Textbook Questions for Math B30


Units of Study


Complex Numbers and Quadratic Equations
1.6 Binomial Theorem - expanding (a b)^10
1.6 Binomial Theorem - slightly harder, expanding (x-2y)^5
1.6 Finding a specific term in a binomial expansion (YouTube)
2.1 Simplifying imaginary number expressions
2.1 Evaluating powers of i
2.1 Standard form of complex numbers (YouTube)
2.1 Adding/Subtracting Complex Numbers
2.1 Multiplying Complex Numbers
2.1 Dividing Complex Numbers
2.2 Solving a Quadratic Using the Quadratic Formula
2.3 Applications of Quadratics (word problem with 2 solutions)
2.3 Applications of Quadratics (word problem with 1 solution)
2.4 Describing the nature of the roots of a quadratic using the discriminant
2.5 Write a quadratic equation that satisfies a given solution set
2.5 Determine the sum and product of a quadratic WITHOUT solving it
2.5 Checking your solutions -- determine if a solution set is correct given a quadratic
2.6 Solving equations using substitution (making them look quadratic)
2.7 Set notation review (part 1) (part 2)
2.7 Solving polynomial inequalities graphically
2.7 Solving polynomial inequalities by sign analysis of factors (easy factors)
2.7 Solving polynomial inequalities by sign analysis of factors (harder) (part 1) (part 2)
Complex Numbers and Quadratics Unit Review Questions

Matrices
3.2 Flash examples - Adding/Subtracting/Multiplying by a Scalar/Multiplying Two Matrices
3.2 Multiplying Two Matrices (by hand)
3.3 Using the TI-83 for Matrices (part 1) (part 2)
3.3 Multiplying two matrices on a TI-83
3.4 Properties of Matrices (AB != BA)
3.5 Solving Systems of Linear Equations Using Row Operations (on a TI-83)
3.6 Finding the inverse of a 2x2 matrix by hand
3.6 Finding the inverse of a 3x3 matrix (or any matrix) on the TI-83
3.6 Solving matrix equations
3.7 Graphing linear inequalities (one inequality)
3.7 Graphing linear inequalities (two inequalities) (part 1) (part 2)
3.7 Graphing linear inequalities (multiple inequalities)
3.8 Maximizing/Minimizing objective quantities (finding the feasible region) (finding vertex points) (max/min values)
3.8 Max/min linear word problems (finding objective quantity and constraints) (sketching and finding vertices) (max/min values)

Polynomial and Rational Functions -- Reciprocals and Inverses of Functions
4.1 Synthetic Division
4.1 Long Division
4.1 Remainder Theorem
4.1 Factoring a higher order polynomial (Factor Theorem)
4.1 Zeroes of a polynomial function
4.3 Sketching the graph of a polynomial function (factoring then sketching)
4.3 Sketching the graph of a polynomial function (already factored)
4.3 Sketching the graph of a polynomial function, given general information (in words)
4.4 Sketching the graph of a rational function (finding important info) (sketching)
4.5 Sketching the graph of a reciprocal function, given the equation of the original (sketch first, then translate) (just sketch the reciprocal)
4.5 Sketching the graph of a reciprocal function, given the graph of the original
4.6 Informally showing two relations are inverses
4.6 Formally showing two relations are inverses
4.6 Determining the equation of the inverse of a function (and determining if the inverse is a function)
4.6 Determining the equation of the inverse of a function (a bit harder)

Exponential and Logarithmic Functions
5.3 Determining the value of a logarithm by sight
5.3 Determining a common logarithm using a calculator
5.3 Solving for a variable in a logarithm
5.4 Sketching the graph of a logarithmic function
5.4 Graphing logarithms on a calculator (TI-83)
5.5 Proving the product law of logarithms
5.5 Proving the quotient law of logarithms
5.5 Proving the power law of logarithms
5.5 Proving the base change law of logarithms
5.5 Using the laws of logarithms to write a logarithmic expression as the logarithm of a single number
5.5 Using the laws of logarithms to determine the value of a logarithmic expression
5.5 Using the change of base law to determine the value of a logarithm on your calculator
5.6 Solving Logarithmic Equations (easy)
5.6 Solving Logarithmic Equations (harder)
5.6 Solving Exponential Equations (easy)
5.6 Solving Exponential Equations (harder) (part 2 - entering a big log expression on a calculator)
5.7 Solving an exponential growth word problem
5.7 Solving an exponential decay word problem

Sequences and Series
6.1 Deriving the arithmetic sequence formula tn = a (n-1)d
6.1 Finding a specific term in an arithmetic sequence
6.1 Given a value, find which term it is in a sequence
6.1 Find a formula for the nth term, then use it
6.1 Given two non-consecutive terms of an arithmetic sequence, find first term and common difference (or, an easier way)
6.2 Deriving the geometric sequence formula tn = ar^(n-1)
6.2 Finding a specific term in a geometric sequence
6.2 Given a term in a sequence, find what term number it was in the sequence
6.2 Given two non-consecutive terms of a geometric sequence, find the first term and common ratio
6.3 Inserting an odd number of arithmetic means
6.3 Inserting an even number of arithmetic means
6.3 Inserting an odd number of geometric means
6.3 Inserting an even number of geometric means
6.4 Expanding sigma notation
6.4 Writing a series in sigma notation
6.4 Deriving the arithmetic series formulas
6.4 Finding the sum of the first n terms of an arithmetic series
6.4 Finding the sum of an arithmetic series, given sigma notation
6.5 Deriving the geometric series formula (converting to the "normal" formula)
6.5 Finding the sum of the first n terms of a geometric series (easy)
6.5 Finding the sum of the first n terms of a geometric series (slightly harder)
6.5 Finding the sum of a geometric series, given sigma notation
6.6 Deriving the infinite geometric series formula
6.6 Finding the sum of an infinite geometric series
6.6 Converting a repeating decimal to fraction form (using an infinite geometric series)

Statistics
7.2 Finding Measures of Central Tendency (on a TI-83)
7.4 Deriving the Standard Deviation Formula
7.4 Finding the Standard Deviation (on a TI-83)
7.6 Finding the area given a z-score inequality
7.6 Finding the z-score given area
7.7 Finding probability, given mean, standard deviation and range of x values
7.7 Finding an x value, given a percentage, mean and standard deviation

Probability