How to Build Mental Math Speed: The Training Protocol

Mental arithmetic speed is a skill, not a talent. The traders who ace Optiver's 80-in-8 test didn't get fast because they were born fast — they got fast because they trained systematically.

This guide covers exactly how to train: the technique stack, the daily protocol, the benchmarks to hit, and the common mistakes that slow people down.

What "Fast" Means in Practice

Optiver's 80-in-8 test: 80 questions in 8 minutes = 6 seconds per question. Questions range from simple addition to 3-digit multiplication, percentages, fractions, and roots.

Passing threshold: Approximately 53–60 correct, depending on the cohort. You don't need to attempt all 80 — you need to answer 53+ correctly.

The implication: You need:

• Simple addition/subtraction: < 2 seconds
• 2-digit multiplication: < 4 seconds
• Percentages and fractions: 3–5 seconds
• Square roots and estimation: 4–6 seconds

You also need to know when to skip a hard question and move on.

Phase 1: Foundational Fluency (Weeks 1–2)

Before learning tricks, you need foundational fluency. Many people skip this and wonder why the tricks don't stick.

Multiplication Tables Through 20 × 20

Go beyond 12 × 12. You need 13 × 13 through 19 × 19 automatic.

You must know cold
13² = 169	14² = 196
15² = 225	16² = 256
17² = 289	18² = 324
19² = 361	25² = 625

How to drill: use flashcards (physical or digital). Go through 15 × 15, 16 × 15, 17 × 15... systematically. Target: any entry in the 20 × 20 table in under 2 seconds.

Time required: Most people achieve this in 10–14 days of 15-minute daily drilling.

Addition and Subtraction Speed

Simple arithmetic should be automatic. Target: any two 2-digit numbers added in under 1.5 seconds.

The technique: Left-to-right calculation. Add tens first, then units.

47 + 68: (40+60) + (7+8) = 100 + 15 = 115 (not 47+68 written out vertically in your head).

Drill: Write or type 20 addition problems (random 2-digit + 2-digit). Time yourself. Target: 20 problems in under 30 seconds = 1.5 seconds each.

Phase 2: Technique Stack (Weeks 2–4)

Once foundational tables are solid, layer in the techniques that turn hard problems into easy ones.

Technique 1: Difference of Squares

For multiplying two numbers close to a round number:

(a+b)(a−b) = a² − b²

Examples:

• 48 × 52 = 50² − 2² = 2500 − 4 = 2,496
• 47 × 53 = 50² − 3² = 2500 − 9 = 2,491
• 97 × 103 = 100² − 3² = 10,000 − 9 = 9,991
• 24 × 26 = 25² − 1² = 625 − 1 = 624

Application domain: Any two numbers where you can find a round midpoint within 10.

Speed gain: 48 × 52 without this technique requires column multiplication in your head — 5+ seconds. With this technique: 1–2 seconds.

Technique 2: Multiply by 25, 125, 75

• × 25 = × 100 ÷ 4
• × 125 = × 1000 ÷ 8
• × 75 = × 300 ÷ 4

Examples:

• 36 × 25 = 3,600 ÷ 4 = 900
• 48 × 25 = 4,800 ÷ 4 = 1,200
• 16 × 125 = 16,000 ÷ 8 = 2,000
• 24 × 75 = 24 × 300 / 4 = 7,200 / 4 = 1,800

Technique 3: Percentage Decomposition

For X% of N:

• 10% = N ÷ 10
• 5% = half of 10%
• 1% = N ÷ 100
• Combine: 15% = 10% + 5%; 17% = 10% + 5% + 2(1%); 37.5% = 25% + 12.5%

Examples:

• 17.5% of $840: 10% = $84, 5% = $42, 2.5% = $21. Total = $147
• 37% of 500: 30% = 150, 7% = 35. Total = 185

Practice target: 15% of any 3-digit number in under 3 seconds.

Technique 4: Multiply Two 2-Digit Numbers (General Method)

When the difference-of-squares trick doesn't apply, use FOIL expanded:

AB × CD = (A×10 + B) × (C×10 + D) = A×C×100 + (A×D + B×C)×10 + B×D

For 37 × 48:

• 3×4 = 12 → 1200
• 3×8 + 7×4 = 24 + 28 = 52 → 520
• 7×8 = 56 → 56
• Total: 1200 + 520 + 56 = 1,776

This takes practice but becomes fast. Target: any 2-digit × 2-digit in under 5 seconds.

