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Not Everything That Stops Working Has Lost Its Value Feeling broken by life's setbacks? Discover why your value never decreases because of failure, pain, or difficult seasons. Learn the powerful lesson behind the broken machine and why your worth remains unchanged. The Broken Machine That Changed Everything Imagine walking into a workshop and finding an old industrial machine covered in dust and rust. It has not worked for years. Most people pass it without a second thought. "It is finished." "It is useless." "It belongs in the scrapyard." Those are the words many would use. Then an experienced engineer enters. Instead of seeing a useless machine, he sees possibility. He opens the casing, examines the internal parts, replaces a few worn components, reconnects the wiring, and powers it on. Within moments, the machine is running again. What changed? Not its value. Only its condition. That simple scene teaches one of the most important lessons about human...
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Algebra Problem Bank

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Algebra Problem Bank — Edwin Ogie Library

Algebra Problem Bank — Progressive Difficulty (JAMB Focus)

Step-by-step solutions and worked examples (3 per topic). Includes a 40-question timed CBT for 15 minutes and a donation section.
Edwin Ogie Library

Algebra Cheat‑Sheet: Key Formulas & Tricks

Essentials

  • (a+b)^2 = a^2 + 2ab + b^2
  • (a−b)^2 = a^2 − 2ab + b^2
  • (a+b)(a−b)=a^2−b^2
  • Quadratic formula: x = [−b ± √(b²−4ac)]/(2a)
  • Sum of roots: α+β = −b/a, Product: αβ = c/a
  • Arithmetic sequence: a_n = a_1 + (n−1)d
  • Sum of first n integers: n(n+1)/2

Speed Tricks

  • Test simple values (0,1,−1) to eliminate impossible MCQ options.
  • Use factor test: If p is root then (x−p) divides polynomial.
  • For quadratics, check discriminant Δ=b²−4ac quickly to know root type.
  • Complete the square to convert quickly when needed.

Recommended Algebra Videos

Embedded videos below are suggestions — replace the VIDEO_ID with any YouTube lesson you prefer.

Algebra Basics — Expand, factor, simplify
Quadratic Techniques — Formula, completing the square

Problem Bank — Progressive Difficulty

Each topic below has 3 worked examples (step-by-step) — ideal for JAMB-level practice.

Topic A: Linear Equations (Easy)

  1. Example 1: Solve 2x − 5 = 9.
    Solution: Add 5: 2x = 14 ⇒ x = 7.
  2. Example 2: Solve 3(x − 2) = 12.
    Solution: Expand: 3x − 6 = 12 ⇒ 3x = 18 ⇒ x = 6.
  3. Example 3: Solve 5x + 2 = 3x + 10.
    Solution: Subtract 3x: 2x + 2 = 10 ⇒ 2x = 8 ⇒ x = 4.

Topic B: Factorization & Identities (Easy–Medium)

  1. Example 1: Factor x^2 − 9.
    Solution: Recognize difference of squares: (x−3)(x+3).
  2. Example 2: Factor x^2 + 5x + 6.
    Solution: Find two numbers multiply 6 and add 5 → 2 and 3 ⇒ (x+2)(x+3).
  3. Example 3: Simplify (x+1)^2 − (x−1)^2.
    Solution: Use a^2−b^2=(a−b)(a+b): [(x+1)−(x−1)][(x+1)+(x−1)] = (2)(2x) = 4x.

Topic C: Quadratic Equations (Medium)

  1. Example 1: Solve x^2 − 5x + 6 = 0.
    Solution: Factor: (x−2)(x−3)=0 ⇒ x=2,3.
  2. Example 2: Solve x^2 + 4x + 4 = 0.
    Solution: Recognize perfect square: (x+2)^2=0 ⇒ x=−2 (double root).
  3. Example 3: Solve 2x^2 − 3x − 2 = 0.
    Solution: Use quadratic formula: x = [3 ± √(9 +16)]/4 = [3 ± 5]/4 ⇒ x = 2 or x = −1/2.

Topic D: Simultaneous Equations (Medium)

  1. Example 1: Solve x + y = 5, x − y = 1.
    Solution: Add: 2x = 6 ⇒ x = 3; then y = 2.
  2. Example 2: Solve 2x + y = 7, x − y = 1.
    Solution: Add equations after manipulating: From second, y = x−1. Substitute: 2x + (x−1)=7 ⇒ 3x=8 ⇒ x=8/3, y=5/3.
  3. Example 3: Solve 3x − 2y = 4, 2x + y = 1.
    Solution: From second, y = 1 − 2x. Substitute: 3x − 2(1−2x)=4 ⇒ 3x − 2 +4x = 4 ⇒ 7x = 6 ⇒ x = 6/7, y = 1 − 12/7 = −5/7.

Topic E: Inequalities & Simplification (Medium–Hard)

  1. Example 1: Solve 2x + 1 > 5.
    Solution: 2x > 4 ⇒ x > 2.
  2. Example 2: Simplify (x^2 − 1)/(x−1) for x ≠ 1.
    Solution: Factor numerator: (x−1)(x+1)/(x−1)=x+1.
  3. Example 3: Solve (x+2)(x−3) < 0.
    Solution: Roots at −2 and 3; sign chart gives solution −2 < x < 3.

Topic F: Indices & Log Basics (Hard)

  1. Example 1: Evaluate x if x^3 = 8.
    Solution: x = ∛8 = 2.
  2. Example 2: If 2^x = 8, find x.
    Solution: 8 = 2^3, so x = 3.
  3. Example 3: Simplify log₁₀ 100.
    Solution: 100 = 10^2, so log₁₀100 = 2.

Short Practice (Quick Fire)

  1. Solve x^2 − 4 = 0.
  2. Factor 4x^2 − 9.
  3. Find f(3) for f(x) = 2x + 1.
  4. Sum of roots of x^2 − 7x + 10.
  5. Solve simultaneous: x + y = 4, x − y = 2.
Answers at the bottom of the page.

40‑Question JAMB‑Style CBT — Time: 15 minutes

Instructions: Click Start Quiz. A 5‑second countdown will play, then the 15‑minute timer starts. Answer all questions and click Submit. You can optionally include your name and email and send results to Edwin Ogie Library.
Time: 15:00
Question: 0/40

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If this resource helps you, please support the work. Use the Flutterwave donate link or transfer via Moniepoint account below.

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Quick Exercise Answers

  1. x^2 − 4 = 0 ⇒ x = ±2
  2. 4x^2 − 9 = (2x − 3)(2x + 3)
  3. f(3) for f(x)=2x+1 ⇒ 7
  4. Sum of roots of x^2 − 7x + 10 ⇒ 7
  5. Solve x + y = 4, x − y = 2 ⇒ x = 3, y = 1

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