Fall 2026

Math 130 — Test 1 Review

A full-unit review organized around the Fall 2026 Canvas sequence. Canvas supplies the master dates; official quiz and test coverage can be adjusted there or in class.

📝 Paper Test 💻 Modular ALEKS Learning 📐 11 Core Topics

Unit 1: learn → practice → checkpoint

Move through these windows in order. Each HTML deck teaches the skills, includes retrieval and worked practice, and ends with a closed-notes readiness check. Then use the matching targeted pool below. Canvas supplies the master dates; your instructor may adjust official assessment coverage.

Unit 1AQuiz 1 · Sep 2

Algebra Foundations: Factor First

Intervals, exponent rules, factoring, and rational expressions. ALEKS Review R.1–R.5 is the pacing anchor.

Open HTML deck

Class sequence: Aug 28: Factor first → Aug 31: Split the middle term and factor by grouping → Sep 2: Review and in-class Quiz 1. Use the full Unit 1A practice and checkpoint for additional R.1–R.5 review.

Open the Aug 31 printable / fillable handout for practice and the exit check on one double-sided sheet.

Unit 1BQuiz 2 · Sep 9

Equations, Formulas, and Roots

Fractional and rational equations, formula rearrangement, special cases, and quadratic roots. This emphasis follows the current ALEKS R.6 and Sections 1.1, 1.2, 1.4 evidence.

Open Sep 4 deck

Class sequence: Sep 4: Equations with fractions and roots → ALEKS-targeted practice → Quiz 2 on Sep 9.

Unit 1CQuiz 3 · Sep 16

Functions and Coordinate Geometry

Functions, domain and range, midpoint, distance, and circles. This closes the Functions/Relations gap in the old review path.

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Unit 1DQuiz 4 · Sep 21

Quadratic Equations and Applications

Standard form, solving quadratics, the vertex, and contextual interpretation. Sections 2.5 and 3.1 are due Sep 23.

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Unit 1ETest 1 · Sep 23

Test 1 Mixed Retrieval

Interleaved work from all four learning windows. Use results to return to one targeted pool rather than restarting everything.

Open HTML deck
Class archiveAug 28

Friday Factor-First Session

The launch-ready class deck built from the ALEKS reports and entrance-check results. Keep it as a focused intervention, not the entire Unit 1 sequence.

Open session deck

Canvas master plan for Test 1

ALEKS work is completed online. Quizzes and Test 1 are paper assessments in class; their Canvas entries supply the master dates and times. The ALEKS group beside a quiz is a pacing marker, not a guarantee of quiz coverage.

Canvas dateALEKS duePaper assessment
Sep 2 · 2:10 PMReview R.1–R.3 and R.4–R.5Quiz 1
Sep 9 · 2:10 PMReview R.6 and Sections 1.1, 1.2, 1.4Quiz 2
Sep 16 · 2:10 PMSections 2.1, 2.2, 2.4Quiz 3
Sep 21 · 2:10 PMContinue current ALEKS moduleQuiz 4
Sep 23 · 2:10 PMSections 2.5 and 3.1Test 1
Use the sequence by stage. Finish the matching A–D deck, then use its targeted practice and checkpoint. Use the mixed Test 1 pools only after the four learning windows.

Key Concepts

  • Set-builder notation: e.g. \{x \mid x \geq 3\}
  • Interval notation: brackets [ ] include; parentheses ( ) exclude
  • Union A \cup B: elements in either set
  • Intersection A \cap B: elements in both sets

Common Intervals

[a, b] \quad (a, b) \quad [a, \infty) \quad (-\infty, b]
⚡ ∞ and −∞ always get parentheses, never brackets!
📺 Video Walkthroughs
How to Find the Intersection and Union of Two Intervals
Interval notation with number line visuals
Intersection and Union of Discrete Sets
Working with finite sets — listing elements in ∩ and ∪

Key Concepts

  • |a| = distance from a to 0 — always ≥ 0
  • |a| = a if a \geq 0; |a| = -a if a < 0
|x| = c \implies x = c \text{ or } x = -c \quad(c \geq 0)
⚡ Remember: \sqrt{x^2} = |x|
📺 Video Walkthrough
Challenging Absolute Value Equations
Quick walkthrough of tricky absolute value problems

Core Laws

  • a^m \cdot a^n = a^{m+n}
  • \frac{a^m}{a^n} = a^{m-n}
  • (a^m)^n = a^{mn}
  • (ab)^n = a^n b^n
  • a^{-n} = \frac{1}{a^n}
⚡ Write all final answers with positive exponents only.
📺 Video Walkthrough
Rational Exponents with a Few Examples
Converting between radicals and fractional exponents

Methods (always start with GCF!)

