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Here is a list of all of the skills students learn in Algebra 1!

Numbers

  • A.1Compare and order rational numbers
  • A.2Absolute value and opposites
  • A.3Number lines
  • A.4Convert between decimals and fractions
  • A.5Convert between repeating decimals and fractions
  • A.6Square roots
  • A.7Cube roots
  • A.8Classify numbers

Operations

  • B.1Add, subtract, multiply, and divide integers
  • B.2Evaluate numerical expressions involving integers
  • B.3Evaluate variable expressions involving integers
  • B.4Add and subtract rational numbers
  • B.5Multiply and divide rational numbers
  • B.6Evaluate numerical expressions involving rational numbers
  • B.7Evaluate variable expressions involving rational numbers

Ratios, rates, and proportions

  • C.1Identify equivalent ratios
  • C.2Write an equivalent ratio
  • C.3Unit rates
  • C.4Unit prices
  • C.5Solve proportions
  • C.6Solve proportions: word problems
  • C.7Scale drawings: word problems

Percents

  • D.1Convert between percents, fractions, and decimals
  • D.2Solve percent equations
  • D.3Percent word problems
  • D.4Percent of change
  • D.5Percent of change: word problems
  • D.6Percent of a number: tax, discount, and more
  • D.7Find the percent: tax, discount, and more
  • D.8Multi-step problems with percents

Measurement

  • E.1Convert rates and measurements: customary units
  • E.2Convert rates and measurements: metric units
  • E.3Unit prices with unit conversions
  • E.4Precision
  • E.5Greatest possible error
  • E.6Minimum and maximum area and volume
  • E.7Percent error
  • E.8Percent error: area and volume

Geometry

  • F.1Perimeter
  • F.2Area
  • F.3Area and perimeter: word problems
  • F.4Volume
  • F.5Surface area
  • F.6Similar figures: side lengths and angle measures
  • F.7Similar triangles and indirect measurement
  • F.8Dilations and scale factors
  • F.9Area and perimeter of similar figures
  • F.10Area between two shapes
  • F.11Similar solids
  • F.12Volume and surface area of similar solids
  • F.13Perimeter, area, and volume: changes in scale
  • F.14Pythagorean theorem
  • F.15Pythagorean theorem: word problems
  • F.16Converse of the Pythagorean theorem: is it a right triangle?
  • F.17Special right triangles

Coordinate plane

  • G.1Coordinate plane review
  • G.2Midpoints
  • G.3Distance between two points

Properties

  • H.1Properties of addition and multiplication
  • H.2Distributive property
  • H.3Simplify variable expressions using properties
  • H.4Properties of equality

Variable expressions and equations

  • I.1Write variable expressions
  • I.2Simplify variable expressions involving like terms and the distributive property
  • I.3Identify equivalent linear expressions
  • I.4Write variable equations
  • I.5Does x satisfy the equation?
  • I.6Which x satisfies an equation?
  • I.7Solve equations using order of operations
  • I.8Rearrange multi-variable equations

Solve equations

  • J.1Model and solve equations using algebra tiles
  • J.2Write and solve equations that represent diagrams
  • J.3Solve one-step linear equations
  • J.4Solve two-step linear equations
  • J.5Solve advanced linear equations
  • J.6Solve equations with variables on both sides
  • J.7Solve equations: complete the solution
  • J.8Find the number of solutions
  • J.9Create equations with no solutions or infinitely many solutions
  • J.10Solve linear equations: word problems
  • J.11Solve linear equations: mixed review

Single-variable inequalities

  • K.1Graph inequalities
  • K.2Write inequalities from graphs
  • K.3Identify solutions to inequalities
  • K.4Solve one-step linear inequalities: addition and subtraction
  • K.5Solve one-step linear inequalities: multiplication and division
  • K.6Solve one-step linear inequalities
  • K.7Graph solutions to one-step linear inequalities
  • K.8Solve two-step linear inequalities
  • K.9Graph solutions to two-step linear inequalities
  • K.10Solve advanced linear inequalities
  • K.11Graph solutions to advanced linear inequalities
  • K.12Graph compound inequalities
  • K.13Write compound inequalities from graphs
  • K.14Solve compound inequalities
  • K.15Graph solutions to compound inequalities

Absolute value equations and inequalities

  • L.1Solve absolute value equations
  • L.2Graph solutions to absolute value equations
  • L.3Solve absolute value inequalities
  • L.4Graph solutions to absolute value inequalities

Matrices

  • M.1Matrix vocabulary
  • M.2Matrix operation rules
  • M.3Add and subtract matrices
  • M.4Multiply a matrix by a scalar
  • M.5Add and subtract scalar multiples of matrices
  • M.6Multiply two matrices

