Search 72,888 tutors

## Review Content for High School Algebra III Course

Interpreting word problems (“of” means multiply, “per” means divide, etc)
solving inequalities and plotting them on number lines (blank circle means excludes, filled circle means includes)
inequalities of absolute values

linear functions entails input points on the domain mapping to single output points on the range
linear vs other forms of equations (inverse, quadratic, polynomial ...also trigonometric, exponential, hyperbolic, logarithmic, etc)
vertical line test for functions
continuous functions vs discontinuous functions
the algebraic order of operations (add, subtract, multiply and divide)
4 different relational properties (commutative, inverse, distributive, and associative)

functions of inequality (shaded regions of greater or less than values)
functions with absolute values in them
different ways of plotting on a graph (table method, calculator method)
simple word problem equations that involve input and output values

2x2 systems of linear equations (consistent means 1 or more solutions, inconsistent means no solutions, independent means multiple lines, and dependent means same line)
shifting graphs horizontally along the domain by adding or subtracting from the x-values
stretching and inverting graphs by multiplying by a coefficient

graphing regions of inequalities
Types of graphs (flat non-sloping lines, flat sloping lines, integer stepping functions, piece-wise functions, absolute value functions)
using standard form “ax+by=c” of equations for plotting {x;y}-intercepts = {(c/a,0); (0, c/b)}
using slope-intercept form “y=mx+b” for plotting … slope=m, {x;y}-intercept = {(-b/m,0);(0,b)}

using a TI-89 calculator
Wolfram Alpha calculation engine

matrix rules: A(B+C)=AB+A, (AB)C=A(BC)...etc
the identity and zero matrices AI=A, A*0=0
finding determinates of square matrices

word problems that require writing systems of equations using substitution and elimination methods for solving systems of linear equations
finding slopes of parallel and perpendicular lines

writing systems of equations in general matrix and conjoined matrix form
elimination method to achieve row echelon form (ref) and then reduced-row echelon form (rref)
finding an inverse matrix by conjoining with identity matrix and eliminating to ref then to rref

using coordinate matrices (similar to bitmap images) to plot figures on graphs
using parametric equations to plot figures on graphs
translating, dilating, and rotating parameterized equations and coordinant matrices

using the cross product of two displacement vectors V12, V13 V12xV13=det([i,j,k][V12][V13]). which is the vector orthogonal to the plane formed by those two displacement vectors, and the magnitude of the new vector is the area of the parallelogram generated by displacement vectors

exponent rules: (A^x)*(A^y) = A^(x+y); (A^x)^y = A^(xy), etc
multiplying conjugates (complex and other)

complex numbers (z = a +bi)
the complex plane made of real and imaginary numbers
degrees and radians on the unit circle: (degrees = 180 * radians/pi)
finding i^n by rotating n*pi/2 radians times counterclockwise along the unit circle from i^0 = 1

finding minimums and maximums of parabolas at the axis of symmetry (x-sym = -b/(2a))
quadratic formula: Xint=(-b +/- sqrt(b^2 -4ac))/(2a), for finding zeros of quadratic equations

parabolas that intersect the X-axis 0, 1, or 2 times as determined by the discriminant values (d<-0, 0=d, +0

quadratic physics problem with constant acceleration, initial velocity, and initial position

completing the square à y= a[(x^2+(b/a)x+K)+(c/a-K)], where K=(b/(2a))^2
finding point vertex form by completing the square of a quadratic: y = a(x+b/(2a))^2 + (4ac-b^2)/(4a); where the vertex point is (-b/(2a), (4ac-b^2)/(4a))

monomial (ax^2), binomial (ax+b) , and polynomial expressions (…+ax^2+bx+c)
dividing polynomials by binomials using long division and synthetic division
foiling expressions (firsts, outers, inners, lasts)
factoring quadratic equations (if ax^2+bx+c=(rx+t)(sx+v); then a=rs, b=rv+st, c=tv)
factoring the difference of two squares and the sum of two cubes