Download Ch. 7 Systems of Linear Equations

Cumulative Tests/Exam Review
You are responsible for everything that has been studied! The following is meant to assist you.
Ch. 1 Measurement
Vocabulary: imperial units, unit analysis, SI system of measures, apex, right pyramid, right cone, slant
height, lateral area, sphere.
1.1 Imperial Measures of Length
- Developing relationships between Imperial units
- Converting between Imperial Units
1.2 Math Lab: Measuring Length and Distance
1.3 Relating SI and Imperial Units
- Developing relationships between Imperial and SI units
- Converting between Imperial and SI Units
1.4 Surface Area of Right Pyramids and Right Cones
- Determining surface areas
- Using surface area formulas to determine other unknown measurements (e.g. height, slant
height)
1.5 Volumes of Right Pyramids and Right Cones
- Determining volumes
- Using volume formulas to determine other unknown measurements (e.g. height, radius)
1.6 Surface Area and Volume of a Sphere
- Determining surface area and volumes of spheres and hemispheres
- Using surface area and volume formulas to determine the radius
1.7 Solving Problems Involving Objects
- Determining surface area and volumes of composites
Ch. 2 Trigonometry
New Vocabulary: angle of inclination, tangent ratio, indirect measurement, sine ratio, cosine ratio, angle
of elevation, angle of depression.
2.1 The Tangent Ratio
- Use the tangent ratio to find angles
2.2 Using the Tangent Ratio to calculate lengths
2.3 Measuring an Inaccessible Height
- Using a clinometer to help find angles to be used to find heights (e.g. of trees or buildings)
2.4 The Sine and Cosine Ratios
- Use the sine and cosine ratios to find angles
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
2.6 Applying the Trigonometric Ratios
- Using the trigonometric ratios to solve problems
2.7 Solving Problems Involving More than One Right Triangle
- Using all the tools of this chapter and the Pythagorean Theorem to solve problems, including
problems involving triangles in two different planes (e.g., fire tower problem)
Ch. 3 Factors and Products
New Vocabulary: prime factorization, greatest common factor, least common multiple, perfect cube,
cube root, radicand, radical, index, factoring by decomposition, perfect square trinomial,
difference of squares
3.1 Factors and Multiples of Whole Numbers
- Used methods such as prime factorization to find prime factors, GCFs, and LCMs.
- Solving problems involving GCFs and LCMs
3.2 Perfect Squares, Perfect Cubes, and Their Roots
- Finding perfect squares and perfect cubes using prime factorization
- Using prime factorization to show values aren’t perfect squares or perfect cubes
3.3 Common Factors of a Polynomial
- Common factoring with algebra tiles (making a rectangle or making groups) and without
algebra tiles
3.5 Polynomials of the Form x2  bx  c
- Multiplying binomials to equal x 2  bx  c with and without algebra tiles and rectangle
diagrams
- Factoring x2  bx  c with binomial factors, with and without tiles
- Factoring x2  bx  c with a common factor and binomial factors, with and without tiles
3.6 Polynomials of the form ax2  bx  c
- Multiplying binomials to equal ax2  bx  c with and without algebra tiles and rectangle
diagrams
- Factoring ax2  bx  c with binomial factors, with and without tiles
- Factoring ax2  bx  c with a common factor and binomial factors, with and without tiles
- Factoring using decomposition
3.7 Multiplying Polynomials
- Multiplying different combinations of polynomials (e.g., binomial×trinomial,
trinomial×trinomial, binomial×binomial×binomial)
- Simplifying sums and differences of polynomial products
3.8 Factoring Special Polynomials
- Difference of Squares
- Perfect Square Trinomials
- Polynomials with more than one variable
Ch. 4 Roots and Powers
New Vocabulary: irrational number, real number, entire radical, mixed radical
4.1 Estimating Roots
- Estimating a root and displaying its approximate location on a number line
4.2 Irrational Numbers
- Determining if numbers are irrational or rational
- Understanding the relationship between number sets (natural, whole, rational, irrational, real)
- Order a set of irrational numbers from greatest to least (or least to greatest)
4.3 Mixed and Entire Radicals
- Write an entire radical as a mixed radical
- Write a mixed radical as an entire radical
4.4 Fractional Exponents and Radicals
- Understanding how fractional exponents are related to radicals
4.5 Negative Exponents and Reciprocals
- Understanding how negative exponents are related to reciprocals
4.6 Applying the Exponent Laws
- Use all the exponent laws together to simplify expressions involving exponents
Preparation Hints

Review quizzes and tests (and redo questions)

Review previous homework assignments (and redo questions)

Read the introductions, summaries and study features in each section of your textbook

Read the examples and try the “Check your Understanding” questions from each section of your
textbook

Read the checkpoints / review pages / study guides in each chapter of your textbook

Do the review and practice test for each chapter of your textbook, and the cumulative review
sections

