Objective 001
N-Q.1
Algebra I
Algebra 1 Practice Problems
Expressions, equations, inequalities, functions, linear and exponential models, quadratics, and data.
76 objectives
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