Pro tip: Track the subtotals running: 1200 → 1720 → 1776. Don't try to hold all three separately.

Technique 5: Squaring Numbers Ending in 5

n5² = n×(n+1) followed by 25.

• 25² = 2×3 | 25 = 625
• 35² = 3×4 | 25 = 1,225
• 45² = 4×5 | 25 = 2,025
• 55² = 5×6 | 25 = 3,025
• 65² = 6×7 | 25 = 4,225
• 85² = 8×9 | 25 = 7,225
• 125² = 12×13 | 25 = 15,625

Application: Any number ending in 5. Instant once memorized.

Technique 6: Fractions to Decimals (The Key Ones)

Fraction	Decimal
1/3	0.333
2/3	0.667
1/6	0.167
5/6	0.833
1/7	0.143
1/8	0.125
3/8	0.375
5/8	0.625
7/8	0.875
1/9	0.111
1/11	0.0909
1/12	0.0833

Know these without computing. If you see 7/8 in a question, you should immediately know 0.875, not compute 7 ÷ 8.

Technique 7: Approximation Under Time Pressure

For roots and harder calculations, approximation beats exact calculation when time is short:

• √150: √144=12, √169=13. 150 is closer to 144: ≈ 12.2
• √200: √196=14, so √200 ≈ 14.1
• ³√100: 4³=64, 5³=125. So ³√100 ≈ 4.6

Key insight: On the Optiver test, you're not penalized for rounding a root answer. 12.2 vs 12.25 doesn't matter.

Phase 3: Speed Under Pressure (Weeks 4–8)

Knowing the techniques is not the same as executing them fast under pressure. This phase builds actual test-taking speed.

The Daily Speed Drill

Every day, do this sequence (15 minutes):

Set 1 — Tables (3 min): 20 random multiplication facts from 2–20 table, timed. Track average time.

Set 2 — Techniques (5 min): 15 technique-specific problems. E.g., 5 difference-of-squares + 5 × 25 multiplications + 5 percentage problems.

Set 3 — Mixed Sprint (7 min): 40 mixed problems (similar to Optiver format). Work as fast as you can. Score: correct answers only.

Track your Set 3 score daily. It should improve roughly linearly over 4–6 weeks.

The Skip Decision

On the actual Optiver test, harder questions steal time from easier ones. Train the skip decision:

• If you don't immediately see a technique to apply in 2 seconds: skip.
• Come back to skipped questions if time allows.

Rule of thumb: Questions you can answer in < 4 seconds: attempt. Questions that require > 6 seconds: skip on first pass.

Simulating Test Conditions

• Physical timer, not phone timer
• No music or distractions
• Seated at a desk
• Write answers (simulate pencil-and-paper format)

Do two full 8-minute simulations per week in weeks 5–8. Your simulation score is the best predictor of your actual test score.

Phase 4: Polishing (Week 8 Onward)

If you're scoring 55+/80 on simulations: you're ready. Shift to maintenance.

If you're scoring 45–55: identify your weak question types and drill those specifically. Common weaknesses:

Fractions in unusual forms (3/7 of 350): practice converting the fraction first, then apply.

Multi-step percentage problems (price increased 20%, then decreased 15%): $100 → $120 → $120 × 0.85 = $102. The answer is not $105.

Square roots of non-perfect squares: Practice the interpolation method until it's fast.

Benchmarks

Weeks of training	Typical simulation score	Status
2	25–35 / 80	Building foundation
4	35–45 / 80	Technique integration
6	45–55 / 80	Near-ready
8	55–65 / 80	Ready for test
10+	65+ / 80	Strong candidate

Most candidates who fail the Optiver test started training 2–3 weeks before the test. 8 weeks is the minimum to be competitive; 12 weeks is better.

The Practice Resource

Fermiq's Optiver blitz mode simulates the 80-in-8 format: timed, scored, mixed difficulty. Use it for Phase 3 simulations.

The math category gives you unlimited practice problems for technique development in Phase 2.

The daily drill keeps your arithmetic reflexes sharp even when you're not actively training for an interview.

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Speed is built incrementally, not in bursts. Ten minutes of deliberate daily practice beats two hours on the weekend. Start now and track your progress — the improvement after even one week of consistent drilling is motivating.