15 Mathematics Shortcuts Every JAMB Candidate Should Know

In JAMB UTME, you have roughly 45 seconds per Mathematics question. That's not enough time to solve every problem from scratch. The students who score highest in JAMB Math aren't necessarily the most brilliant — they're the most efficient. Here are 15 shortcuts and techniques that will help you solve questions faster and more accurately.

Number and Arithmetic Shortcuts

1. The Elimination Method

Before solving a question, look at the answer options. Often you can eliminate 2-3 options immediately based on quick reasoning:

• If the question involves multiplying two odd numbers, eliminate any even answer.
• If a percentage question asks "what is 15% of 240?" — the answer must be less than 240 and less than 24 (which is 10%). Quick mental math: 10% = 24, 5% = 12, so 15% = 36.
• Check the magnitude. If you're calculating the area of a small shape, eliminate any unreasonably large answers.

2. Percentage Shortcuts

Break percentages into easy chunks:

• 10% = divide by 10
• 5% = half of 10%
• 25% = divide by 4
• 33.3% = divide by 3
• 1% = divide by 100

Example: 17.5% of 400 = 10%(40) + 5%(20) + 2.5%(10) = 70. Done in seconds without a calculator.

3. Divisibility Rules

Save time checking factors:

• Divisible by 2: last digit is even
• Divisible by 3: sum of digits is divisible by 3
• Divisible by 4: last two digits form a number divisible by 4
• Divisible by 5: ends in 0 or 5
• Divisible by 9: sum of digits is divisible by 9
• Divisible by 11: alternating sum of digits is divisible by 11

Algebra Shortcuts

4. Substitution for Multiple Choice

Instead of solving an equation algebraically, substitute the answer options back into the original equation to see which one works. This is often faster, especially for complex equations.

Example: "Find x if 2x² - 5x + 3 = 0." Options: A) 1, B) 3/2, C) 2, D) 1 and 3/2. Try x=1: 2(1) - 5(1) + 3 = 0 ✓. Try x=3/2: 2(9/4) - 5(3/2) + 3 = 4.5 - 7.5 + 3 = 0 ✓. Answer: D.

5. The Discriminant Shortcut

For quadratic equations ax² + bx + c = 0, the discriminant D = b² - 4ac tells you everything:

• D > 0: two real roots
• D = 0: one repeated root (equal roots)
• D < 0: no real roots

Many JAMB questions ask about the nature of roots without needing you to actually find them.

6. Sum and Product of Roots

For ax² + bx + c = 0: Sum of roots = -b/a, Product of roots = c/a. This lets you answer questions about roots without using the quadratic formula.

7. Factoring Patterns to Memorize

• a² - b² = (a+b)(a-b) — difference of two squares
• a² + 2ab + b² = (a+b)² — perfect square trinomial
• a³ - b³ = (a-b)(a² + ab + b²) — difference of cubes
• a³ + b³ = (a+b)(a² - ab + b²) — sum of cubes

Geometry and Trigonometry Shortcuts

8. Special Triangle Values

Memorize these — they appear in almost every JAMB exam:

• sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3
• sin 45° = √2/2, cos 45° = √2/2, tan 45° = 1
• sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3

9. The Angle Sum Shortcut

Quick formulas you should know cold:

• Sum of angles in a triangle = 180°
• Sum of angles in a polygon = (n-2) × 180°
• Each angle of a regular polygon = (n-2) × 180° / n
• Exterior angle of a regular polygon = 360° / n

10. Circle Theorem Shortcuts

• Angle at center = 2 × angle at circumference (same arc)
• Angle in a semicircle = 90°
• Angles in the same segment are equal
• Opposite angles of a cyclic quadrilateral = 180°
• Tangent is perpendicular to radius at point of contact

Statistics and Probability Shortcuts

11. Mean from Frequency Table

Mean = Σ(fx) / Σf. When using assumed mean method: Mean = A + Σ(fd) / Σf, where d = x - A. Choose A as the value near the middle of the distribution to make calculations easier.

12. Probability Quick Rules

• P(A or B) = P(A) + P(B) - P(A and B) for non-exclusive events
• P(A and B) = P(A) × P(B) for independent events
• P(not A) = 1 - P(A) — often easier than calculating directly
• For "at least one" problems: P(at least one) = 1 - P(none)

13. Permutation vs Combination

Order matters? Use permutation (nPr). Order doesn't matter? Use combination (nCr). Quick check: "In how many ways can a committee be formed?" = combination. "In how many ways can positions be filled?" = permutation.

General JAMB Math Tactics

14. Work Backwards from Answers

For some problems, it's faster to check which answer option satisfies the question conditions rather than solving from scratch. Start with option B or C (the middle values) — if the result is too high, try a smaller option, and vice versa.

15. Unit Analysis

When you're stuck, check the units. If the question asks for area, your answer must be in square units. If it asks for speed, it must be in distance/time units. This alone can eliminate wrong options.

How to Practice These Shortcuts

Knowing shortcuts isn't enough — you need to practice until they become automatic. Here's the approach:

• Do 20 JAMB Math questions daily using these techniques.
• Time yourself: aim for under 45 seconds per question.
• Review wrong answers: understand which shortcut you could have used.
• Use ExamPro's practice mode: our AI explanations show the most efficient solution method for each question.

Mathematics is the subject where consistent practice makes the biggest difference. These shortcuts will save you minutes in the exam — minutes that translate directly into more correct answers and a higher score.