20 Problems · All Topics · With Full Solutions
Concepts → Examples → Practice → Review
Step 1 — Master the Concepts
A prime has exactly 2 factors. The number of factors of n = pᵃqᵇrᶜ... equals (a+1)(b+1)(c+1)...
LCM(a,b) × GCD(a,b) = a × bSum of 1 to n = n(n+1)/2Set up variables carefully. Distance = Rate × Time. Work problems: if A does a job in p days and B in q days, together they finish in pq/(p+q) days.
d = r × tTogether: pq / (p+q) daysTriangle area = ½bh. Circle area = πr². The sum of interior angles of an n-gon = (n−2)×180°.
Circle area = π r²Interior angles: (n−2)×180°P(event) = favorable outcomes ÷ total outcomes. Combinations: C(n,k) = n! / (k!(n-k)!). Permutations: P(n,k) = n!/(n-k)!
C(n,k) = n! / (k!(n−k)!)Mean = sum ÷ count. Median = middle value when sorted. Percent change = (new−old)/old × 100%. Mark up, mark down, and tax are all percent applications.
% change = (new−old)/old × 100Arithmetic sequence: aₙ = a₁ + (n−1)d. Geometric sequence: aₙ = a₁ · rⁿ⁻¹. Sum of arithmetic series = n(a₁+aₙ)/2.
Arith. sum = n(a₁ + aₙ)/2Step 2 — Study the Examples
How many positive integers less than 50 are divisible by both 3 and 4?
A rectangle has a perimeter of 30 and one side of length 7. What is its area?
A bag contains 3 red and 5 blue marbles. If one marble is drawn at random, what is the probability it is red?
Step 3 — Test Yourself