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 (x^{y}) =
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.