Math I
Build connected understanding across quantities, equations, functions, coordinate geometry, congruence, and data.
- Problem types
- 659
- Practice variants
- 2,636
Page 1 of 19
Each problem type has four distinct practice variants. Open a preview to move among all four.
Write and solve a one-variable equation for equal groups
Create and solve a one-variable linear equation from a short context.
The unknown is one notebook’s cost, and the four identical costs combine to make the total. We’ll represent one cost with n, multiply by the number of notebooks, and set …
Preview problemFixed amount plus repeated amount equals total
Create and solve a one-variable linear equation from a short context.
This situation has two different kinds of cost: one fixed fee and one charge that repeats for every hour. We’ll write the repeating part as the hourly rate times h, …
Preview problemUse parentheses for repeated groups
Create and solve a one-variable linear equation from a short context.
The key is that each pack is a complete group containing both the regular and bonus pencils. We’ll put that whole per-pack amount in parentheses, multiply it by the number …
Preview problemWrite and solve a one-variable inequality from a limit
Create and solve a one-variable linear equation from a short context.
This is a limit problem, so the wording determines the inequality direction before any algebra begins. The total cost is the price per notebook times the whole-number count, and “at …
Preview problemWrite a compound inequality for values between two bounds
Create and solve a one-variable linear equation from a short context.
The temperature has to satisfy a lower bound and an upper bound at the same time. We’ll translate “at least” and “at most” as inclusive inequalities, combine them around the …
Preview problemSolve an absolute-value equation as distance from a target
Create and solve a one-variable linear equation from a short context.
Absolute value is useful here because it measures distance from a target. We’ll express the temperature’s distance from the target as an absolute-value equation, then split that equation into the …
Preview problemWrite and graph an absolute-value inequality from distance language
Create and solve a one-variable linear equation from a short context.
This is a tolerance problem: absolute value measures how far the part’s length is from its target. The word “within,” together with included boundary lengths, means the distance is no …
Preview problemWrite and solve a break-even equation with the variable on both sides
Create and solve a one-variable linear equation from a short context.
Each plan has a starting cost and a monthly cost, so we need one complete expression for each plan. Break-even occurs when those two totals are equal for the same …
Preview problemUse a percent multiplier to find an original or final amount
Create and solve a one-variable linear equation from a short context.
A discount tells us what fraction of the original price remains, not the fraction removed. We’ll subtract the discount rate from one to get the remaining multiplier, multiply the unknown …
Preview problemWrite an equation for an average or mixture
Create and solve a one-variable linear equation from a short context.
An average links two totals: the sum of all scores and the number of scores. We’ll include the unknown score in the complete sum, divide that grouped sum by the …
Preview problemChoose the correct equation branch before solving
Create and solve a one-variable linear equation from a short context.
This problem is decided in two stages: first determine which pricing condition the package satisfies, then use only that branch. We’ll compare the actual weight with the cutoff, keep the …
Preview problemTranslate a described layout into an equation
Create and solve a one-variable linear equation from a short context.
The diagram represents a perimeter, so every side of the rectangle contributes to one total. We’ll use the fact that twice the length plus twice the width equals the given …
Preview problemConvert units before solving a one-variable equation
Create and solve a one-variable linear equation from a short context.
Before the time amounts can be combined, they need to use the same unit. Using one hour equals sixty minutes, we’ll convert the hour portion to minutes, then write known …
Preview problemWrite a two-variable equation using a constant rate
Create equations in two or more variables, graph them, and label axes/scales appropriately.
This is a proportional relationship: every ticket contributes the same amount to the total, and there is no starting charge. We’ll treat the ticket count as the input and total …
Preview problemWrite a two-variable equation with a starting value and rate
Create equations in two or more variables, graph them, and label axes/scales appropriately.
The plant’s height is built from a starting amount plus steady growth over time. We’ll use weeks as the input, multiply by the growth per week, and then add the …
Preview problemWrite a linear equation from a table
Create equations in two or more variables, graph them, and label axes/scales appropriately.
A linear table is organized by its constant rate and its starting output. We’ll find the rate as the change in y divided by the change in x, then use …
Preview problemGraph a context equation
Create equations in two or more variables, graph them, and label axes/scales appropriately.
