California State Standards for Mathematics:

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CA.NS. Number Sense

1.0. Students understand the relationship between numbers and quantities (i.e., that a set of objects has the same number of objects in different situations regardless of its position or arrangement). 10
Suggested Titles for California Mathematics State Standard 1.0.

1.1. Compare two or more sets of objects (up to 10 objects in each group) and identify which set is equal to, more than, or less than the other. 10
Suggested Titles for California Mathematics State Standard 1.1.

1.2. Count, recognize, represent, name, and order a number of objects (up to 30). 24
Suggested Titles for California Mathematics State Standard 1.2.

1.3. Know that the larger numbers describe sets with more objects in them than the smaller numbers have. 36
Suggested Titles for California Mathematics State Standard 1.3.

2.0. Students understand and describe simple additions and subtractions. 27
Suggested Titles for California Mathematics State Standard 2.0.

2.1. Use concrete objects to determine the answers to addition and subtraction problems (for two numbers that are each less than 10). 47
Suggested Titles for California Mathematics State Standard 2.1.

3.0. Students use estimation strategies in computation and problem solving that involve numbers that use the ones and tens places. 7
Suggested Titles for California Mathematics State Standard 3.0.

3.1. Recognize when an estimate is reasonable. 7
Suggested Titles for California Mathematics State Standard 3.1.

CA.AF. Algebra and Functions

CA.MG. Measurement and Geometry

1.4. Identify the time (to the nearest hour) of everyday events (e.g., lunch time is 12 o'clock; bedtime is 8 o'clock at night). 17
Suggested Titles for California Mathematics State Standard 1.4.

2.2. Compare familiar plane and solid objects by common attributes (e.g., position, shape, size, roundness, number of corners). 34
Suggested Titles for California Mathematics State Standard 2.2.

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

CA.NS. Number Sense

1.0. Students understand and use numbers up to 100.

1.1. Count, read, and write whole numbers to 100. 97
Suggested Titles for California Mathematics State Standard 1.1.

1.2. Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than. 12
Suggested Titles for California Mathematics State Standard 1.2.

1.3. Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., 8 may be represented as 4 +4, 5 +3, 2 +2 +2 +2, 10 - 2, 11 - 3).

1.4. Count and group object in ones and tens (e.g., three groups of 10 and 4 equals 34, or 30 +4).

1.5. Identify and know the value of coins and show different combinations of coins that equal the same value. 52
Suggested Titles for California Mathematics State Standard 1.5.

2.0. Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.

2.1. Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory.

2.2. Use the inverse relationship between addition and subtraction to solve problems.

2.3. Identify one more than, one less than, 10 more than, and 10 less than a given number.

2.4. Count by 2s, 5s, and 10s to 100.

2.5. Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference).

2.6. Solve addition and subtraction problems with one- and two-digit numbers (e.g., 5 +58 = __).

2.7. Find the sum of three one-digit numbers.

3.0. Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, and hundreds places.

3.1. Make reasonable estimates when comparing larger or smaller numbers.

CA.AF. Algebra and Functions

CA.MG. Measurement and Geometry

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

CA.NS. Number Sense

1.0. Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000.

1.1. Count, read, and write whole numbers to 1,000 and identify the place value for each digit.

1.2. Use words, models, and expanded forms (e.g., 45 = 4 tens +5) to represent numbers (to 1,000).

1.3. Order and compare whole numbers to 1,000 by using the symbols is less than, =, is greater than.

2.0. Students estimate, calculate, and solve problems involving addition and subtraction of two- and three-digit numbers.

2.1. Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 +6 = 14 is14 - 6 = 8) to solve problems and check solutions.

2.2. Find the sum or difference of two whole numbers up to three digits long.

2.3. Use mental arithmetic to find the sum or difference of two two-digit numbers.

3.0. Students model and solve simple problems involving multiplication and division.

3.1. Use repeated addition, arrays, and counting by multiples to do multiplication.

3.2. Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division.

3.3. Know the multiplication tables of 2s, 5s, and 10s (to ''times 10'') and commit them to memory.

4.0. Students understand that fractions and decimals may refer to parts of a set and parts of a whole.

4.1. Recognize, name, and compare unit fractions from 1/12to 1/2.

4.2. Recognize fractions of a whole and parts of a group (e.g., one-fourth of a pie, two-thirds of 15 balls).

4.3. Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one.

