Algebra Diagnostic & Mastery Drills

Work through these sets to identify gaps in your algebraic reasoning. Algebra is less about memorizing formulas and more about internalizing the 'legal moves' you can make on an equation.

Instructions: Complete each tab. Use the scratchpad for your work. Use the Teacher's Hints if you get stuck, but try to resolve the equation yourself first.

Drill Levels

Level 1: Linear Foundations #

At this level, we focus on isolating the variable. Remember the core principle: whatever operation you apply to one side, you must apply to the other to maintain the equality.

Worked Example: Solve for xx: x4+9=12\frac{x}{4} + 9 = 12

  • 1.
    Subtract 99 from both sides: x4=3\frac{x}{4} = 3
  • 2.
    Multiply both sides by 44: x=12x = 12
  • Basics Sprint
    10:00
    Open question

    Solve for xx: 7x12=307x - 12 = 30

    Single choice

    Which value of xx satisfies the inequality: 52x>135 - 2x > 13?

    Teacher's Hints: Basics
    The Undo Method
    Negative Coefficients

    Session Analysis #

    Log your performance for this sitting to track your current accuracy. High-performing students review their mistakes immediately while the logic is still fresh.

    Current Session Accuracy
    Info

    Expert Strategy: If you missed a question, rewrite it on a physical notepad and solve it three times in a row. This builds the muscle memory required for timed exams.