Practice
Quick math
Two ways in. Learn shows the trick on every question with no clock. Sprint is the timed test. Start on level 1 and move up when accuracy is above 80%.
Categories
Level
No sprints yet. Your best score per category shows here.
The tricks, each with its own practice
Swap the percent
a% of b equals b% of a. Pick whichever is easier.
8% of 25 = 25% of 8 = 2
Percent ladder
Find 10% by moving the decimal, halve it for 5%, take a tenth of it for 1%, then add the pieces.
17% of 340: 34 + 17 + 6.8 = 57.8
Times 5, 25, 50
× 5 is half of × 10. × 25 is a quarter of × 100. × 50 is half of × 100.
48 × 25 = 4,800 ÷ 4 = 1,200
Divide by 5
Double it, then divide by 10.
135 ÷ 5 = 270 ÷ 10 = 27
Round, multiply, adjust
Round one number to the nearest 10, multiply, then add or subtract the difference.
19 × 21 = 20 × 21 − 21 = 399
Squares near a round number
(a + b)² = a² + 2ab + b². Use a = 10, 20, 50, or 100.
23² = 400 + 120 + 9 = 529
Square roots by squeezing
Find the two perfect squares around it, then interpolate. Memorize √n for common sample sizes.
√50: between 7² = 49 and 8² = 64, so about 7.07
Mean by gaps from a base
Pick a round base, add up the gaps from it, divide by n, and add back to the base.
72, 81, 78, 69, 76: base 75, gaps −3, +6, +3, −6, +1 add to 1, 1 ÷ 5 = 0.2, mean 75.2
Median in two moves
Sort, then take the middle. With an even count, average the two middles.
82, 74, 65, 80, 58 → 58, 65, 74, 80, 82 → 74
How many SDs away
(value − mean) ÷ SD. The sign matters. Then the anchors: 1 SD above is about 84% below it, 2 SD above is about 97.7%.
Mean 400, SD 50, value 475: (475 − 400) / 50 = 1.5
Probability fractions
The fractions that show up constantly. Learn them as percents.
1/6 = 16.7%, 13/52 = 25%, 12/51 = 23.5%, 1/36 = 2.8%
Powers of 0.8 and 0.9
None-of-n questions. Each step drops by 20% or 10%.
0.8⁵ = .33, 0.9¹⁰ = .35, 0.95¹⁰ = .60
e to a negative power
Poisson P(0) and the empty-window question. Each step divides by about 2.7.
e⁻¹ = .37, e⁻² = .135, e⁻³ = .05, e⁻⁴ = .018
z anchors
The area to the left of z. Everything else is subtracting from these.
z = 1 → 84%, 1.645 → 95%, 1.96 → 97.5%, 2 → 97.7%
Standard error by √n
σ ÷ √n. Use the √n table: √16 = 4, √25 = 5, √36 = 6, √49 = 7, √64 = 8, √100 = 10.
σ = 18, n = 36: 18 ÷ 6 = 3
Ballpark it
Round both numbers to one digit, multiply or divide, then nudge. Anything within 15% counts.
47 × 62 ≈ 50 × 60 = 3,000 (exactly 2,914)