Scope and Sequence
Module Name |
Section Name |
Keywords |
Fractions |
Fractions and Mixed Numbers |
fractions, mixed numbers, equivalent fractions, multiply fractions, divide fractions, add fractiona, subtract fractions, numerator, denominator, improper fraction, complex fraction, cross product, equivalent fraction |
Equivalent Fractions |
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Multiply and Divide Fractions |
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Add and Subtract Fractions |
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Fractions Comparison |
Compare Fractions with the Same Denominator or Numerator |
compare fractions, same denominator or numerator, different denominator or numerator, convert fractions |
Compare Fractions with Different Numerators and Denominators |
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Convert to Equivalent Fractions |
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Ratios and Proportions |
Ratios |
ratios, ratio variations, proportions, conversion, units |
Ratio Variations |
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Proportions |
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Conversion of Units |
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Decimals |
Multiply and Divide by Powers of 10 |
multiply, divide, powers of 10, conversion, decimals, fractions, arithmetic, scientific notation, decimal points, divisor, dividend, quotient |
Convert Between Decimals and Fractions |
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Perform Arithmetic with Decimals |
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Scientific Notation |
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Percents |
What's a Percent? |
percent, conversion, decimals, fractions, equivalents, calculate interest, calculate discount, find percent |
Change from Decimals to Percents or Fractions |
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Identify Equivalents |
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Use Percent to Calculate Interest |
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Use Percent to Calculate Discount |
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Find Percent of a Given Quantity |
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Algebra and Signed Numbers |
Transitivity |
transitivity, add same number, subtract same number, multiply by same number, divide by same number, commutativity, signed numbers, algebraic sums, multiply signed numbers, divide signed numbers, associative properties, distributive properties, order of o |
Add or Subtract the Same Number in Equations |
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Multiply or Divide by the Same Number in Equations |
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Commutativity |
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Signed Numbers |
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Algebraic Sums of Signed Numbers |
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Multiply or Divide Signed Numbers |
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Associative and Distributive Properties |
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Order of Operations |
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Algebraic Expressions |
Add and Subtract Algebraic Expressions |
add algebraic expressions, subtract algebraic expressions, multiply algebraic expressions, divide algebraic expressions, substitution, coefficients, variables, fraction, numerator, denominator |
Add Expressions That Are Fractions |
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Multiply Algebraic Expressions |
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Divide Algebraic Expressions |
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Use Substitution to Solve Algebraic Expressions |
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Factors |
Find Common Factors |
common factors, factor differences, two squares, factor trinomials, binomials, factor expressions, perfect square, FOIL, firsts, outers, inners, lasts |
Factor Differences of Two Squares |
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Factor Trinomials into Binomials |
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Factor an Expression Completely |
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Equations |
Solve Equations by Substitution |
solve equations, substitution, linear equations, one unknown, quadratic equations, multiple unknowns, solutions to solve equations, use a formula, determinant |
Solve Linear Equations With One Unknown |
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Solve Quadratic Equations |
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Solve Equations With More Than One Unknown |
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Use a Solution of One Equation to Solve Another |
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General Quadratic Equations Using a Formula |
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Rate, Work, and Mixture Problems |
Distance Problems |
distance problems, work problems, alternative methods, mixture problems, rate, distance, time, volume |
Work Problems |
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Work Problems--An Alternative Method |
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Mixture Problems |
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Inequalities |
Add or Subtract Quantities to Inequalities |
add quantities to inequalities, subtract quantities from inequalities, multiply an inequality, divide an inequality, find products in inequalities, linear inequalities, one unknown, higher order inequalities, compare fractions, greater than, less than, eq |
Multiply or Divide an Inequality |
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Find the Product of Two Numbers or Expressions in Inequalities |
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Solve Linear Inequalities in One Unknown |
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Solve Higher Order Inequalities in One Unknown |
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Use Inequalities to Compare Fractions |
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Exponents and Roots |
Exponents |
exponents, roots, evaluate expressions, power zero, base number, square root, cube, cube root |
Roots |
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Evaluate Expressions Involving Exponents |
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Coordinate Geometry |
Number Lines |
number lines, definitions, distances, points, midpoint, line segment, plot graphs, y-intercept, x-intercept, slope, coordinate plane, x-axis, y-axis, ordered pair |
Definitions |
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Distance Between Two Points |
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Determine the Midpoint of a Line Segment |
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Plot the Graph of a Line |
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The Y-Intercept |
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The X-Intercept |