  • GCF — always factor out first
  • Grouping — split into pairs
  • Difference of squares: a^2 - b^2 = (a-b)(a+b)
  • Difference of cubes: a^3 - b^3 = (a-b)(a^2+ab+b^2)
  • Sum of cubes: a^3 + b^3 = (a+b)(a^2-ab+b^2)
  • Trinomials: find two numbers that multiply to ac and add to b
⚡ Mnemonic for cubes: "SOAP" — Same, Opposite, Always Positive.
📺 Video Walkthroughs
Factor a Quadratic with Lead Coefficient = 1
Finding two numbers that multiply and add correctly
How to Factor Quadratics with a Lead Coefficient
AC method for trinomials when a ≠ 1
How to Solve Quadratics by Factoring
GCF, trinomials without & with lead coefficients
  • Always factor first
  • Add/subtract: find LCD, rewrite, combine numerators
  • Multiply: factor → cancel → multiply
  • Divide: flip second fraction → multiply
⚡ Factor first! This is the #1 mistake on rational expression problems.
📺 Video Walkthrough
Solving Rational Equations
Finding LCD, clearing fractions, checking for extraneous solutions

Linear

  • Distribute, combine like terms, isolate variable
  • With fractions: multiply by LCD
  • Watch for no solution or all reals

Quadratic

  • Factor or use quadratic formula
  • Rational equations: check for extraneous solutions!
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
📺 Video Walkthroughs
How to Solve Quadratics by Factoring
GCF, trinomials without & with lead coefficients
Solving Rational Equations
Finding LCD, clearing fractions, checking for extraneous solutions
\text{Midpoint} = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)
d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
⚡ Round to one decimal place when instructed!
📺 Video Walkthrough
Midpoint & Distance Formula
Step-by-step examples with coordinate pairs
(x-h)^2 + (y-k)^2 = r^2

Center = (h,k), Radius = r

⚡ Right side is r², not r. Radius 5 → write 25.
📺 Video Walkthrough
Standard Equation of a Circle Formula Explained!
Center, radius, and writing the equation step by step
  • Slope-intercept: y = mx + b
  • Point-slope: y - y_1 = m(x - x_1)
  • General: Ax + By + C = 0
\text{Parallel: } m_1 = m_2 \qquad \text{Perp: } m_1 \cdot m_2 = -1
⚡ Perpendicular: flip and negate. Slope 3 → perp slope −1/3.
📺 Video Walkthroughs
Slope Intercept vs Point Slope Form
When to use each form and converting between them
Finding Slopes of Parallel and Perpendicular Lines
Identifying slopes and graphing parallel & perpendicular lines
x = -\frac{b}{2a}

Plug back into f(x) for the max/min value.

  • a > 0 → minimum
  • a < 0 → maximum
⚡ The question usually wants the y-value (height, etc.), not the x-value.
📺 Video Walkthrough
How to Find the Vertex of a Parabola
NancyPi — clear walkthrough of the vertex formula

Key Concepts

  • A relation is a function when each input has exactly one output.
  • f(a) means substitute a for every input variable.
  • Domain is the set of allowable inputs; range is the resulting outputs.
  • Exclude denominator zeros; require an even-root radicand to be nonnegative.
\operatorname{dom}\!\left(\frac{1}{x-a}\right)=(-\infty,a)\cup(a,\infty)
⚡ Repeated outputs are allowed. A repeated input with two different outputs is not a function.

📐 Core Algebra

Difference of Squares
a^2-b^2=(a-b)(a+b)
Difference of Cubes
a^3-b^3=(a-b)(a^2+ab+b^2)
Sum of Cubes
a^3+b^3=(a+b)(a^2-ab+b^2)
Quadratic Formula
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

📏 Coordinate Geometry

Midpoint
M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)
Distance
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
Slope
m=\frac{y_2-y_1}{x_2-x_1}
Circle
(x-h)^2+(y-k)^2=r^2

📈 Lines

Point-Slope
y-y_1=m(x-x_1)
Slope-Intercept
y=mx+b
Parallel
m_1=m_2
Perpendicular
m_1 \cdot m_2=-1

⛰️ Quadratic Vertex

Vertex x-coordinate
x=-\frac{b}{2a}
Rule
a > 0 → min | a < 0 → max

🔢 Exponent Rules

Product
a^m \cdot a^n=a^{m+n}
Quotient
\frac{a^m}{a^n}=a^{m-n}
Power
(a^m)^n=a^{mn}
Negative
a^{-n}=\frac{1}{a^n}

🔁 Functions & Domain

Function value
f(a):\;\text{substitute }a\text{ for every }x
Rational domain
\text{denominator}\ne0
Even-root domain
\text{radicand}\ge0
Graph test
A vertical line intersects a function graph at most once.
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