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:
Find the slope between (2,3) and (5,7).
Graph: y = −2x + 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
Daily Practice: Spend 30–60 minutes solving problems each day.
Track Weaknesses: Keep a list of topics that need more review.
Use Resources: Online videos (like Khan Academy) and your textbook for additional help.