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Find the Slope |
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Plane Geometry |
Plane Geometry—Basic Concepts |
plane geometry, angles, complimentary angles, supplementary angles, vertical angles, parallel lines, point, line, line segment, plane |
Angles |
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Complimentary and Supplementary Angles |
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Vertical Angles |
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Parallel Lines |
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Triangles |
Triangle Basics |
triangles, perpendicular bisectors, equilateral triangles, altitude, area of triangles, perimeter of triangles, area of right triangles, perimeter of right triangles, area of equilateral triangles, perimeter of equilateral triangles, right triangles |
Perpendicular Bisectors |
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Equilateral Triangles |
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Altitude |
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Area and Perimeter of Triangles |
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Area and Perimeter of Right Triangles |
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Area and Perimeter of Equilateral Triangles |
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Figures with Four Sides or More |
Parallelograms |
parallelograms, rectangles, rhombus, squares, trapezoids, regular polygons, irregular polygons, other shapes, quadrilateral, right angle, vertex angle, |
Rectangles |
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Rhombus |
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Squares |
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Trapezoids |
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Regular and Irregular Polygons and Other Shapes |
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3-D Figures |
Rectangular Solids |
rectangular solids, cubes, cylinders, rectangular prism |
Cubes |
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Cylinders |
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Circles |
Tangents to a Circle |
tangents, circles, central angles, inscribed angles, tangents, area of a circle, circumference of a circle, radius, diameter, cord, line, ray, line segment, intercepted arc, vertex |
Central Angles |
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Inscribed Angles |
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Two Tangents to a Circle |
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Area and Circumference of a Circle |
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Statistics |
Averages |
averages, medians, modes, histograms, percentiles, quartiles, range, standard deviation, variance |
Medians |
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Modes |
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Histograms |
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Percentiles, Quartiles, and Range |
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Standard Deviation and Variance |
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Numbers and Integers |
Numbers |
numbers, sum of two integers, product of two integers, divisibility, absolute values |
Sum and Product of Two Integers |
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Divisibility |
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Absolute Values |
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Approximations |
Round Off |
rounding, approximate sums, approximate products, approximate square roots |
Approximate Sums |
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Approximate Products |
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Approximate Square Roots |
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Permutations, Combinations, and Probability |
Permutations and Combinations |
permutations, combinations, probability |
Probability |
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Graphs |
Tables and Charts |
tables, charts, graphs, bar graphs, circle graphs, line graphs, scale |
Graphs |
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Bar Graphs |
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Circle Graphs |
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Line Graphs |
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Logic |
Statements, Negations, and Compound Sentences |
statements, negations, compound sentences, language of logic, truth values, venn diagrams, conjunction, disjunction, conditional statement, biconditional statement, converse, inverse, contrapositive |
The Language of Logic |
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Truth Values |
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Venn Diagrams |
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Measurement |
Measurement Instruments and Techniques |
measurement instruments, measurement techniques, measurement problems, metric systems, formulas, area, volume |
Measurement Problems |
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Trigonometry |
Angles and Trigonometric Functions |
angles, trigonometric functions, trigonometric identities, trigonometric formulas, periodicity of trigonometric functions, sides,vertex, initial side, terminal side, acute, obtuse, reflex, right, straight, round, sine, cosine, tangent, cotangent, secant, |
Trigonometric Identities and Formulas |
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Periodicity of Trigonometric Functions |
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Data Presentation |
Graphs |
graphs, diagrams, tables |
Diagrams |
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Tables |
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Find a Reasonable Solution |
Determine the Reasonableness of a Solution |
reasonableness of solutions, evaluate predictions, evaluate conclusions, numerical information, graphical information |
Evaluate Predictions or Conclusions Based on Numerical or Graphical Information |
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Visualize Equations |
Graph Equations |
graph equations |
Loci |
Loci Basics |
loci, intersections of loci, locus problems, coordinate geometry |
Find Intersections of Loci |
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Solve Locus Problems in Coordinate Geometry |
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Special Graphs |
Box-and-Whisker and Stem-and-Leaf Plots |
box-and-whisker plots, stem-and-leaf plots, median, upper quartile, lower quartile, extreme values |
Transformation Geometry |
Translation and Reflection |
translation, reflection, dilation, rotation |
Dilation and Rotation |
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More 3-D Figures |
Prisms |
prisms, pyramids, cones, spheres, bases, sides, lateral faces, edge, vertex, surface area, net, radius, diameter |
Pyramids |
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Cones |
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Spheres |
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Chances Are: More Probability |
A Closer Look at Probablity |
