The 10 Placement Test Categories

(Categories 1 ... 5 Comprise the Basic QL Requirement)

1)  Arithmetic

A) Operations / Simplifying:  +, -, *, /, exponents, order of operations

B) Decimal – Fractions – Percentages: Conversion

C) Real Number Line Open/closed intervals; Inequalities

D) Ratios and Proportions:

E) Misc:  Absolute Value, and other arithmetic operations. 

2)  Algebra

A) Factoring / Simplification:

B) Algebraic Manipulation: The log, exponential, power, and root rules 

C) Distance / Midpoint Formulas: 

D) Solving a Linear Equation: 

E) Solving a Quadratic Equation: 

F) Solving a simple Inequality: 

G) Finding the equation of a line: 

H) Misc. (1): Rational Expressions / Equations; Different forms of lines, parabolas,

circles and ellipses, solving a system of two simple equations.

3)  Numbers and Units

A) Scientific Notation:

B) Estimating Magnitude:  

C) Unit prefixes:

D)  Unit Conversion:

E) Problems with many zeroes:

F)  Misc: Approximate versus exact values; Number types: Real, Rational,

Irrational, Integer.

4)  Graphing: 

A) Which graph represents the function f(x) =  …?

B) Which function is represented by the graph shown:  

C) Simple transformations, and their before / after graphs:

D)  Properties of functions via their graphs: Even, odd, asymptotic, undefined,

 functions vs. relations, domain, range, 

E) Evaluation / Estimation: Evaluating or estimating function values, slopes,

composed values. 

F)  Misc:  Best graph to model a word problem; Roots; Quadrants; Construction

of an inverse function (y = x criteria); etc.

5)  Geometry: 

A) Perimeter, Area, Volume formulas:

B)  Congruent and Similar triangles: 

C)  Arcs, chords, segments, sector formulas:

D)  Pythagorean Theorem:

E) Polygons and Circles:

F) Parallel and Perpendicular:

G) Misc:

6)  Functions: 

A) Properties: Even, odd, increasing, decreasing, symmetric, one to one, onto,

continuity, definition of function, vertical line test

B) Representations of functions: Formula, description in words, table, graph

C) Domain / Range:

D) Piecewise functions:

E) Composition of functions:

F) Inverses:  Computing an inverse, horizontal line test,

G) Linearity: Slope of secant lines; average rate of change over an interval;

H) Misc: Evaluation, implicit functions, limits, relations versus functions,

7)  Trigonometry

A) Trigonometric Identities:

B)  Evaluating the basic functions: sin(30°), tan(0°), sec(45°), cos(5p), csc(p/6), etc.

C) Radians, Degrees, and Radian – degree conversion:

D)  Solving Trigonometric Equations:

E) Inverse trigonometric functions:

F) Modelling physical phenomena with trigonometric functions:

G) Angles and polygons:  Sum of degrees in a polygon; determining angular

 measure within polygons or sets of intersecting lines.