Data and graphs

  • N.1Interpret bar graphs, line graphs, and histograms
  • N.2Create bar graphs, line graphs, and histograms
  • N.3Circle graphs
  • N.4Interpret stem-and-leaf plots
  • N.5Interpret box-and-whisker plots
  • Problem solving
  • O.1Word problems: mixed review
  • O.2Word problems with money
  • O.3Consecutive integer problems
  • O.4Rate of travel: word problems
  • O.5Weighted averages: word problems

Number sequences

  • P.1Identify arithmetic and geometric sequences
  • P.2Arithmetic sequences
  • P.3Geometric sequences
  • P.4Evaluate variable expressions for number sequences
  • P.5Write variable expressions for arithmetic sequences
  • P.6Write variable expressions for geometric sequences
  • P.7Number sequences: mixed review

Relations and functions

  • Q.1Relations: convert between tables, graphs, mappings, and lists of points
  • Q.2Domain and range of relations
  • Q.3Identify independent and dependent variables
  • Q.4Identify functions
  • Q.5Identify functions: vertical line test
  • Q.6Find values using function graphs
  • Q.7Evaluate a function
  • Q.8Evaluate a function: plug in an expression
  • Q.9Complete a function table from a graph
  • Q.10Complete a function table from an equation
  • Q.11Interpret the graph of a function: word problems

Direct and inverse variation

  • R.1Identify proportional relationships
  • R.2Find the constant of variation
  • R.3Graph a proportional relationship
  • R.4Write direct variation equations
  • R.5Write and solve direct variation equations
  • R.6Identify direct variation and inverse variation
  • R.7Write inverse variation equations
  • R.8Write and solve inverse variation equations

Linear functions

  • S.1Identify linear functions
  • S.2Find the slope of a graph
  • S.3Find the slope from two points
  • S.4Find a missing coordinate using slope
  • S.5Slope-intercept form: find the slope and y-intercept
  • S.6Slope-intercept form: graph an equation
  • S.7Slope-intercept form: write an equation from a graph
  • S.8Slope-intercept form: write an equation
  • S.9Slope-intercept form: write an equation from a table
  • S.10Slope-intercept form: write an equation from a word problem
  • S.11Linear equations: solve for y
  • S.12Write linear functions to solve word problems
  • S.13Complete a table and graph a linear function
  • S.14Compare linear functions: graphs, tables, and equations
  • S.15Write equations in standard form
  • S.16Standard form: find x- and y-intercepts
  • S.17Standard form: graph an equation
  • S.18Equations of horizontal and vertical lines
  • S.19Graph a horizontal or vertical line
  • S.20Point-slope form: graph an equation
  • S.21Point-slope form: write an equation
  • S.22Point-slope form: write an equation from a graph
  • S.23Slopes of parallel and perpendicular lines
  • S.24Write an equation for a parallel or perpendicular line
  • S.25Transformations of linear functions

Linear inequalities

  • T.1Does (x, y) satisfy the inequality?
  • T.2Linear inequalities: solve for y
  • T.3Graph a two-variable linear inequality
  • T.4Linear inequalities: word problems
  • T.5Is (x, y) a solution to the system of inequalities?
  • T.6Solve systems of linear inequalities by graphing

Systems of linear equations

  • U.1Is (x, y) a solution to the system of equations?
  • U.2Solve a system of equations by graphing
  • U.3Solve a system of equations by graphing: word problems
  • U.4Find the number of solutions to a system of equations by graphing
  • U.5Find the number of solutions to a system of equations
  • U.6Classify a system of equations by graphing
  • U.7Classify a system of equations
  • U.8Solve a system of equations using substitution
  • U.9Solve a system of equations using substitution: word problems
  • U.10Solve a system of equations using elimination
  • U.11Solve a system of equations using elimination: word problems
  • U.12Solve a system of equations using augmented matrices
  • U.13Solve a system of equations using augmented matrices: word problems
  • U.14Solve a system of equations using any method
  • U.15Solve a system of equations using any method: word problems

Exponents

  • V.1Exponents with integer bases
  • V.2Exponents with decimal and fractional bases
  • V.3Negative exponents
  • V.4Multiplication with exponents
  • V.5Division with exponents
  • V.6Multiplication and division with exponents
  • V.7Power rule
  • V.8Evaluate expressions using properties of exponents
  • V.9Identify equivalent expressions involving exponents
  • V.10Evaluate integers raised to rational exponents
  • Scientific notation
  • W.1Convert between standard and scientific notation
  • W.2Compare numbers written in scientific notation
  • W.3Multiply numbers written in scientific notation
  • W.4Divide numbers written in scientific notation
  • Exponential functions
  • X.1Evaluate an exponential function
  • X.2Match exponential functions and graphs
  • X.3Domain and range of exponential functions: graphs
  • X.4Domain and range of exponential functions: equations
  • X.5Exponential growth and decay: word problems

