Download Math Skills Assessment

Salem Academy Math Skills Checklist
To be completed by current Math Teacher.
Name of applicant___________________________________________________________________
The items listed below represent the typical topics completed in Salem Academy’s math courses. Please check
those topics which the student has completed. For more specifics on these topics see Salem Academy’s Course
Descriptions at www.salemacademy.com/page.cfm?p=300
Algebra One Topics:
Solve multi-step equations using addition, subtraction,
multiplication, division, and distribution, reciprocals,
collecting like terms and having variables on both sides.
Solve equations in two variables over a given domain.
Graph ordered pairs and linear equations in two
variables on a Cartesian coordinate system.
Set-up and use slope-intercept form or point-slope form
of a linear equation.
Find the equation of a line given the slope and one point
on the line, or given two points on the line.
Set-up and simplify expressions involving positive or
negative exponents.
Add, subtract, and multiply polynomial expressions.
Recognize problems that do not have solutions.
Factor integers and find the greatest common factor
(GCF) of several integers.
Divide polynomials by monomials and find monomial
factors of polynomials.
Simplify products of the form (a+b)(a-b) and factor the
difference of two squares.
Factor general quadratic trinomials with integer
coefficients.
Factor polynomials by grouping terms.
Add, subtract, multiply, and divide algebraic fractions,
getting common denominators when appropriate.
Solve equations that contain fractional coefficients or
variables in the denominator.
Solve problems involving fractions, percents, and
decimals, including mixture problems, percent of
change problems, and work problems.
Solve systems of linear equations using graphs,
substitution, or elimination.
Use properties of equality to transform and solve
inequalities.
Find solution sets of combined inequalities.
Solve equations and inequalities involving absolute
value.
Graph linear inequalities in two variables.
Find the square roots of numbers that have rational
square roots.
Simplify products, quotients, sums, and differences of
radicals.
Find square roots of variable expressions and use them
to solve equations and problems.
Use the Pythagorean theorem and its converse to solve
geometric problems.
Solve quadratic equations by graphing, factoring,
completing the square or with the quadratic formula
Geometry Topics:
Define and apply the terms equidistant, point, line,
plane, collinear, coplanar, angle, and intersection.
Apply postulates and theorems relating points, line, and
planes.
Apply properties from algebra and properties of
congruence in proofs.
Apply the definitions of congruent, complementary,
supplementary and vertical angles.
Plan proofs and then writes them in two- column form,
paragraph form, or as a flow proof.
Apply postulates and theorems about parallel and
perpendicular lines.
Classify the angles formed when two lines are cut by a
transversal.
Apply theorems about a point on the perpendicular
bisector of a segment or on the bisector of an angle.
Prove that certain quadrilaterals are parallelograms and
if the parallelogram is a rectangle, rhombus, or square.
State and apply the properties of similar polygons.
Use the AA or SAS Similarity Postulate, or the SSS
Similarity Theorem to prove triangles similar.
Use similar triangles to deduce information about
segments or angles
State and apply the Pythagorean Theorem.
Determine the lengths of two sides of a 45o-45o-90o or a
30o-60o-90o triangles given the length of the third.
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Salem Academy Math Skills Checklist
Geometry Topics contd:
Categorize triangles according to sides and to angles.
Apply theorems and corollaries about the sum of the
measures of the interior and exterior angles of a triangle.
Identify and name convex polygons and regular
polygons and find their interior and exterior angles.
Prove congruency of triangles using the SSS, the SAS
or the ASA Postulate as well as the AAS and HL
Theorem for right triangles.
Gather information about segments and angles after
proving that two triangles are congruent
Apply theorems and corollaries about isosceles
triangles.
Apply the definitions of the median and the altitude of a
triangle and the perpendicular bisector of a segment.
State tangent, sine, and cosine ratios for acute angles.
Apply theorems and properties that relate tangents,
radii, arcs, chords, and central angles of a circle.
Solve problems involving lengths of chords, secant
segments, and tangent segments.
Know and apply the formula for the area of regular
polygons including rectangles, parallelograms, triangles,
rhombuses, and trapezoids.
Know and apply the formulas for the circumference,
area, arc length, and area sector of a circle.
Identify the parts and find the lateral areas, total areas,
and volumes of right prisms, regular pyramids, right
cylinders, and right cones.
Find the area and the volume of a sphere.
Algebra Two Topics:
Find the slope of a line and graph a line given its slope
and a point on the line.
Write the equation of a line given its slope and a point
on the line, two points, or its slope and y-intercept.
Use slope to determine whether two lines are parallel,
perpendicular, or neither.
