First, Understand What PMDC Actually Tests
MDCAT Physics isn't a math exam. It's a conceptual physics exam that happens to involve numbers. The MCQ options are almost always spaced far enough apart that a 2–3% approximation won't change your answer. PMDC knows you don't have a calculator — the paper is designed so that dimensional analysis, conceptual reasoning, and rough numerical work get you to the right option.
What kills students isn't the lack of a calculator. It's freezing up when a number looks messy, spending 90 seconds trying to do long division in their head, and then rushing through the next three questions. This guide fixes that by giving you a mental math toolkit you can deploy automatically.
Rule one, and it's non-negotiable: If your mental math is taking longer than 20 seconds on a single physics MCQ, you're doing it wrong. Learn to approximate, pick the closest option, and move on. The 80/20 rule applies brutally here — 80% of your points come from 20% of the arithmetic effort.
1. Scientific Notation — The Exponential Shortcut
Physics loves ×10^3, ×10^−6, and ×10^9. Here's the quick way to handle them without writing zeros:
- Multiplying: Add the exponents.
(3×10⁴) × (2×10⁵) = 6×10⁹ - Dividing: Subtract the exponents.
(6×10⁷) / (2×10³) = 3×10⁴ - Moving the decimal: Each step left increases the exponent by 1; each step right decreases it by 1.
4500 → 4.5×10³
Practice this until it's automatic. Nearly every MDCAT physics calculation starts with converting given values into scientific notation — do it in your head in 2 seconds and save the real thinking for the physics.
2. Rounding g = 9.8 to 10 — When and How
Rounding gravitational acceleration from 9.8 m/s² to 10 m/s² introduces a 2.04% error. In MDCAT, that's almost always acceptable because answer options are typically 5–10% apart. But here's the nuance:
When NOT to round: If the options are clustered closely — e.g., 98.2, 99.1, 100.4, 101.3 — rounding 9.8 to 10 could land you between two options. In that case, either use exact 9.8 or use the 10 − 2% trick: calculate with 10, then subtract 2% of the result. So if 10 gives you 100, 9.8 gives you ~98 — a meaningful difference in tight options.
For most projectile motion, force, and energy problems, the 2% rounding is invisible. Use it confidently and save the mental energy for harder concept checks.
3. The Essential Trig Values — Memorized, Not Derived
You don't have time to derive sin 60° from the unit circle in the exam hall. Memorize these cold:
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | ∞ |
Pattern to remember: sin increases from 0 to 1 as angle goes 0→90. Cos is the reverse. Tan is sin/cos — so at 45°, it's 1; at 60°, it's √3 ≈ 1.73. These values appear in projectile range, inclined planes, vector components, and wave equations — arguably the most repeated calculation in MDCAT Physics.
4. Square Roots — The 5-Second Estimation
You'll often need √2, √3, √5, or the square root of a number like 50, 72, or 128. Here's the universal estimation trick:
- Find the nearest perfect square below your number. Call it
a². - Use:
√n ≈ a + (n − a²) / (2a) - Example:
√50— nearest perfect square below is 49 (7²). Soa = 7.√50 ≈ 7 + (50−49)/(14) = 7 + 1/14 = 7.07. Real value is 7.071 — exact to three decimals. - Example:
√72— nearest below is 64 (8²).√72 ≈ 8 + (72−64)/16 = 8 + 0.5 = 8.5. Real value is 8.485 — close enough for MDCAT.
For √2, √3, √5: Just memorize them. √2 ≈ 1.41, √3 ≈ 1.73, √5 ≈ 2.24. They appear constantly and memorizing saves you from re-estimating every time.
5. Quick Unit Conversions — No, You Don't Need to Write Them
Unit conversions are the silent time-killers. Here's a reference table you should internalize:
| Conversion | Mental Rule |
|---|---|
| km/h → m/s | Multiply by 5/18 (or ×0.28). 72 km/h = 20 m/s. |
| m/s → km/h | Multiply by 18/5 (or ×3.6). 10 m/s = 36 km/h. |
| cm → m | Divide by 100. 50 cm = 0.5 m. |
| g → kg | Divide by 1000. 500 g = 0.5 kg. |
| mm → m | Divide by 1000. 250 mm = 0.25 m. |
The 5/18 trick alone appears in at least 2–3 MDCAT Physics questions every single year. Memorize it.
6. The "π ≈ 3.14" Shortcut
For circular motion, wave speed, rotational problems — π shows up everywhere. Use π ≈ 22/7 ≈ 3.14. If you're approximating, π ≈ 3 is a 4.5% error — risky but sometimes acceptable if options are broad. When in doubt, use 3.14 and multiply.
Pro move: If you see 2π, just use 6.28 (or 6.3 for speed). If you see π/2, use 1.57. These are the only variants you'll realistically encounter.
7. The Mental Math Practice Tool
Test your estimation skills with this quick practice tool — try each calculation mentally, then check your answer.
⚡ Quick Estimation Challenge
Putting It All Together — The 20-Second Rule
Here's your mantra for every MDCAT physics calculation: 20 seconds, then move. If you can't get to an answer in 20 seconds using these tricks, you're overthinking. Guess intelligently, flag it if possible, and come back later. MDCAT rewards speed over precision — a rough answer on all 40 questions beats a perfect answer on 30.
The real hack: Students who practice these mental math tricks for just 3–4 hours before the exam report feeling significantly less anxious about physics calculations. The fear of big numbers dissolves when you have a systematic way to handle them. That's the real value here — not just speed, but confidence.
Master Physics Faster
Mental math alone won't get you a top score — you also need concept clarity and timed practice. Start with our full MDCAT Physics subject guide.
Physics Subject Guide →Frequently Asked Questions
No. PMDC strictly prohibits calculators, smartwatches, or any electronic devices in the exam hall. You must rely entirely on mental math and approximation techniques.
Use the nearest perfect square method: √n ≈ a + (n−a²)/(2a) where a² is the closest perfect square below n. For √50: 7 + (50−49)/14 = 7.07 — extremely close to the real 7.071.
Memorize sin, cos, and tan for 0°, 30°, 45°, 60°, and 90°. The pattern: sin goes 0, 1/2, √2/2, √3/2, 1; cos is the reverse. These appear constantly in projectile, force, and wave problems.
Rounding g=9.8 to 10 introduces a 2% error. This is safe when answer options are spaced more than 2% apart. If options are tight, use the 10−2% trick: calculate with 10, then subtract 2% of the result.
Maximum 20 seconds on the arithmetic part. If you're spending more, you're not approximating aggressively enough. The concepts matter more than the numbers — choose the closest option and move forward.