probability, replacement, compound events, charts, tree diagrams |
Effect of Replacement |
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Compound Events |
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Number Patterns |
Recognize Famous Patterns |
famous patterns, pattern problems, Fibonacci, Mersenne, matrix |
Solve Pattern Problems |
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Getting Into Shape |
The Language of Geometry |
language of geometry, congruence, similarity, reflection, rotation, translation, dialation |
Congruence and Similarity |
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Systems of Linear Equations |
Solve Systems of Linear Equations Algebraically |
linear equations, algebraic solutions, graphic solutions, slope-intercept |
Solve Systems of Linear Equations Graphically |
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Systems of Nonlinear Equations |
Solve a Line-Parabola System Algebraically |
line-parabola systems, line-circle systems, algebraic solutions, graphic solutions |
Solve a Line-Parabola System Graphically |
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Solve a Line-Circle System Algebraically |
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Solve a Line-Circle System Graphically |
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Systems of Inequalities |
Solve Systems of Inequalities Algebraically |
inequalities, algebraic solutions, graphic solutions |
Solve Systems of Inequalities Graphically |
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Solve Word Problems Using Equations |
Set Up the Equation |
set up equations, use linear equations, use quadratic equations, variable, factoring, binomial |
Use Linear Equations |
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Use Quadratic Equations |
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Find Hidden Conditions |
Extract the Formula |
formula, givens, simultaneous |
Find the Given |
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Fractions in Equations |
Solve Equations Containing Fractional Coefficients |
fractional coefficients, fractional equations |
Solve Fractional Equations |
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Solve Graph Problems |
Study the Graph's Shape |
shapes of graphs, slope, x-intercept, y-intercept, real solutions, max, min |
Look at the Slope |
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Examine the X- and Y- Intercepts |
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Search for the Real Solutions |
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Determine Max or Min |
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Logarithms |
Bases and Powers |
bases, powers, base number, exponent |
Matrices |
Addition and Subtraction |
addition, subtraction, scalar multiplication, matrix |
Scalar Multiplication |
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Discrete Mathematics |
Concepts in Discrete Mathematics |
discrete mathematics, sets, induction, iteration, recurrence, mathematical models |
Sets |
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Induction, Iteration, and Recurrence |
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Make Mathematical Models |
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Functions |
Time for a Change |
change, form, function, rate of change, continuous, limit, distribution, deviation, linear |
A Matter of Proportion |
Change a Dimension |
change dimensions, change variables, two dimensional, three dimensional |
Change a Variable |
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Scatterplots |
Understand Scatterplot Data |
scatterplot data, ordered pairs, positive correlation, negative correlation, line of best fit |
Use and Misuse of Statistics |
Numbers Can Lie |
decisions based on data |
Make Decisions Based on Data |
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Get Rid of Pesky Numbers |
Cancel Out Numbers or Expressions |
cancel numbers, factor, add, subtract, multiply divide, common denominator, common numerator, reduce terms |
Math Speak |
Translate Words into Math |
translate word problems, mathematical notation |
Use the Known to Find the Unknown |
Use What You Know |
geometry, area, distance, angles, unknowns, knowns |
Pick a Number, Any Number |
Plug in a Number |
substitute whole numbers, variables, integers, average formula |
Keep Your Units Straight |
Set Up or Verify with Units |
work with same units, manipulate units to match, verify units, variables |
Simply Simplify |
Simplify to Avoid Tedious Calculations |
simplify expressions, avoid long calculations, easier ways, multiply, add, divide, subtract |
Become an Artist |
Add Labels and Draw on Diagrams |
draw lines in diagrams, label unknown quantities |
And Then There Was One |
Eliminate Choices |
eliminate answers |
Use the Best, Leave the Rest |
Recognize Relevant Information |
use known information, use relevant information |
Test-Taking Tips and Tricks |
Don't Panic |
don't panic, focus, time, take notes, process of elimination, deep breathing, visualization, counting, affirmation, box, circle, underline |
Use Your Time Wisely |
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Own Your Exam |
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Use the Process of Elimination |
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Know Yourself |
Are You a Tortoise or a Hare? |
pace, speed, use strengths, sort questions, classify questions, easy questions first, focus, relax, accuracy, |
Use Your Strengths |
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Know Your Test History |
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Master Math Questions |
Round Off and Guesstimate |
round, guesstimate, simplify numbers, simplify calculations, only necessary calculator use, make notes, show work, graphs, diagrams, check answers |
Use Your Calculator Sparingly |
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Show Your Work |
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Check Backwards |
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What’s Up, Doc? |
Define Your Variables |
define variables, rewrite questions, translate word problems |
Morph When Necessary |
Change to Equivalent Forms |
appropriate expressions, simplify expressions, equivalent forms |
It’s The Words that Count |
Check Your Answers, Not Your Equations |
check answers, use equations, translate word problems |
Be Fair |
Distribute All The Way Through |
distributive property, multiplication, addition, rewrite expressions, simplify expressions |
Get the Point |
Plot Clear Points |
graph, visual picture, draw neatly, draw clearly, small points, end points, line segments, range, solution, upper bounds, lower bounds, |
Check End Points |
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Look At It Another Way |
Interpret Different Views of an Object |
visualize problem, top view, side view, front view, perspective, 2-dimensional, 3-dimensional, length, height, keywords, sketch, missing blocks |
Break It Up |
Divide Weird Shapes into Familiar Shapes |
simple figure, complex figure, 3-dimensional, composite figure, area, volume |