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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