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United StatesMaths

Algebra

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you solve exponential and radical equations on the ACT, and how do you avoid extraneous solutions?

Solve exponential equations by matching bases and radical equations by isolating and squaring, checking for extraneous solutions (Algebra).
An ACT Algebra answer on solving exponential equations by matching bases and radical equations by isolating the radical and squaring, with the crucial step of checking for extraneous solutions, and worked ACT-style questions.
10 min answer →

How do you manipulate algebraic expressions and find the equation of a line in the coordinate plane on the ACT?

Evaluate and rearrange algebraic expressions, solve literal equations for a variable, and find the slope and equation of a line in the coordinate plane (Algebra).
An ACT Algebra answer on manipulating expressions and the coordinate plane: evaluating and rearranging expressions, solving literal equations for a variable, and finding the slope and equation of a line through points, with worked ACT-style questions.
10 min answer →

How do you solve linear equations and inequalities, including those with variables on both sides, on the ACT?

Solve linear equations and inequalities in one variable, including multi-step and variables-on-both-sides cases, and remember to flip the inequality when multiplying or dividing by a negative (Algebra).
An ACT Algebra answer on solving linear equations and inequalities: isolating the variable, clearing fractions, handling variables on both sides, and flipping the inequality sign when multiplying or dividing by a negative, with worked ACT-style questions.
10 min answer →

How do you expand, factor and simplify polynomial expressions on the ACT?

Expand products of polynomials, factor by common factor, grouping and special patterns, and simplify polynomial and rational expressions (Algebra).
An ACT Algebra answer on polynomials: expanding products (FOIL and distribution), factoring out a common factor, the difference of squares and other patterns, factoring quadratics, and simplifying rational expressions, with worked ACT-style questions.
10 min answer →

How do you solve quadratic equations on the ACT by factoring, the quadratic formula, and the discriminant?

Solve quadratic equations by factoring, the quadratic formula and square roots, and use the discriminant to count real solutions (Algebra).
An ACT Algebra answer on solving quadratic equations by factoring, the quadratic formula and taking square roots, plus using the discriminant to count real solutions, with worked ACT-style questions and common traps.
11 min answer →

How do you solve a system of two linear equations on the ACT by substitution or elimination?

Solve systems of two linear equations by substitution and elimination, interpret the solution as an intersection point, and recognise systems with no solution or infinitely many solutions (Algebra).
An ACT Algebra answer on solving systems of two linear equations by substitution and elimination, interpreting the solution as the intersection of two lines, and recognising parallel (no solution) and identical (infinitely many) systems, with worked ACT-style questions.
10 min answer →