Monomials

  • Y.1Identify monomials
  • Y.2Multiply monomials
  • Y.3Divide monomials
  • Y.4Multiply and divide monomials
  • Y.5Powers of monomials

Polynomials

  • Z.1Polynomial vocabulary
  • Z.2Model polynomials with algebra tiles
  • Z.3Add and subtract polynomials using algebra tiles
  • Z.4Add and subtract polynomials
  • Z.5Add polynomials to find perimeter
  • Z.6Multiply a polynomial by a monomial
  • Z.7Multiply two polynomials using algebra tiles
  • Z.8Multiply two binomials
  • Z.9Multiply two binomials: special cases
  • Z.10Multiply polynomials

Factoring

  • AA.1GCF of monomials
  • AA.2Factor out a monomial
  • AA.3Factor quadratics using algebra tiles
  • AA.4Factor quadratics with leading coefficient 1
  • AA.5Factor quadratics with other leading coefficients
  • AA.6Factor quadratics: special cases
  • AA.7Factor by grouping
  • AA.8Factor polynomials

Quadratic equations

  • BB.1Characteristics of quadratic functions
  • BB.2Complete a function table: quadratic functions
  • BB.3Transformations of quadratic functions
  • BB.4Graph quadratic functions in vertex form
  • BB.5Solve a quadratic equation using square roots
  • BB.6Solve a quadratic equation using the zero product property
  • BB.7Solve a quadratic equation by factoring
  • BB.8Complete the square
  • BB.9Solve a quadratic equation by completing the square
  • BB.10Solve a quadratic equation using the quadratic formula
  • BB.11Using the discriminant
  • BB.12Match quadratic functions and graphs
  • BB.13Systems of linear and quadratic equations

Functions: linear, quadratic, exponential

  • CC.1Identify linear, quadratic, and exponential functions from graphs
  • CC.2Identify linear, quadratic, and exponential functions from tables
  • CC.3Write linear, quadratic, and exponential functions
  • CC.4Linear functions over unit intervals
  • CC.5Exponential functions over unit intervals
  • CC.6Describe linear and exponential growth and decay

Absolute value functions

  • DD.1Complete a function table: absolute value functions
  • DD.2Graph an absolute value function
  • DD.3Domain and range of absolute value functions: graphs
  • DD.4Domain and range of absolute value functions: equations
  • DD.5Transformations of absolute value functions

Radical expressions

  • EE.1Simplify radical expressions
  • EE.2Simplify radical expressions involving fractions
  • EE.3Multiply radical expressions
  • EE.4Add and subtract radical expressions
  • EE.5Simplify radical expressions using the distributive property
  • EE.6Divide radical expressions
  • EE.7Simplify radical expressions: mixed review

Radical functions and equations

  • FF.1Evaluate a radical function
  • FF.2Domain and range of radical functions: graphs
  • FF.3Domain and range of radical functions: equations
  • FF.4Solve radical equations I
  • FF.5Solve radical equations II

Rational functions and expressions

  • GG.1Rational functions: asymptotes and excluded values
  • GG.2Simplify complex fractions
  • GG.3Simplify rational expressions
  • GG.4Multiply and divide rational expressions
  • GG.5Divide polynomials
  • GG.6Add and subtract rational expressions
  • GG.7Solve rational equations
  • GG.8Evaluate rational expressions

Trigonometry

  • HH.1Trigonometric ratios: sin, cos, and tan
  • HH.2Find trigonometric ratios using a calculator
  • HH.3Inverses of trigonometric functions
  • HH.4Trigonometric ratios: find a side length
  • HH.5Trigonometric ratios: find an angle measure
  • HH.6Solve a right triangle

Logic

  • II.1Identify hypotheses and conclusions
  • II.2Counterexamples

Probability

  • JJ.1Theoretical probability
  • JJ.2Experimental probability
  • JJ.3Compound events: find the number of outcomes
  • JJ.4Identify independent and dependent events
  • JJ.5Probability of independent and dependent events
  • JJ.6Permutations
  • JJ.7Counting principle
  • JJ.8Permutation and combination notation

Statistics

  • KK.1Identify biased samples
  • KK.2Mean, median, mode, and range
  • KK.3Quartiles
  • KK.4Identify an outlier
  • KK.5Identify an outlier and describe the effect of removing it
  • KK.6Mean absolute deviation
  • KK.7Variance and standard deviation
  • KK.8Interpret a scatter plot
  • KK.9Outliers in scatter plots
  • KK.10Match correlation coefficients to scatter plots
  • KK.11Calculate correlation coefficients
  • KK.12Scatter plots: line of best fit
  • KK.13Find the equation of a regression line
  • KK.14Interpret regression lines
  • KK.15Analyze a regression line of a data

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