MATH 110 Exam Questions With Answers Verified By Experts

Real #s - ANSWER-Irrational, rational, and whole #s Find the distance between 2 pts. on # line - ANSWER-Take the absolute value of the difference between the 2 pts. d(P,Q) = | b - a | Which values must be excluded from the domain of the variable in the expression? - ANSWER-Substitute the variables into the problem - the denominator cannot equal 0. Negative exponents - ANSWER-a⁻ⁿ = 1/aⁿ Law of Exponents - ANSWER-(a×)ⁿ = a×·ⁿ (a · b)ⁿ = aⁿ · bⁿ (aⁿb*)^ = aⁿ^b*^ xⁿx* = xⁿ⁺* xⁿyⁿ = (xy)ⁿ xⁿ/x* = xⁿ⁻* xⁿ/yⁿ = (x/y)ⁿ x⁰ = 1 a⁰ = 1 if a ≠ 0 When multiplying exponents, you add them. Cannot distribute exponents when adding or subtracting Ex → (5x-7)² Square roots - ANSWER-√a² = |a| Tip: Rewrite expressions without negs or neg exponents - ANSWER-... Circle - ANSWER-A = πr² C = πd or 2πr Rectangular box - ANSWER-v = l · w · h S.A. = 2LH + 2WH + 2LW Sphere - ANSWER-V = 4/3πr³ S.A. = 4πr² Right circular cylinder - ANSWER-V = πr²h S.A. = 2πr² +2πrh Triangle - ANSWER-A = 1/2bh Divide fractions - ANSWER-a/b ÷ c/d = a/b · d/c Monomial - ANSWER-axⁿ OR axⁿy* To find the degree of a monomial with two exponents add them together. Cannot have negative exponents or exponents that are fractions. Polynomial - ANSWER-Cannot have negative exponents Ex of polynomial → 8x³-9x⁷ Cube of Binomials or Perfect Cubes - ANSWER-(x-a)³ = x³ - 3ax² + 3a²x - a³ Factoring Polynomials when the L. Coefficient ≠ 1 - ANSWER-Find 2 #s that multiply to equal the first and last term and when added equal the middle term. Then write these #s into the equation. Ex → 9x² + 15x + 4 → 9x² + 12x + 3x +4 Then factor by grouping. → 3x (3x +4) + 1(3x+4) Perfect square trinomial? - ANSWER-1st term is perfect square, last term is perfect square, middle term is 2x the product of the square roots. Prime - ANSWER-If a polynomial has no factors other than 1 and itself. When x² + a², where a is a real # Factoring - Ex: 16x² - 81 - ANSWER-See if the terms share a common monomial factor Check if the polynomail is a special product - rewrite as x² - a² If special then