Use the table of contents to refresh your memory on the topics
Cumulative Tests/Exam Review
You are responsible for everything that has been studied! The following is meant to assist you.
Please also refer to the Ch. 1-4 Review. Financial Math is not included on the outline since it was just
completed, but you are responsible for that unit.
Ch. 5 Relations and Functions
New Vocabulary: relation, arrow diagram, function, domain, range, function notation, discrete,
continuous, rate of change, linear function, vertical intercept, horizontal intercept
5.1 Representing Relations
- Represent a relation using a rule, a table, a set of ordered pairs, an arrow diagram, and a graph
5.2 Properties of Functions
- Determine the domain and range of a relation and function
- Determine if a relation is a function or not by examining a table, a set of ordered pairs, an
arrow diagram, and a graph
- Determine, from a context, which variable is independent and which variable is dependent
- Use function notation, f  x  , to solve for dependent and independent variables
5.3 Interpreting and Sketching Graphs
- Determine a possible situation for a given graph
- Sketch a possible graph for a given situation
- Reading and interpreting graphs
5.4 Graphing Data
- Properly representing dependent ( y -axis) and independent ( x -axis) variables, and discrete
(not connected) and continuous (connected) data on a graph
5.5 Graphs of Relations and Functions
- Determine the domain and range of a graph and represent it in words, set notation*, and
interval notation* [*you must use your notes for these as they are not covered in your book]
5.6 Properties of Linear Relations
- Determine if tables, equations, ordered pairs, situations are linear
- Determine and interpret rates of change
5.7 Interpreting Graphs of Linear Functions
- Determine the x and y intercepts of the graph of a linear relation, state the intercepts as values
or ordered pairs, and interpret them
- Identify the graph that corresponds to a given rate of change/slope and y -intercept
- Sketch the graph of a linear function expressed in function notation
- Solve problems in context involving linear functions
NS Curriculum Companion/Length and Midpoint Supplements
The NS Curriculum Framework includes material that is not included in the WNCP Curriculum Framework,
and is therefore not in the textbook. Separate handouts were provided at the end of chapters 5 and 6 to
address this extra material.
New Vocabulary: distance formula, midpoint, midpoint formula
The Length of a Line Segment
- Use the Pythagorean Theorem to find the length of a line segment on a grid
- Use the distance formula to find the distance between two points
The Midpoint of a Line Segment
- Use the midpoint formula to find the midpoint of a line segment given the endpoints of the
segment
- Determine the endpoint of a line segment, given the other endpoint and the midpoint
Ch. 6 Linear Functions
New Vocabulary: slope, rise, run, negative reciprocals, slope-intercept form, slope-point form,
general form, equivalent equations
6.1 Slope of a Line
- Determine the slope of line by counting or calculating rise and run
-m=
y  y1
rise
changein y
,m=
,m= 2
run
changein x
x2  x1
- positive slope, negative slope, slope = 0, undefined slope
- interpreting slope in context
6.2 Slopes of Parallel and Perpendicular Lines
- Identifying parallel and perpendicular lines using slope (parallel: equal slopes, perpendicular:
negative reciprocal slopes)
6.4 Slope-Intercept Form of the Equation for a Linear Function: y = mx + b
- Determining and writing linear equations in slope intercept form
- Graphing linear equations from slope intercept form
- Solving problems in context using linear equations in slope intercept form
6.5 Slope-Point Form of the Equation for a Linear Function: y – y1 = m(x – x1)
- Determining and writing linear equations in slope-point form
- Graphing linear equations from slope-point form
- Solving problems in context using linear equations in slope-point form
6.6 General Form of the Equation for a Linear Relation: Ax + By + C = 0
- Determining and writing linear equations in general form
- Graphing linear equations from general form
- Solving problems in context using linear equations in slope-point form
- Rearranging and writing linear equations in different forms (e.g. slope intercept
general)
- Equivalent equations
NS Curriculum Companion/Ch. 6 Supplement – Scatterplots,
Lines of Best Fit and Equations of Lines of Best Fit
The NS Curriculum Framework includes material that is not included in the WNCP Curriculum Framework,
and is therefore not in the textbook. Separate handouts were provided at the end of chapters 5 and 6 to
address this extra material.
New Vocabulary: scatterplot, line of best fit, equation of the line of best fit, correlation, correlation
coefficient
Scatterplots and Lines of Best Fit
- Create a scatterplot for a set of data
- Describe trends in the data
- Create a line of best fit for a scatterplot
- Use a line of best fit to make predictions
Equation of the Line of Best Fit
- Use technology to create a scatterplot and the line of best fit for a set of data
- Use technology to determine the correlation coefficient ( r ) for a line of best fit and describe
how well the line fits the data
- Make predictions from lines of best fit using technology
Ch. 7 Systems of Linear Equations
New Vocabulary: system of linear equations, linear system, solving by substitution, equivalent systems,
solving by elimination, infinite, coincident lines
7.1 Developing Systems of Linear Equations
- Write two linear equations to model a situation and state what the variables represent
- Relate a linear system to the context of a problem
- Verify the solution of a linear system
- Write a situation that might be modelled by a given linear system
7.2 Solving a System of Linear Equations Graphically
- Determine the solution of a system of linear equations graphically, without technology
- Explain the meaning of the point of intersection of a system of linear equations
7.3 Math Lab: Using Graphing Technology to Solve a System of Linear Equations
- Determine the solution of a system of linear equations graphically, using technology
7.4 Using a Substitution Strategy to Solve a System of Linear Equations
- Use substitution to solve a system of linear equations algebraically
7.5 Using an Elimination Strategy to Solve a System of Linear Equations
- Use elimination to solve a system of linear equations algebraically
7.6 Properties of Systems of Linear Equations
- Determine the number of solutions of linear system graphically and algebraically.
- Explain why a linear system might have no solution, one solution, or infinite solutions.
- Write a second equation to create linear systems with different numbers of solutions, given
the first equation.
Preparation Hints

Review quizzes and tests (and redo questions)

Review previous homework assignments (and redo questions)

Read the introductions, summaries and study features in each section of your textbook

Read the examples and try the “Check your Understanding” questions from each section of your
textbook

Read the checkpoints / review pages / study guides in each chapter of your textbook

Do the review and practice test for each chapter of your textbook, and the cumulative review
sections

Use the table of contents to refresh your memory on the topics