Final Review

Here is the final exam review guide.

Everything listed below will be covered on the exam.  The exam is 40 multiple choice questions and 21 long answer questions worth 60 marks, for a total of 100.  You should be working through the cummulative exercises at the end of the worktext as well as going back and reviewing each chapter. 

I will be available Monday, Tuesday and Wednesday mornings ( 9 - 12:15) in my classroom.  Please feel free to come and work in there.  Also a reminder that your blog promts and test blogging needs to be finished up.  Deadline is Tuesday, Jan. 31.  If it is not completed by then you will recieve an incomplete as your mark. 

Your exam is Thursday morning, Feb 2, 2012 at 9am.

Pre-Calc 30S Exam Review

Unit 1 – Chapter 1 – Sequences and Series

·    Determine the first term, the common difference, the number of terms or the value of a specific term in a problem involving an arithmetic sequence.

·    Determine the first term, the common difference, the number of terms or the value of the sum of specific numbers of terms in a problem involving an arithmetic series.

·    Determine the first term, the common ratio, the number of terms or the value of a specific term in a problem involving a geometric sequence.

·    Determine the first term, the common ratio, the number of terms or the value of the sum of a specific number of terms in a problem involving a geometric series.

·    Solve a problem that involves a geometric sequence or series.

Unit 2 – Chapter 2 – Absolute Value and Radicals

·         determine the distance between two real numbers.

·         determine the absolute value of a positive or negative real number.

·         Express an entire radical with a numerical radicand as a mixed radical.

·         Express a mixed radical with a numerical radicand as an entire radical.

·         Perform one or more operations (+, -, x, / ) to simplify radical.

·         rationalize the denominator of a rational expression with monomial or binomial denominators.

·         determine any restrictions on values for the variable in a radical equation.

·         determine the roots of a radical equation.

Unit 3 – Chapter 3 – Solving Quadratic Equations

·         Factor polynomial expressions  -  common factoring, trinomial factoring ( by inspection and decomposition), and difference of squares.

·         Solve a quadratic equation of the form ax²+ bx + c = 0  by  determining square roots,  factoring,  completing the square,  applying the quadratic formula, or graphing its corresponding function.

·         Solve a problem by determining or analyzing a quadratic equation. 

Unit 4 – Chapter 4 – Analyzing Quadratic Functions

·         Compare the graphs of a set of functions of the form y = ax² to the graph of y = x² , and generalize, using inductive reasoning, a rule about the effect of a.

·         Determine the coordinates of the vertex for a quadratic function of the form y = a(x-p)²+q

·         Write a quadratic function given in the form ax²+ bx + c = y  as a quadratic function in the form y = a(x-p)² +q by completing the square.

·         Sketch the graph of a quadratic function given in the form ax²+ bx + c = y.

·         Sketch the graph of y = a(x-p)² +q, and identify the vertex, domain and range, direction of opening, axis of symmetry and x - and y -intercepts. 

Unit 5 – Chapter 5 – Graphing Inequalities and Systems of Equations

·         Sketch the graph of a linear or quadratic inequality.

·         Determine the solution of a system of linear-quadratic or quadratic-quadratic equations algebraically.

·         Solve a problem that involves a linear or quadratic inequality.

·         Solve a problem that involves a system of linear-quadratic or quadratic-quadratic equations. 

Unit 6 – Chapter 6 – Trigonometry

·         sketch an angle in standard position, given the measure of the angle.

·         determine the reference angle for an angle in standard position.

·         determine the quadrant in which an angle in standard position terminates.

·         draw an angle in standard position given any point P (x, y ) on the terminal arm of the angle.

·         determine the value of  sin Ɵ, cos Ɵ or tan Ɵ, given any point P (x, y ) on the terminal arm of angle .

·         determine, without the use of technology, the value of sin Ɵ, cos Ɵ or tan Ɵ, given any point P (x, y )       on the terminal arm of angle , where = 0^o, 90^o, 180^o, 270^o or 360^o.

·         determine the sign of a trigonometric ratio for an angle, without the use of technology (CAST Rule).

·         solve an equation of the form sin Ɵ = a, cos Ɵ = a or tan Ɵ = a

·         determine the exact value of the sine, cosine, or tangent of an angle with a reference angle of 30 ^o, 45 ^o, or 60 ^o.

Unit 7 – Chapter 7 – Rational Expressions and Equations

·         determine, in simplified form, the sum or difference of rational expressions

·         determine, in simplified form, the product or quotient of rational expressions.

·         simplify an expression that involves two or more operations on rational expressions

·         determine the solution to a rational equation.

Unit 8 – Chapter 8 – Absolute Value and Reciprocal Functions

·         Sketch the graph of y=|f(x)|; state the intercepts, domain and range; and explain the strategy used.

·         Generalize a rule for writing absolute value functions in piecewise notation.

·         Solve, algebraically, absolute value equations, and verify the solution.

·         Compare the graph of to the graph of y = 1/f(x)   to the graph of y = f(x)

·         Identify, given a function f(x), values of x for which y = 1/f(x)  will have vertical asymptotes; and describe their relationship to the non-permissible values of the related rational expression.

·         Graph, without technology, y = 1/f(x), given  y = f(x) .