Course Prerequisite Skills
Message from Kent Hansan (NYC ’05):
“This section has the prerequisite skills for each chapter spelled out. This is by no means a completely comprehensive list, but it does give basic skills with which students must be very comfortable before they will be able to master the new material in the chapter. The SSBAT (Students should be able to) are the unbolded items, and should be addressed before the chapters begin. The SMBAT (Students must be able to) skills are bolded, and should be addressed by the end of the chapter. The SMBATs are not as focused as some of the objectives, but they are more general and more manageable.”
Prerequisite Skills I.1
Vocabulary
Fewest, Most, Decrease, Increase, Plus, Times, Terminating Decimal, Repeating Decimal, Less than, More than, Fewer, More, Consecutive
Numeracy
Converting between decimals, fractions/mixed numbers, and percents
Identification and knowledge of prime vs. composite numbers
Prime Factorization
Basic operations with positive numbers
Using exponents on positive numbers
Plotting points on the coordinate plane
Perimeter and Area of a rectangle
Perimeter and Area of a triangle
Circumference and Area of a circle
Plot a point on the coordinate plane
Count on a number line starting with zero
Order rational and irrational numbers
Use the order of operations
Plug values into expressions
Find measures of central tendency
Prerequisite Skills I.2
Reduce fractions
Operations with fractions
Determine theoretical probability
Translate between graph, equation and table of a function
Write a function rule from words or a table
Prerequisite Skills I.3
Calculate percent
Operations with signed numbers
Recognize that subtraction of a positive and addition of a negative are equivalent
Use the Distribute Property
Solve simple one step equations
Solve two step equations
Know when it is necessary and be able to combine like terms
Prerequisite skills I.4
Translate between the graph and symbolic representation of inequalities
Use Venn Diagrams
Rewrite an equation for a given variable
Solve ratios using cross multiplication
Solve equations with variables on both sides
Solve linear inequalities
Prerequisite skills I.5
Plot a point on the coordinate plane
Manipulate equations to isolate a variable
Identify parallel and perpendicular lines
Find the slope of line
Identify slope and intercept of a line
Write the equation of a line from a graph
Write the equation of a line given two points
Find perpendicular and parallel lines
Prerequisite skills I.6
Add and subtract polynomials
Plug in values for a variable
Use distributive property
Write a system of equations from a word problem
Solve systems of linear equations graphically and algebraically
Graph systems of linear inequalities
Prerequisite skills I.7
Rewrite equations so one side equals zero
Plug values in for a given variable
Graphs of linear inequalities, significance of solid vs. dashed line
Identify the parts of a parabola, i.e. line of symmetry, vertex, roots
Describe changes to a parabola resulting from changes in the equation
Solve quadratic equations using the quadratic formula
Prerequisite skills I.8
Expand a number raised to a power
Rewrite a number multiplied by itself repeatedly as an exponent
Write numbers in scientific notation
Use the rules of exponents
Use positive, negative and zero exponents
Prerequisite skills I.9
Find the area and perimeter of various figures
Take the square root of a perfect square
Simplify radicals
Perform operations with radicals
Use the Pythagorean theorem to find missing sides of triangles
Use the distance formula to find the distance between two points
Use trigonometric ratios to find missing sides of triangles
Prerequisite skills I.10
Combine like terms
Multiply monomials
Perform operations with polynomials
Multiply polynomials
Factor polynomials
Use factoring to solve quadratic equations
Identify when one must combine like terms, expand, or factor polynomials
Prerequisite skills I.11
Factor trinomials
Add, subtract, multiply and divide fractions
Simplify rational expressions
Perform operations with rational expressions
Find permutations and combinations
Prerequisite skills II.1
Supplementary and Complementary angles
Types of angles
Parallel vs. Perpendicular lines
Find measures of angles from given information about lines and other angles
Use the distance formula
Use a protractor and compass to draw simple figures and measure
Prerequisite skills II.2
Solve problems involving ratios
Graph on the coordinate plane
Describe the number of degrees in a triangle and circle
Classify triangles
Classify quadrilaterals
Work with circles and proportions of circles
Find measures of interior and exterior angles of polygons
Prerequisite skills II.3
Describe basic transformations
Reflect, translate, rotate, and dilate a figure or point
Determine and identify all types of symmetry of a figure
Prerequisite skills II.4
Find the missing angle of a triangle
Identify different logical constructions
Use a Venn Diagram to solve problems
Draw loci of points for different situations
Prerequisite skills II.5
Explain perimeter and area of a figure
Write and use trigonometric ratios
Calculate the area of a quadrilateral, circle, triangle, simple polygon
Identify the special properties of 45/45/90 and 30/60/90 triangles
Use inverse trig functions to solve problems
Prerequisite skills II.6
Explain volume
Calculate the volume of prisms and cylinders
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