5.0. Students model and solve problems by representing, adding, and subtracting amounts of money.

5.1. Solve problems using combinations of coins and bills.

5.2. Know and use the decimal notation and the dollar and cent symbols for money.

6.0. Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places.

6.1. Recognize when an estimate is reasonable in measurements (e.g., closest inch).

CA.AF. Algebra and Functions

CA.MG. Measurement and Geometry

1.4. Tell time to the nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year).

1.5. Determine the duration of intervals of time in hours (e.g., 11: 00 a.m. to 4: 00 p.m.).

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

CA.NS. Number Sense

1.0. Students understand the place value of whole numbers.

1.1. Count, read, and write whole numbers to 10,000.

1.2. Compare and order whole numbers to 10,000.

1.3. Identify the place value for each digit in numbers to 10,000.

1.4. Round off numbers to 10,000 to the nearest ten, hundred, and thousand.

1.5. Use expanded notation to represent numbers (e.g., 3,206 = 3,000 +200 +6).

2.0. Students calculate and solve problems involving addition, subtraction, multiplication, and division.

2.1. Find the sum or difference of two whole numbers between 0 and 10,000.

2.2. Memorize to automaticity the multiplication table for numbers between 1 and 10.

2.3. Use the inverse relationship of multiplication and division to compute and check results.

2.4. Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = __).

2.5. Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 / 5 = __).

2.6. Understand the special properties of 0 and 1 in multiplication and division.

2.7. Determine the unit cost when given the total cost and number of units.

2.8. Solve problems that require two or more of the skills mentioned above.

3.0. Students understand the relationship between whole numbers, simple fractions, and decimals.

3.1. Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4).

3.2. Add and subtract simple fractions (e.g., determine that 1/8 +3/8 is the same as 1/2).

3.3. Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors.

3.4. Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar).

CA.AF. Algebra and Functions

CA.MG. Measurement and Geometry

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

CA.NS. Number Sense

1.0. Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.

1.1. Read and write whole numbers in the millions.

1.2. Order and compare whole numbers and decimals to two decimal places.

1.3. Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.

1.4. Decide when a rounded solution is called for and explain why such a solution may be appropriate.

1.5. Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalence of fractions (see Standard 4.0).

1.6. Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or 0.50; 7/4 = 1 3/4 = 1.7.5).

1.7. Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.

1.8. Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in ''owing'').

1.9. Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

2.0. Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals.

2.1. Estimate and compute the sum or difference of whole numbers and positive decimals to two places.

2.2. Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.

3.0. Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.

3.1. Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.

3.2. Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results.

3.3. Solve problems involving multiplication of multidigit numbers by two-digit numbers.

3.4. Solve problems involving division of multidigit numbers by one-digit numbers.

4.0. Students know how to factor small whole numbers.

4.1. Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).

4.2. Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

CA.AF. Algebra and Functions

CA.MG. Measurement and Geometry

2.3. Understand that the length of a vertical line segment equals the difference of the y-coordinates.

3.5. Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90 degrees, 180 degrees, 270 degrees, and 360 degrees are associated, respectively, with 1/4, 1/2, 3/4, and full turns.

3.6. Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.

3.7. Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.

3.8. Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

2.4. Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.5. Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.6. Make precise calculations and check the validity of the results from the context of the problem.

CA.NS. Number Sense

1.0. Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers.

1.1. Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.

1.2. Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. What is 40 percent of 250? (CST released test question, 2004)

1.3. Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication.

1.4. Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor

1.5. Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

2.0. Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals.

2.1. Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.

2.2. Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

2.3. Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.

2.4. Understand the concept of multiplication and division of fractions.

2.5. Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

CA.AF. Algebra and Functions

CA.MG. Measurement and Geometry

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

2.6. Make precise calculations and check the validity of the results from the context of the problem.

3.0. Students move beyond a particular problem by generalizing to other situations.

3.1. Evaluate the reasonableness of the solution in the context of the original situation.

3.2. Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3. Develop generalizations of the results obtained and apply them in other circumstances.

CA.NS. Number Sense

1.0. Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.

1.1. Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

1.2. Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a: b).

1.3. Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

1.4. Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

2.0. Students calculate and solve problems involving addition, subtraction, multiplication, and division.

2.1. Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.

2.2. Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., ).

