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Mathematics Placement Guidelines

On Welcome Day, all Finalists and Waitlist Finalists will be given a mathematics
placement test. This test determines the math course each NCSSM student will take during the
first semester at NCSSM. The placement test that you take will be determined by the math course
you are currently taking and the course that normally follows that course at your high school.

• If you are currently enrolled in an Algebra I course or Geometry course and the course
that normally follows it at your high school is Geometry or Algebra II, then you will take
an Algebra II placement test.
• If you are currently enrolled in an Algebra II or Algebra III course and the course that
normally follows it at your high school is Precalculus, Advanced Math, or IB level II
mathematics, then you will take a Precalculus placement test.
• If you are currently enrolled in a Precalculus or Advanced Math course and the course
that normally follows it at your high school is Calculus, then you will take a Calculus
placement test.
• If you have completed AP Calculus, you will not take a placement test, but will complete
forms about your math background during the placement time slot.
• If you are enrolled in Integrated Math II then you will take the Algebra II placement test.
• If you are enrolled in Integrated Math III then you will take the Precalculus placement
test.
• If you are enrolled in Integrated Math IV then you will take the Calculus placement test.
If you are enrolled in IB Mathematics HL or Further Mathematics SL, bring a copy of
your course syllabus to Welcome Day so that you can take the appropriate placement test.
• If none of the above situations applies to you, then the appropriate placement test for you
to take will be determined individually.

To do your best on the placement test you take, you should study your text and notes from the
course in which you are currently enrolled or which you took most recently. This test is
important to the mathematics work of each student who enrolls at NCSSM. Please take time to
prepare for it. Your placement in mathematics at NCSSM will be based on your score on the
appropriate placement test. On the following pages are lists of topics covered on the Precalculus
placement test and the Calculus placement test.

Bring your calculator to the placement test on NCSSM’s Welcome Day.

Topics covered on the NCSSM Precalculus Placement Test (to place into Precalculus next
year).

Bring your calculator to the mathematics placement test on NCSSM’s Welcome Day.
• Function notation: Evaluating functions at different numeric values. Simplifying functions
evaluated at different expressions, such as simplifying f (2a + b) when f (x) is given.
• Function domain: Determining the domain of a function from a graph or from an algebraic
expression.
• Linear functions: Determining the equation for a line when given sufficient information,
including slope and intercept, slope and a point on the line, two points on the line. Predicting
y - values from given x -values and vice-versa. Approximating the equation of a line given a
graph. Knowing the relationship between slopes of parallel or perpendicular lines.
• Quadratic functions: Identifying characteristics of quadratic functions (e.g., vertex, x - and
y -intercepts). Graphing quadratic functions. Rewriting quadratic expressions in different
forms ( factored form , “standard form”—Ax^2 + Bx +C , vertex form ). Solving quadratic
equations.
Radical expressions : Simplifying radical expressions. Rationalizing the numerator or
denominator
of a fraction (possibly using conjugates).
• Rational expressions: Adding, subtracting, multiplying, and dividing fractions whose
numerator and/or denominator may contain variables.
• Inequalities: Simplifying inequalities. Solving linear inequalities and writing solution sets
using appropriate notation (e.g., interval notation or set notation). Solving linear inequalities
involving absolute value.
• Rational exponents: Multiplying, dividing, adding and subtracting expressions containing
rational exponents. Writing rational exponents in radical form or vice-versa.
Rules of exponents : Symbolic manipulation of exponential forms, such as etc.
• Solving equations: Solving a single linear equation. Solving systems of linear equations.
Solving an equation for a single variable when the equation contains more than one variable.
Solving equations containing quadratic expressions, rational expressions, or radical
expressions.
• Problems in context: Translating “word problems” into appropriate algebraic problems.
Interpreting graphs representing real quantities or real data. Creating graphs to represent the
relationship between two real quantities.
• Using technology: Using a graphing calculator to produce graphs of functions, tables, and
scatterplots of data.

During the placement test, you may use any calculator you have brought with you and with which
you are comfortable. Bring your calculator to the math placement test.

Topics covered on the NCSSM Calculus Placement Test (to place into Calculus next
year).

Bring your calculator to the mathematics placement test on NCSSM’s Welcome Day.

Students taking the calculus placement test should be able to solve problems involving the topics
in the list for the NCSSM Pre-Calculus Placement Test, and such problems may appear on the
calculus placement test. Additional topics covered on the calculus placement test are:

• Functions: Determining domain and range of a function from an algebraic expression or a
graph. Determining the inverse of a function, including its domain.
• Function composition: Simplifying (i.e., f (g (x))) when f (x) and g(x) are
given. Finding the domain of . Recognizing when a function is a composition of other
functions (e.g. h(x) = can be written as f (g(x)) where and
g(x) = sin(3x) ).
• Logarithms: Knowing rules of logarithms (any base, including the natural logarithm) and
knowing how to use them appropriately. (e.g., ln (ab) = ln a + ln b , log (xy) = y log x ,
etc.) Solving equations involving logarithms. Simplifying logarithmic expressions. Graphing
logarithmic functions.
• Exponential functions: Graphing exponential functions given sufficient information (e.g.,
two known points, one known point and a growth/decay rate). Solving equations involving
exponential functions.
• Trigonometric functions: Determining characteristics of sine, cosine, and tangent functions,
including domain, range, period, amplitude, and phase shift (horizontal shift). Creating
graphs of trigonometric functions from equations and vice-versa. Solving equations
involving trigonometric functions, giving all real solutions. Determining characteristics of
the inverse functions of the trigonometric functions. Understanding right-triangle definitions
of sine and cosine as well as unit circle definitions of sine and cosine.
• Function transformations: Recognizing vertical and horizontal translations (shifts) of
functions and horizontal and vertical compressions/stretchings of functions. Given a graph of
f (x) , producing a graph of f (x + k) , f (x) + k , f (kx) , kf (x) , or a combination of these,
such as a ⋅ f (bx + c) + d . Given a graph of a linear transformation of a function f ,
producing an expression for the graph in terms of f (x) .
• Function compositions: Given a graph of f (x) , producing a graph of the following
functions:
• Systems of equations: Solving systems of equations of which one or more may be non-linear.
• Using technology: Using a graphing calculator to manipulate data lists; e.g., linearizing nonlinear
data by log-log or semi-log transformations, etc.

During the placement test, you may use any calculator you have brought with you and with which
you are comfortable. Bring your calculator to the math placement test.

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