylinders, cones, pyramids, and/or spheres using formulas on the reference sheet.
M11.B.2.2.2 Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres using formulas on the reference sheet.
M11.B.2.2.3 Estimate area, perimeter, or circumference of an irregular figure.
M11.B.2.2.4 Find the measurement of a missing length given the perimeter, circumference, area, or volume. M11.B.2.3 Describe how a change in one dimension of a figure affects other measurements of that figure.
M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area, or volume.
Anchor C
M11.C.1.1 Identify and/or use parts of circles and segments associated with circles.
M11.C.1.1.1 Identify and/or use the properties of a radius, diameter, chord, tangent, and/or secant of a circle.
M11.C.1.1.2 Recognize or use the properties of arcs, semicircles, inscribed angles, and/or central angles.
M11.C.1.2 Recognize and/or apply properties of angles, triangles, and quadrilaterals.
M11.C.1.2.1 Identify and/or use properties of triangles (median, altitudes, bisectors, side/angle relationships).
M11.C.1.2.2 Identify and/or use properties of quadrilaterals (parallel sides, diagonals, bisectors, congruent sides/angles, supplementary angles).
M11.C.1.2.3 Identify and/or use properties of isosceles and equilateral triangles.
M11.C.1.4 Solve problems involving right triangles using the Pythagorean Theorem.
M11.C.1.4.1 Find the measure of a side of a right triangle using the Pythagorean Theorem.
M11.C.3.1 Solve problems using analytic geometry.
M11.C.3.1.1 Calculate the distance and/or midpoint between 2 points on a number line or on coordinate plane.
M11.C.3.1.2 Relate slope to perpendicularity and/or parallelism.
Anchor D
M11D.1.1 Analyze and/or use patterns or relations.
M11.D.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
M11.D.1.1.2 Determine if a relation is a function, given a set of points or a graph.
M11.D.1.1.3 Identify the domain, range, or inverse of a relation.
M11.D.2.1 Represent and/or analyze mathematical situations using numbers, symbols, words, tables, and/or graphs.
M11.D.2.1.1 Solve compound inequalities and/or graph their solution sets on a number line.
M11.D.2.1.2 Identify or graph functions, linear equations, or linear inequalities on a coordinate plane.
M11.D.2.1.3 Write, solve, and/or apply a linear equation.
M11.D.2.1.4 Write and/or solve systems of equations using graphing, substitution, and/or elimination.
M11.D.2.1.5 Solve quadratic equations using factoring.
M11.D.2.2 Simplify expressions involving polynomials.
M11.D.2.2.1 Add, subtract, and/or multiply polynomial expressions.
M11.D.2.2.2 Factor algebraic expressions, including difference of squares and trinomials.
M11.D.2.2.3 Simplify algebraic fractions.
M11.D.3.1 Describe and/or determine change.
M11.D.3.1.1 Identify, describe, and/or use constant or varying rates of change.
M11.D.3.1.2 Determine how a change in one variable relates to a change in a second variable.
M11.D.3.2 Compute and/or use the slope of a line.
M11.D.3.2.1 Apply the formula for the slope of a line to solve problems.
M11.D.3.2.2 Write or identify the linear equation in point-slope, standard, and/or slope-intercept form when given the graph of a line, 2 points on the line, or the slope and a point on a line.
M11.D.3.2.3 Compute the slope and/or y-intercept represented by a linear equation or graph.
M11.D.4.1 Interpret and/or use linear, quadratic, and/or exponential functions and their equations, graphs, or tables.
M11.D.4.1.1 Match the graph of a given function to its table or equation.
Anchor E
M11.E.1.1 Display and/or use data appropriately in problem-solving settings.
M11.E.1.1.1 Create and/or use appropriate graphical representations of data, including box-and-whisker plots, stem-and-leaf plots, scatter plots, line/double line graphs, bar/double bar graphs, and circle graphs.
M11.E.1.1.2 Answer questions based on displayed data.
M11.E.4.2 Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.
M11.E.4.2.1 Draw, find, and/or write an equation for a line of best fit for a scatter plot.
M11.E.4.2.2 Make predictions using the equations or graphs of best-fit lines of scatter plots.