2.3. Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

2.4. Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

CA.AF. Algebra and Functions

3.0. Students investigate geometric patterns and describe them algebraically.

3.1. Use variables in expressions describing geometric quantities (e.g., P = 2w +2l, A = 1/2 bh, C = pi d - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).

3.2. Express in symbolic form simple relationships arising from geometry.

CA.MG. Measurement and Geometry

CA.SDAP. Statistics, Data Analysis, and Probability

2.5. Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.

3.3. Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of an event not occurring.

3.4. Understand that the probability of either 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.

3.5. Understand the difference between independent and dependent events.

CA.MR. Mathematical Reasoning

2.6. Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.7. Make precise calculations and check the validity of the results from the context of the problem.

CA.NS. Number Sense

1.0. Students know the properties of, and compute with, rational numbers expressed in a variety of forms.

1.1. Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general.

1.2. Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

1.3. Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

1.4. Differentiate between rational and irrational numbers.

1.5. Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.

1.6. Calculate the percentage of increases and decreases of a quantity.

1.7. Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

2.0. Students use exponents, powers, and roots and use exponents in working with fractions.

2.1. Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.

2.2. Add and subtract fractions by using factoring to find common denominators.

2.3. Multiply, divide, and simplify rational numbers by using exponent rules.

2.4. Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.

2.5. Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.

CA.AF. Algebra and Functions

3.0. Students graph and interpret linear and some nonlinear functions.

3.1. Graph functions of the form y = nx to the power of 2 and y = nx to the power of 3 and use in solving problems.

3.2. Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).

3.3. Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (rise over run) is called the slope of a graph.

3.4. Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

4.0. Students solve simple linear equations and inequalities over the rational numbers.

4.1. Solve two-step linear equations and inequalities 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.

4.2. Solve multistep problems involving rate, average speed, distance, and time or a direct variation.

CA.MG. Measurement and Geometry

3.5. Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.

3.6. Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. Mathematical Reasoning

2.6. Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.7. Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.8. Make precise calculations and check the validity of the results from the context of the problem.

CA.AI. Algebra I

1.0. Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.

1.1. Students use properties of numbers to demonstrate whether assertions are true or false.

2.0. Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

3.0. Students solve equations and inequalities involving absolute values.

4.0. Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) +4(x-2) = 12.

5.0. Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

6.0. Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x +6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x +6y is less than 4).

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.

8.0. Students understand the concepts of parallel lines and perpendicular lines and how their slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

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.

10.0. Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.

11.0. Students apply basic factoring techniques to second- and simple third- degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

12.0. Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

13.0. Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.

14.0. Students solve a quadratic equation by factoring or completing the square.

15.0. Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.

16.0. Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

17.0. Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.

18.0. Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.

19.0. Students know the quadratic formula and are familiar with its proof by completing the square.

20.0. Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.

21.0. Students graph quadratic functions and know that their roots are the x-intercepts.

22.0. Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

23.0. Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

24.0. Students use and know simple aspects of a logical argument:

24.1. Students explain the difference between inductive and deductive reasoning and identify and provide examples of each.

24.2. Students identify the hypothesis and conclusion in logical deduction.

24.3. Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.

25.0. Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements.

25.1. Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

25.2. Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.

25.3. Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.

CA.G. Geometry

CA.AII. Algebra II

11.1. Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

11.2. Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.

CA.T. Trigonometry

3.1. Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).

3.2. Students prove other trigonometric identities and simplify others by using the identity cos2 (x) +sin2 (x) = 1. For example, students use this identity to prove that sec2 (x) = tan2 (x) +1.

CA.MA. Mathematical Analysis

5.1. Students can take a quadratic equation in two variables; put it in standard form by completing the square and using rotations and translations, if necessary; determine what type of conic section the equation represents; and determine its geometric components (foci, asymptotes, and so forth).

5.2. Students can take a geometric description of a conic section - for example, the locus of points whose sum of its distances from (1, 0) and (-1, 0) is 6 - and derive a quadratic equation representing it.

CA.LA. Linear Algebra

CA.PS. Probability and Statistics

CA.APPS. Advanced Placement Probability and Statistics

CA.C. Calculus

1.2. Students use graphical calculators to verify and estimate limits.

1.3. Students prove and use special limits, such as the limits of (sin(x))/x and (1-cos(x))/x as x tends to 0.

4.1. Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function.

4.2. Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function.

4.3. Students understand the relation between differentiability and continuity.

4.4. Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions.

26.0. Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.

27.0. Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems.