CSET Math Guru: Let the Guru Lead the Way!
  • Welcome! How to BEST use the Site!
  • What is the CSET? How to become a Math Teacher?
  • Getting Started for CSET Math
  • About my CSET Q Banks
  • Order CSET Math Q Banks
  • Buyer Beware!
  • Have Qs? CALL ME!
  • Testimonials and Feedback
  • The BEST $499 You'll Spend
  • Subtest I California Math Content Standards
  • Subtest I Algebra Prep Resources
  • Subtest I Online Resources
  • Subtest I Abstract Algebra / Number Theory Prep Resources
  • Subtest I Algebra Practice Qs
  • Subtest I Algebra Top 8 Concepts to Master
  • Subtest I Algebra Checklist of Skills
  • Subtest I Algebra FRQ Patterns
  • Subtest I Trignometry Requirements
  • Subtest II California Math Content Standards
  • Subtest II Common Core Standards
  • Subtest II Geometry Prep Resources
  • Subtest II Online Resources
  • Subtest II Geometry Practice Qs
  • Subtest II Geometry Top 8 Concepts to Master
  • Subtest II Geometry Writing Proofs the Painless Way
  • Subtest II Geometry Vital Theorems
  • Subtest II Statistics Prep Resources
  • Subtest II Statistics Practice Qs
  • Subtest II Statistics Top 6 Concepts to Master
  • Subtest II Geometry Checklist of Skills
  • Subtest I and II Formulae
  • Subtest III California Math Content Standards
  • Subtest III Calculus / Trigonometry Prep Resources
  • Subtest III Calculus / Trigonometry Practice Qs
  • Subtest III Checklist of Basic Skills
  • The CSET SS Math Blog
  • Using Calculators on the CSET
  • Calculator Tips for the TI-83 and 84 Family
  • How many Subsets Should You take at One Time
  • How should Free Response Questions be written
  • Studying for the Test rather than to it
  • Teaching Assignments for Rookie H.S. Teachers
  • Are the CSET Subtests Valid
  • How Good in Math must One be?
  • A Pass is a Pass, Right?
  • Recommended websites for CSET Preparation
  • Tackling Test Anxiety and Repeated Failure
  • Test Strategies for Passing the CSET
  • Advice for Middle School Math Teachers

CSETMathGuru: THE Site for Single Subject Math

What skills must one possess for Subtest I: Algebra?

You must:

  • Know distance formula.
  • Midpoint formula
  • Know symmetricity of graphs with respect to x-axis, y-axis, origin, y = x, line y = -x.
  • Know the points slope form and slope intercept form of equation of lines.
  • Know the condition for parallel and perpendicular lines using slopes.
  • Prove the theorem on parallel and perpendicular lines using slopes.
  • Know the definition of a function and relation.
  • Know the Vertical Line Test for determining if a set of points belongs to a function.
  • Be able to determine the domain and range of a function algebraically and graphically.
  • Be able to factorize expressions using (a ± b)2, (a ± b)3, a2 – b2 , a3 ± b3
  • Know how to complete the square of a quadratic expression.
  • Determine if a function is even/odd.
  • Be able to rationalize the denominator to simplify complex (i) and irrational (√) expressions

For QUADRATIC FUNCTIONS, you must:

  • Be able to derive the quadratic formula
  • Derive the sum of roots of a quadratic equation is –b/a and the product of roots is c/a.
  • Know the relationship between the roots of a quadratic equation and its graph based on the discriminant, D = b2 – 4ac, being positive, negative or equal to zero
  • Be able to convert a quadratic function in standard form to parabola form by completing the square.
  • Determine the vertex, axis of symmetry, roots/x-intercepts of a quadratic function/ parabola.
  • Determine if a parabola opens up or down, and based on that, know if the function has a maximum or minimum.
  • Be able to solve variations of quadratic equations using substitution: for example, ax4 + bx2 + c = 0, √(ax4 + bx2 + c) = 0, ax2 + b/x2 + c = 0, √(ax + b) + √ (cx + d) = 0, etc. and find the maximum/ minimum of such functions.
  • Be able to derive the coordinates of the vertex of a quadratic function in standard form.
  • Model word problems related to quadratic functions and determine maximum/ minimum values.
  • Determine roots/ x intercepts through quadratic formula/ completing the square.
  • Know properties of complex numbers: addition, subtraction, multiplication, and division.
  • Be able to represent the sum, difference, product and quotient of complex numbers in a + bi form.
  • Know that irrational and complex roots of functions occur as conjugates.
  • Be able to graph and interpret inequalities relating to quadratic functions: know for which intervals the graph lies above/ below the x-axis
Qs? Call (Jay): 951-489-7665 
OR email me: innovationguy@gmail.com. 


