algebra one study plan

Week 1: January 22–28

Topics: Algebra basics

  • Review: Order of operations (PEMDAS)

  • Practice: Simplifying expressions

  • Key Concepts: Variables, constants, and coefficients

  • Example Problems:

    • Simplify: 3(2x+5) - 4

    • Combine like terms: 4x + 7 - 2x + 3


Week 2: January 29–February 4

Topics: Solving linear equations

  • Review: One-step, two-step, and multi-step equations

  • Practice:

    • Solving equations with variables on both sides

    • Using the distributive property

  • Example Problems:

    • 2x + 5 = 15

    • 3(x - 2) = 9


Week 3: February 5–11

Topics: Inequalities

  • Review: One-step and multi-step inequalities

  • Practice: Graphing solutions on a number line

  • Key Concept: Reversing the inequality sign when multiplying/dividing by a negative

  • Example Problems:

    • Solve: −2x >10

    • Graph: x ≤ 4


Week 4: February 12–18

Topics: Functions and relations

  • Review: Function notation f(x), domain, and range

  • Practice: Determining if a relation is a function

  • Example Problems:

    • Is {(1,2),(3,4),(5,2)} a function?

    • Find f(3) if f(x)=2x−5


Week 5: February 19–25

Topics: Linear functions

  • Key Concepts:

    • Slope (m): m = (x2−x1) / (y2−y1)

    • Slope-intercept form: y = mx + b.

    • Point-slope form: y − y1 = m(x−x1).

  • Practice:

    • Graphing linear equations.

    • Writing equations in slope-intercept and point-slope form.

  • Example Problems:

    1. Find the slope between (2,3) and (5,7).

    2. Graph: y = −2x + 3.

    3. Write the equation of a line passing through (4,−1) with a slope of 3 using point-slope form.


Week 6: February 26–March 3

Topics: Systems of equations

  • Review: Solving systems by substitution and elimination

  • Practice: Word problems with systems

  • Example Problems:

    • Solve: x+y=7, 2x-y=3

    • Solve using substitution: y=2x+1, 3x−y=7


Week 7: March 4–10

Topics: Exponents, exponential functions, arithmetic and geometric sequences.

Review:

  • Properties of exponents:

a^m * a^n = a^(m+n), (a^m) / (a^n) = a^(m-n), (a^m)^n = a^(mn), a^(-n) = 1/(a^n), a^0 = 1 (if a is not equal to 0)

  • Exponential growth / decay: a = initial amount, r = rate of growth/decay, t = time

growth: y = a(1 + r)^t

decay: y = a(1 - r)^t

  • Arithmetic Sequence Formula: write on paper

  • Geometric sequence formula : write on paper]

  • Practice: Simplifying expressions with exponents

  • Example Problems:

    • Simplify: (2x^3)^2

    • Simplify: (3x^4) / x^2


Week 8: March 11–17

Topics: Polynomials

  • Review: Adding, subtracting, and multiplying polynomials

  • Practice:

    • Simplifying expressions

    • Multiplying binomials using FOIL

  • Example Problems:

    • Add: (3x^2 + 2x) + (5x^2 - x + 4)

    • Multiply: (x+3)(x−4)


Week 9: March 18–24

Topics: Factoring

  • Review:

    • Factoring trinomials

    • Factoring by grouping

  • Practice: Solving quadratic equations by factoring

  • Example Problems:

    • Factor: x^2 + 5x + 6

    • Solve: x^2−9 = 0


Week 10: March 25–31

Topics: Quadratic functions

  • Review:

    • Vertex form (y = a (x - h)^2 + k)

    • Finding vertex and axis of symmetry

  • Practice: Graphing quadratic functions

  • Example Problems:

    • Graph: y = (x − 2)^2−3

    • Find the vertex of y = 2x^2 + 4x + 1


Week 11: April 1–7

Topics: Radical expressions and equations

  • Review: Simplifying square roots and solving radical equations

  • Practice:

    • Solving equations with radicals

    • Rationalizing denominators

  • Example Problems:

    • Simplify: sqrt{50}

    • Solve: sqrt{x+3} = 5


Week 12: April 8–14

Topics: Data analysis and probability

  • Review: Mean, median, mode, and range

  • Practice: Scatter plots and line of best fit

  • Example Problems:

    • Find the mean and median of 3, 7, 9, 10

    • Create a scatter plot for a given data set


Week 13: April 15–21

Topics: Comprehensive review

  • Practice:

    • Mixed problem sets covering all topics

    • Focus on areas of weakness

  • Example Problems:

    • Solve a mix of equations, inequalities, and functions

    • Revisit challenging problems from earlier weeks


Tips for Success

  1. Daily Practice: Spend 30–60 minutes solving problems each day.

  2. Track Weaknesses: Keep a list of topics that need more review.

  3. Use Resources: Online videos (like Khan Academy) and your textbook for additional help.