# Solving algebraic equations and inequalities linear

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Solving algebraic equations and inequalities (linear, quadratic, higher order using synthetic division, rational, radical, and absolute value equations) F. Simultaneous equations II. Graphing and Functions*A. Lines (intercepts, slopes, write equations using point-slope and slope intercept, parallel, perpendicular, distance and midpoint formulas) B. Conic Sections (circle, parabola, ellipse, and hyperbola) *C. Functions (definition, notation, domain, range, inverse, composition) *D. Basic shapes and transformations of the following functions (absolute value, rational, root, higher order curves, log, ln, exponential, trigonometric. piece-wise, inverse functions) E. Tests for symmetry: odd, even III. Geometry A. Pythagorean Theorem B. Area Formulas (Circle, polygons, surface area of solids) C. Volume formulas D. Similar Triangles * IV. Logarithmic and Exponential Functions *A. Simplify Expressions (Use laws of logarithms and exponents) *B. Solve exponential and logarithmic equations (include ln as well as log) *C. Sketch graphs *D. Inverses * V. Trigonometry **A. Unit Circle (definition of functions, angles in radians and degrees) B. Use of Pythagorean Identities and formulas to simplify expressions and prove identities *C. Solve equations *D. Inverse Trigonometric functions E. Right triangle trigonometry *F. Graphs VI. Limits A. Concept of a limit B. Find limits as x approaches a number and as x approaches * A solid working foundation in these areas is very important.
Calculus Prerequisite ProblemsWork the following problems on your own paper. Show all necessary work. I. AlgebraA. Exponents: 1)´µ´µ´µ133311233824x yzxxyz±B. Factor Completely: Hint: Factor as difference of squares first, then as the sum and difference of cubes second. 2) 9x2+ 3x -3xy-y (use grouping)3) 64x 6-1 4) 42x 4+ 35x 2-28 5) 531222224±±15xxxHint: Factor GCF x 1/2first. 6) x -1-3x -2 + 2x -3Hint: Factor out GCF x-3first. C. Rationalize denominator / numerator: 7) xx±±±3128) x + 1 +1 x D. Simplify the rational expression: 9) (x + 1)3 (x - 2) + 3(x + 1 )2(x + 1)4E. Solve algebraic equations and inequalities 10. – 11. Use synthetic division to help factor the following, state all factors and roots.
- 16x + 7 12) Explainwhy 32cannot be a root of f(x) = 4x5+ cx3 - dx + 5 , where c and d are integers. (hint: You can look at the possible rational roots.) 13)Explainwhy f(x) = x4+ 7x2+ x - 5 must have a root in the interval [0, 1], ( 0 x Check the graph and use signs of f(0) and f(1) to justify you’re answer. 1)
x
9
+
0
< 14
F. Solve the system. Solve the system algebraically and then check the solution by graphing each function and using your calculator to find the points of intersection.
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