Solve systems of linear equations in two variables, and
use systems to solve word problems.
Find values of functions and graph functions.
Graph linear inequalities in two variables and graph
systems of linear inequalities.
Find equations for linear functions and apply properties
of linear functions to solve problems.
Simplify, add, subtract, multiply, and divide
polynomials.
Factor polynomials using GCF, difference of two
squares, sum/difference of two cubes, perfect square
trinomials, and/or grouping.
Solve polynomial equations, inequalities, or word
problems and inequalities by factoring.
Solve word problems that include polynomial functions.
Simplify complex fractions and products or quotients of
binomials that contain radicals.
Solve equations that contain radicals.
Use the imaginary number i to simplify square roots of
negative numbers.
Perform combinations of complex numbers including
addition, subtraction, multiplication, and division
Solve quadratic equations by factoring, completing the
square, and the quadratic formulas.
Graph parabolas from vertex form, describing its vertex,
minimum or maximum value, and axis of symmetry.
Solve problems using direct, inverse, or joint variation.
Divide one polynomial by another polynomial use long
or synthetic division.
Use the remainder and factor theorems to find factors of
polynomials and solve polynomial equations.
Use theorems regarding roots of polynomial equations
to find or solve polynomial equations.
Find rational roots of polynomial equations with integer
coefficients.
Determine the equation of a circle, ellipse, hyperbola,
parabola, and sketch its graph.
Find the distance or midpoint between two points.
Define logarithmic functions and learn how they are
related to exponential functions.
Use common and natural logarithms to solve equations
involving powers and evaluate logarithms of any base.
Use exponential and logarithmic functions to solve
growth and decay problems.
Find the sums and differences of matrices products of a
scalar and a matrix or the product of two matrices.
Find the determinant and inverse of a matrix by hand or
calculator.
Use matrices to display and interpret data, as well as
solve systems of equations.
Use degrees to measure angles.
Define trigonometric functions of angles.
Use trigonometric functions to find sides and angles of
right triangles.
Solve problems using the Fundamental Counting
Principle, combinations, or permutations.
Find the probability of two or more independent or
dependent events.
Find the probability of mutually exclusive or inclusive
events.
Find joint probability or conditional probability.
Make displays for univariate data.
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Salem Academy Math Skills Checklist
Pre-Calculus Honors Topics:
Identify a function analytically and graphically.
Determine the domain, range, and zeros of a function,
and use the information to graph the function.
Perform combination and composition operations on
functions and determine the domains of the resultant
function
Translate graphs by reflecting, stretching/shrinking, or
shifting both vertically and horizontally.
Use a graphing calculator to find the maximum or
minimum value(s) of the function.
Analyze a function for boundedness, continuity,
asymptotes, and end behavior.
Identify and apply common or natural logarithms.
Understand and apply laws and properties of logarithms.
Solve exponential equations using properties and laws
of logarithms.
Apply translations, dilations, and shifts to exponential
and logarithmic functions.
Use growth/decay and compound interest models to
interpret exponential functions.
Use exponential/logarithmic functions to model and
solve problems including a justification of results.
Determine angle measure in either degrees or radians
and find co-terminal angles.
Determine the arc length and area of a sector of a circle.
Use the definitions of sine, cosine, tangent, secant,
cosecant, and cotangent to find values and solve simple
trigonometric equations.
Sketch the graphs of sine, cosine, tangent, secant,
cosecant, and cotangent functions.
Find values of the inverse trigonometric functions.
Find general and particular solutions to trigonometric
equations
Find equations of sine and cosine curves and use these
equations to model periodic behavior such as harmonic
motion.
Simplify trigonometric expressions and verify
trigonometric identities.
Find the area of a triangle given the lengths of two sides
and the measure of the included angle.
Use the Law of Sines and/or Law of Cosines to find
unknown parts of a triangle.
Use trigonometry to solve application problems such as
surveying or navigation.
Apply addition and subtraction formulas for sine,
cosine, and tangent.
Apply double-angle and half-angle formulas for sine,
cosine, and tangent.
Find the limit of a function via a graph or equation.
Determine whether a function is continuous.
Sketch the graph of a rational function using the
intercepts and asymptotes (horizontal, vertical or slant).
Find derivatives of functions using geometric concepts
and the difference quotient.
Find the integral of functions using geometric properties
Identify an arithmetic or geometric sequence and find a
formula for the nth term.
Understand recursive sequences.
Determine the sum of the first n terms of arithmetic or
geometric series.
Determine the limit or sum of an infinite sequence when
it exists.
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