College Pre-Algebra & College Algebra

The first coordinate in an ordered pair. For the point (8, -2) the abscissa is 8.

Absolute value makes a negative number positive. Positive numbers and 0 are left unchanged. The absolute value of x is written |x|. We write |-6| = 6 and |8| = 8.

Algebra rules for absolute values are listed below. Piecewise Definition: Square root definition: Rules: 1. |-a| = |a| 2. |a| ≥ 0 3. Products: |ab| = |a||b| 4. Quotients: |a / b| = |a| / |b| 5. Powers: |an| = |a|n 6. Triangle Inequality: |a + b| ≤ |a| + |b| 7. Alternate Triangle Inequality: |a - b| ≥ |a| - |b| CAREFUL!! Sums: |a + b| is not the same as |a| + |b| Differences: |a - b| is not the same as |a| - |b|

The rate of change of velocity over time. For motion along the number line, acceleration is a scalar. For motion on a plane or through space, acceleration is a vector.

How close an approximation is to an actual value. Accuracy: 3.14 is a fairly accurate approximation of π (pi). Precision: 3.199 is a more precise approximation, but it is less accurate.

The matrix obtained by changing the sign of every matrix element. The additive inverse of matrix A is written -A. Note: The sum of a matrix and its additive inverse is the zero matrix.

The mathematics of working with variables.

The study of geometric figures using the coordinate plane or coordinates in space. Formulas from analytic geometry include the distance formula, midpoint formula, point of division formula, centroid formula, area of a convex polygon.

The use of algebraic and/or numeric methods as the main technique for solving a math problem. The instructions "solve using analytic methods" and "solve analytically" usually mean that no calculator is allowed.

The coordinate plane used to graph complex numbers. The x-axis is called the real axis and the y-axis is called the imaginary axis. The complex number x + yi is graphed as the point (x, y).