For POLYNOMIAL FUNCTIONS, you must:

  • Be able to determine the number of turning points for a function.
  • Determine the end behavior of the function.
  • Determine by visual inspection if a graph represents a certain polynomial function.
  • Know characteristics of even/ odd functions.
  • Know shapes of the most important BASE GRAPHS:
  1. f(x) = √x
  2. f(x) = x2
  3. f(x) = xn, for n = odd/ even
  4. f(x) = 1/x
  5. f(x) = 1/xn, for n = odd/ even
  6. f(x) = 3√x
  7. f(x) = n√x, for n = odd/ even
  8. f(x) = |x |

  • Be able to transform the above base graphs for the following cases:

  1. Given f(x), graphing f(x + c) or f(x – c)
  2. Given f(x), graphing f(x) + c or f(x) – c
  3. Given f(x), graphing c f(x), for c > 1 and c <> 1
  4. Given f(x), graphing f(-x) and –f(x)

  • Be able to graph polynomial functions in factored form

  1. X-intercepts
  2. Y-intercepts

  3. End behavior of function
  4. Intervals where graph is above/ below the x-axis by using a sign table.

  • Be able to divide two polynomial functions using long division
  • Be able to divide a polynomial and a linear (binomial) expression using Synthetic Division, and determine the Quotient and Remainder
  • Know the proofs of Remainder Theorem and Factor Theorem
  • Use the Factor Theorem and Remainder Theorem to determine if a monomial is a factor of the polynomial function.
  • Be able to prove the Rational Roots Theorem.
  • Apply the Rational Roots Theorem to determine the possible roots of a polynomial.
  • Apply the Descartes Rule of Signs to determine the number of positive, negative and imaginary roots of a polynomial.
  • Determine the polynomial function given its roots and their multiplicity
  • Be able to calculate the roots, real and imaginary, of a polynomial.
  • Be able to graph and interpret inequalities relating to polynomial functions: know for which intervals the graph lies above/ below the x-axis.

Qs? Call (Jay): 951-489-7665 
OR email me: innovationguy@gmail.com. 


For RATIONAL FUNCTIONS, f(x) = P(x)/ Q(x), you must:

  • Be able to graph various forms of rational functions by determining its:
  1. x intercepts (solve: numerator = 0)
  2. y intercepts (substitute: x = 0 into the function)
  3. vertical asymptotes (solve: denominator = 0)
  4. horizontal asymptotes (imagine x to be a large number, M, and simplify.)
  5. slant asymptotes, if any, if the numerator has degree 1 more than the denominator

For INVERSE OF FUNCTIONS you must

  • Be able to determine the inverse of functions (swap x and y in the original function and solve for y)
  • Know properties of inverse functions
  • Know the behavior of the inverse function, when given the graph of the original function (ie. the inverse function and the original function are symmetrical about the line y =x).
  • Know the relationship of the domain and range of inverse functions and the original function.
  • Know the horizontal line test for determining if a function has an inverse.
  • Know what a one-to-one function is.

Qs? Call (Jay): 951-489-7665 
OR email me: innovationguy@gmail.com. 


