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Algebra I

Algebra 1 Practice Problems

Expressions, equations, inequalities, functions, linear and exponential models, quadratics, and data.

76 objectives
Objective 001 N-Q.1

Use units to guide multi-step problem solving and choose/interpret units, scales, and graph origins.

Objective 002 N-Q.2

Define appropriate quantities for descriptive modeling.

Objective 003 N-Q.3

Report quantities with accuracy appropriate to measurement limitations.

Objective 004 N-RN.1

Explain rational exponents as extensions of integer exponent rules and as radical notation.

Objective 005 N-RN.2

Rewrite expressions with radicals and rational exponents using exponent properties.

Objective 006 N-RN.3

Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.

Objective 007 A-SSE.1.a

Interpret terms, factors, and coefficients in linear and exponential expressions.

Objective 008 A-SSE.1.b

Interpret complex expressions by treating meaningful sub-expressions as single units.

Objective 009 A-SSE.1.a

Interpret terms, factors, and coefficients in quadratic and exponential expressions.

Objective 010 A-SSE.1.b

Interpret quadratic/exponential expressions by treating sub-expressions as meaningful units.

Objective 011 A-SSE.2

Use expression structure to identify useful rewrites, such as difference-of-squares factoring.

Objective 012 A-SSE.3.a

Factor quadratics to reveal zeros of the function they define.

Objective 013 A-SSE.3.b

Complete the square to reveal maximum or minimum values of quadratic functions.

Objective 014 A-SSE.3.c

Use exponent properties to transform exponential expressions and interpret growth/decay rates.

Objective 015 A-APR.1

Add, subtract, and multiply polynomials; understand polynomial closure under these operations.

Objective 016 A-CED.A.1

Create and solve a one-variable linear equation from a short context.

Objective 017 A-CED.2

Create equations in two or more variables, graph them, and label axes/scales appropriately.

Objective 018 A-CED.3

Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.

Objective 019 A-CED.4

Rearrange formulas to isolate a chosen quantity and interpret the result.

Objective 020 A-CED.1

Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.

Objective 021 A-CED.2

Create equations in two or more variables and graph them with appropriate labels and scales.

Objective 022 A-CED.4

Rearrange formulas to isolate a chosen quantity, including formulas with quadratic terms.

Objective 023 A-REI.1

Explain equation-solving steps as logical consequences of equality and justify solution methods.

Objective 024 A-REI.10

Understand that a two-variable equation's graph is the set of all ordered-pair solutions.

Objective 025 A-REI.11

Solve equations of the form f(x)=g(x) approximately by finding graph/table intersections.

Objective 026 A-REI.12

Graph linear inequalities and systems of linear inequalities as half-plane solution regions.

Objective 027 A-REI.3

Solve linear equations and inequalities in one variable, including literal linear equations.

Objective 028 A-REI.3.1

Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.

Objective 029 A-REI.5

Justify elimination: replacing one equation in a two-variable system with a linear combination preserves solutions.

Objective 030 A-REI.6

Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.

Objective 031 A-REI.4.a

Complete the square to transform quadratics and derive the quadratic formula.

Objective 032 A-REI.4.b

Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.

Objective 033 A-REI.7

Solve simple linear-quadratic systems algebraically and graphically.

Objective 034 F-IF.1

Understand functions as mappings from inputs to exactly one output; connect f(x) to graph y=f(x).

Objective 035 F-IF.2

Use function notation, evaluate functions on their domains, and interpret notation in context.

Objective 036 F-IF.3

Recognize sequences, including recursive sequences, as functions whose domains are subsets of integers.

Objective 037 F-IF.4

Interpret and sketch key graph/table features in context: intercepts, intervals, maxima/minima, symmetry, end behavior, and periodicity.

Objective 038 F-IF.5

Relate a function's domain to its graph and to the real-world quantities it describes.

Objective 039 F-IF.6

Calculate, estimate, and interpret average rate of change over an interval.

Objective 040 F-IF.7.a

Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.

Objective 041 F-IF.7.e

Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.

Objective 042 F-IF.9

Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.

Objective 043 F-IF.4

Interpret key graph/table features of quadratic models in context.

Objective 044 F-IF.5

Relate the domain of a quadratic function to its graph and situation.

Objective 045 F-IF.6

Calculate, estimate, and interpret average rate of change for quadratic functions.

Objective 046 F-IF.7.a

Graph linear and quadratic functions and identify intercepts, maxima, and minima.

Objective 047 F-IF.7.b

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.

Objective 048 F-IF.8.a

Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.

Objective 049 F-IF.8.b

Use exponent properties to interpret exponential expressions, including percent growth and decay.

Objective 050 F-IF.9

Compare function properties across representations, especially quadratic comparisons.

Objective 051 F-BF.1.a

Build a function from context by determining an explicit formula, recursive rule, or calculation process.

Objective 052 F-BF.1.b

Combine standard functions using arithmetic operations to build models.

Objective 053 F-BF.2

Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.

Objective 054 F-BF.3

Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.

Objective 055 F-BF.1.a

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Objective 056 F-BF.1.b

Combine standard function types arithmetically to create models.

Objective 057 F-BF.3

Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.

Objective 058 F-BF.4.a

Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.

Objective 059 F-LE.1.a

Distinguish linear from exponential situations by equal differences versus equal factors over equal intervals.

Objective 060 F-LE.1.b

Recognize constant rate of change as evidence for a linear model.

Objective 061 F-LE.1.c

Recognize constant percent growth or decay as evidence for an exponential model.

Objective 062 F-LE.2

Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.

Objective 063 F-LE.3

Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.

Objective 064 F-LE.5

Interpret parameters in linear and exponential functions in context.

Objective 065 F-LE.3

Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.

Objective 066 F-LE.6

Apply quadratic functions to physical situations such as projectile motion under gravity.

Objective 067 S-ID.1

Represent one-variable data with dot plots, histograms, and box plots.

Objective 068 S-ID.2

Compare data sets using center and spread measures appropriate to distribution shape.

Objective 069 S-ID.3

Interpret differences in shape, center, spread, and outliers in context.

Objective 070 S-ID.5

Summarize two-category data with two-way tables and interpret joint, marginal, and conditional relative frequencies.

Objective 071 S-ID.6.a

Use scatter plots to represent two quantitative variables and fit functions to model relationships.

Objective 072 S-ID.6.b

Assess model fit informally using residuals.

Objective 073 S-ID.6.c

Fit a linear function to data when a scatter plot suggests a linear association.

Objective 074 S-ID.7

Interpret slope and intercept of a linear model in the data context.

Objective 075 S-ID.8

Use technology to compute and interpret the correlation coefficient of a linear fit.

Objective 076 S-ID.9

Distinguish correlation from causation.