A useful graph plan has to connect the equation’s variables to the context and to the fixed windows on both axes. We’ll place the input ticket count horizontally and the …
Preview problemWrite a two-variable constraint for one total
Create equations in two or more variables, graph them, and label axes/scales appropriately.
The total comes from two separate ticket categories, so each category needs its own cost contribution. We’ll multiply each ticket price by its matching count, keep those unlike contributions separate, …
Preview problemSolve a two-variable equation for y before graphing
Create equations in two or more variables, graph them, and label axes/scales appropriately.
The goal is to make the equation graph-ready by isolating y without changing its solution set. We’ll remove the x-term from y’s side using the same operation on both sides, …
Preview problemInterpret an ordered pair in context
Create equations in two or more variables, graph them, and label axes/scales appropriately.
Interpreting the point depends on reading coordinate order through the graph’s axis labels and units. In an ordered pair, the input comes first and output comes second, so we’ll match …
Preview problemDefine variables and write a formula with units
Create equations in two or more variables, graph them, and label axes/scales appropriately.
This task is really about building a formula whose units make sense. We’ll define density, mass, and volume with their units, use the word per to decide that the relationship …
Preview problemWrite a two-variable linear equation from graph features
Create equations in two or more variables, graph them, and label axes/scales appropriately.
The graph gives the two features needed for a linear equation. We’ll read the vertical-axis crossing as the starting value, use the change in y divided by the change in …
Preview problemState reasonable domain and range restrictions from context
Create equations in two or more variables, graph them, and label axes/scales appropriately.
The algebraic rule alone allows many inputs, but the context narrows them to realistic notebook counts. We’ll combine the nonnegative whole-number requirement with the budget ceiling to find the allowable …
Preview problemWrite a single inequality constraint for a budget, capacity, or time limit
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
This is a resource-limit model. We’ll write the amount spent as the price per shirt times the number of shirts, then compare that expression with the budget. The phrase “at …
Preview problemWrite a system of inequalities for multiple constraints
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
There are two independent limits here, so one inequality cannot capture the whole situation. We’ll build a dollar expression by pairing each price with its item count, write a separate …
Preview problemTest whether a point is viable for a system of constraints
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
A point is viable for a system only if it passes every constraint, not just most of them. We’ll substitute the same two coordinates into each labeled inequality, evaluate every …
Preview problemGraph a feasible region from inequalities
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
The feasible region is the overlap of all three half-planes. We’ll first turn each inequality into its boundary and decide whether that boundary is included, then use the nonnegative conditions …
Preview problemList feasible whole-number solutions
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
The solution set is discrete because both variables must be nonnegative whole numbers. We’ll take each possible x-value in order, use the sum constraint to determine the allowed y-values for …
Preview problemInterpret a boundary point in context
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
A boundary point tells us both what the coordinates mean and which resource limit is met exactly. We’ll match each coordinate to its item type, multiply each count by its …
Preview problemChoose the best feasible option from candidate values
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Because the candidates are already feasible, the remaining task is to apply the stated objective correctly. We’ll preserve each point’s pairing with its profit value, compare the objective values rather …
Preview problemIdentify a missing context constraint
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
The given inequality controls total spending, but it does not automatically make every algebraic value realistic. We’ll identify what the existing constraint already handles, then use the fact that the …
Preview problemTranslate a graph region description into inequalities
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
The region is determined by three boundaries that must be translated together. We’ll turn the first-quadrant description into restrictions on both coordinates, keep the descending line as the third boundary, …
Preview problemRecognize when inequalities are incompatible
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Feasibility requires at least one value that satisfies both bounds simultaneously. We’ll interpret one inequality as a lower ray and the other as an upper ray, then compare their endpoints …
Preview problemChoose the better feasible plan using the stated goal
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
The decision has to follow the stated goal in its given order. We’ll keep each plan’s output and cost paired, compare the outputs first, and only use cost once we …
Preview problemWrite an inequality from a ratio requirement
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
This ratio describes capacity: each adult accounts for a fixed maximum group of students. We’ll multiply the per-adult capacity by the number of adults, then compare the actual student count …
Preview problemIdentify a redundant constraint
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
A redundant constraint is one that adds no restriction beyond what another condition already guarantees. We’ll compare the two upper bounds to find the tighter one, test which implication works, …
Preview problem