For COMPOSITE FUNCTIONS,f(x) = h(g(x)); h(x)/g(x); h(x)g(x), etc. you must

  • Be able to determine the domain and range.
  • Find values of composite functions for given values of x (x = a…)

For LOGARITHMIC AND EXPONENTIAL FUNCTIONS you must

  • Know the general form (algebraically and graphically) of logarithmic (ie. log x) and exponential (ie. ax or ex) functions.
  • Know the relationship between logarithmic (log10 x or log ex) and exponential (axor ex) functions, and transform exponential to logarithmic functions and vice versa.
  • Be able to calculate the inverse of logarithmic and exponential functions.
  • Graph logarithmic and exponential functions using elementary transformations
  • Be able to determine the domain and range of transformed logarithmic and exponential functions.
  • Know the properties of logarithms and exponents, and apply properties to simplify expressions
  • Solve equations and inequalities with logs and exponents using definitions and properties of logs and exponents
  • Be able to determine extraneous solutions to equations/inequalities
  • Know the formula for compound interest for the case of continuous compounding
  • Be familiar with exponential growth and decay situations, and related doubling time and half-life problems

Qs? Call (Jay): 951-489-7665 
OR email me: innovationguy@gmail.com. 


For VECTORS you must:

  • Be able to determine the magnitude and direction of a vector
  • Know the representation of vectors in standard (ai + bj) and component form
  • Know basic vector operations
  • Be able to determine unit vectors in a given direction
  • Be able to calculate the direction angles of vectors
  • Apply elementary vector properties to solve real-world problems
  • Be able to calculate the angle between 2 vectors using dot product of vectors, and determine if 2 vectors are parallel or perpendicular

For SYSTEMS OF EQUATIONS, you must:

  • Be able to solve systems of equations (lines, circles, ellipses, parabolas, hyperbolas) simultaneously to determine points of intersection.
  • Solve systems of inequalities and be able to graph the shaded region representing all possible values of (x, y).
  • Be able to determine the maximum and minimum values of an objective function of a linear programming problem/ situation.
  • Be able to solve word problems involving a linear programming situation: choose appropriate variables, determine constraints and objective function, plot lines representing constraints, determine corner points for shaded polygon and calculate maximum/ minimum values of the objective function.
  • Be able to solve systems of linear equations by finding the reduced echelon form of a matrix by performing row transformations
  • Be able to classify systems of linear equations as consistent/ inconsistent/ possessing infinite solutions.

Qs? Call (Jay): 951-489-7665 
OR email me: innovationguy@gmail.com. 


​For MATRICES and DETERMINANTS, you must:

  • Know basic properties of matrices
  • Know the criteria for multiplying matrices
  • Be able to multiply matrices
  • Know properties of matrix multiplication.
  • Be able to find the inverse of a matrix using determinants.
  • Be able to calculate the inverse of a matrix by reducing it to echelon form.
  • Be able to solve systems of linear equations by calculating the inverse of a matrix.
  • Be able to find the value of a 2 X 2 and 3 X 3 determinants.
  • Know properties of determinants pertaining to row and column transformations.
  • Know Cramer’s Rule for solving linear equations using determinants.

For SEQUENCES, SERIES, PERMUTATIONS AND COMBINATIONS you must:

  • Be able to determine the general term of an arithmetic/ geometric series using the common difference/ ratio.
  • Be able to calculate the sum of n terms of an arithmetic/ geometric series.
  • Be able to calculate the sum of an infinite geometric series.
  • Know the principle of Mathematical Induction.
  • Be able to apply the Principle of Mathematic Induction to prove elementary propositions/ conjectures.
  • Know the (r + 1)th term in the expansion of (a + b)n using the binomial theorem.
  • Expand binomial expressions using the binomial theorem and calculate specific terms.
  • Be familiar with Pascal’s Triangle.
  • Know the fundamental counting principle.
  • Be able to calculate the number of different permutations & combinations of r elements that can be obtained from a set of n elements.
Qs? Call (Jay): 951-489-7665 
OR email me: innovationguy@gmail.com. 

​

    Contact Me

Submit
Powered by Create your own unique website with customizable templates.