## Placement Test Topics

### B Test Topics

- Arithmetic of signed numbers, fractions, mixed numbers, decimals, scientific notation
- The number line -- rational and real numbers
- Properties of numbers -- distributive property, prime factors, divisibility, order of operations, least common multiple, greatest common divisor
- Exponents -- integral and fractional exponents, laws of exponents, simplification of expressions containing exponents and radicals
- Applied problems and formulas -- word problems, percent, ratio and proportion, geometric formulas, units of measure
- Linear equations -- slope, intercepts, slope-intercept form, parallel lines, solving linear equations
- Solving linear inequalities and inequalities involving absolute value
- Graphing -- ordered pairs, linear equations and inequalities, parabolas, and other equations
- Pythagorean Theorem, distance in the plane, perimeter, area and basic properties of geometric figures including triangles, circles, and parallelograms
- Systems of equations in two and three variables, and applications
- Polynomials -- addition, subtraction, multiplication, division
- Factoring -- common monomial factor, quadratics, by grouping
- Solving quadratic equations, complex numbers
- Simplifying rational expressions, complex fractions, solving fractional equations
- Logarithms and exponentials
- Right triangle trigonometry

### D Test Topics

- Fundamental concepts of algebra -- including all topics on the B test listed above
- Equations and inequalities -- linear and quadratic equations, fractional equations, equations with radicals, equations quadratic in form, inequalities and sets, equations and inequalities in absolute value, quadratic inequalities, systems of two equations in two variables
- Functions -- coordinate systems, relations, one to one functions, domain and range, graphs of functions (expansions, contractions, translations and reflections), determination of symmetry and asymptotes, composite and inverse functions
- Quadratic functions (properties and graphs), graphs of polynomial functions of degree >2, rational functions (properties and graphs), conic sections (standard forms and graphs)
- Exponential and logarithmic functions, properties and graphs, solving log and exponential equations
- Right triangle trigonometry, angles, evaluation of trig and inverse trig functions
- General trigonometry, trig functions and their properties, evaluating trig functions, reference angles, graphs of trig and inverse trig functions, amplitude, phase shift
- Analytic trigonometry, trig identities and equations, addition formulas and multiple angle formulas, sum and product formulas, law of sines and cosines, vectors
- Complex numbers, definition, conjugates, inverses, complex roots of equations, trig form of complex numbers, powers and roots of complex numbers, DeMoivre's theorem

## Sample Tests

Below are pdf versions of each sample test with solutions. If alternative versions of these sample tests are needed, please contact the math advisors.

- B Test Sample Questions [pdf]
- B Test Sample Solutions [pdf]

- D Test Sample Questions [pdf]
- D Test Sample Solutions [pdf]

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