Integrated Math 3 – Exam Topics
- Functions – Find the zeroes (x-intercepts). Find maximum or minimum points.
- Systems of Equations – Find intersection in linear system, or identify if there is not a solution. Find the number of intersections and where they are for a system involving a quadratic equation.
- Inequalities / System of Inequalities – Identify the solution to an inequality on a number line (one-variable problem) or graph (two-variable problem). Know the difference on the graph between a strict inequality (< or >) and one including equality (≤ or ≥), and also how these look in interval notation. For a system of inequalities, be able to find the solution – where one inequality is greater than the other. Identify the inequality or graph that matches a word description. Videos: Linear Inequalities, Quadratic Inequalities
- Polynomials – A function that is the sum of different powers of x. You will be asked to identify the zeroes (same this as x-intercepts) of the function. You will need to know the degree (the highest power of the variable) and the leading coefficient (the number that is multiplied by the highest power of the variable).
- Rational Functions – these are fractions where the numerator and denominator are both functions. The major focus is to identify discontinuities, which occur when the denominator equals zero. Look at just the denominator – when it is zero, the graph of the whole function cannot exist at that value of x. Usually this is an asymptote, a line the graph approaches but does not reach. A rational function is zero when the numerator is zero.
- Trig Functions – Given an angle and a side of a right triangle, find another side of the triangle. One problem will be a word problem (ex: height of a tree, length of a ladder, etc.)
- Inverse Trig Functions – You will be given two sides of a right triangle, and have to find a specific angle. To do this choose the correct function based on the side given (sin-1, cos-1, or tan-1) and put in the correct ratio with the given sides. One problem will be a word problem.
- Coordinates and Shapes – Use coordinates of points to find the length and slope of line segments. Based on this, identify a shape. Know how to find if two lines (or segments) are parallel — same slope; or perpendicular — negative reciprocal slopes.
- Parallel Lines & Angles – Identify types of angle pairs; use properties of angles (congruent or supplementary) to solve for the measure of a given angle.
- Triangle Inequality – Determine maximum and minimum size of an unknown side. Use side lengths to determine which angle is largest/smallest; or to find if a triangle is acute, right, or obtuse.
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