Complete Syllabus & Gap Fillers

Study Sheet

Complete Syllabus & Gap Fillers

Everything the AMC 8 tests, with the pieces that were missing

What the AMC 8 Tests

Concept
The checklist

Arithmetic and fractions/decimals/percents; ratios, rates, and unit conversion; basic number theory (divisibility, primes, LCM/GCD, remainders, digit problems); counting (lists, complements, simple casework, permutations of small sets); probability of simple events; averages and simple statistics (mean, median, mode, range); geometry (perimeter, area, angle sums, triangles, circles, coordinate basics, Pythagorean triples); patterns and sequences; logic puzzles and reading carefully. Twenty-five questions, forty minutes, no calculators.

Gap Fillers

Tip
Rates and work

Distance == rate ×\times time; average speed is TOTAL distance over TOTAL time, never the average of speeds (6060 km at 3030 km/h and 6060 at 6060 km/h averages 4040). Work problems add RATES: pipes filling in 66 and 33 hours together fill 16+13=12\tfrac16 + \tfrac13 = \tfrac12 per hour.

Tip
Statistics in one box

Mean = total ÷\div count (so "the mean of 77 numbers is 1010, remove one, mean becomes 99" means the removed number is 70−54=1670 - 54 = 16). Median is the middle of the sorted list; mode the most frequent; range max minus min. Adding a constant shifts mean/median; multiplying scales them.

Tip
Clock and calendar angles

The minute hand moves 6∘6^\circ per minute, the hour hand 0.5∘0.5^\circ per minute (and 30∘30^\circ per hour). At 3:403{:}40: minute at 240∘240^\circ, hour at 110∘110^\circ, angle 130∘130^\circ. Days of the week cycle mod 77; leap years add a day.