math Actual Questions and Correct Answers
Q1
9 Properties of a field
Answer: 1. a + (b + c) = (a + b) + c (associative +)
Q2
Three additional rules (that make R a line)
Answer: 10. For all a, either a = 0, a < 0, or a > 0.
Q3
Triangle inequality
Answer: |a + b| ≤ |a| + |b|
Q4
Well-ordering principle
Answer: If a set A has no smallest member, it must be empty. (Proof by using another
set B which contains all numbers not in A, and through induction, prove that 1...n has
to be in B, so not A)
Q5
(n k)
Answer: n!/(k!(n-k)!) = (n(n-1)...(n-k+1))/k!
Q6
Function
Answer: a collection of sets that satisfies that if (a,b) and (a,c) are in f then c = b
(vertical line test)
Q7
(a+b)^n
Answer: sum of j = 1 to n: (n j)(a^(n-j)b^j)
, Q8
Difference of perfect cubes
Answer: a^3-b^3=(a-b)(a^2+ab+b^2)
Q9
Even function
Answer: f(x) = f(-x)
Q10
Odd function
Answer: f(x) = -f(-x)
Q11
Injection function (one-one)
Answer: If (a,b), (c,b) are in f, then a = c (horizontal line test)
Q12
Surjection function (onto)
Answer: For every b in codomain there is an a in domain such that (a,b) is in the
function (all of the codomain is covered)
Q13
Circle
Answer: (x-a)^2 + (y-b)^2 = r^2 r = radius of circle
Q14
Ellipse
Answer: (x^2)/(a^2) + (y^2)/(b^2) = 1
Q15
Hyperbola
Answer: (x^2)/(a^2) - (y^2)/(b^2) = 1
Q1
9 Properties of a field
Answer: 1. a + (b + c) = (a + b) + c (associative +)
Q2
Three additional rules (that make R a line)
Answer: 10. For all a, either a = 0, a < 0, or a > 0.
Q3
Triangle inequality
Answer: |a + b| ≤ |a| + |b|
Q4
Well-ordering principle
Answer: If a set A has no smallest member, it must be empty. (Proof by using another
set B which contains all numbers not in A, and through induction, prove that 1...n has
to be in B, so not A)
Q5
(n k)
Answer: n!/(k!(n-k)!) = (n(n-1)...(n-k+1))/k!
Q6
Function
Answer: a collection of sets that satisfies that if (a,b) and (a,c) are in f then c = b
(vertical line test)
Q7
(a+b)^n
Answer: sum of j = 1 to n: (n j)(a^(n-j)b^j)
, Q8
Difference of perfect cubes
Answer: a^3-b^3=(a-b)(a^2+ab+b^2)
Q9
Even function
Answer: f(x) = f(-x)
Q10
Odd function
Answer: f(x) = -f(-x)
Q11
Injection function (one-one)
Answer: If (a,b), (c,b) are in f, then a = c (horizontal line test)
Q12
Surjection function (onto)
Answer: For every b in codomain there is an a in domain such that (a,b) is in the
function (all of the codomain is covered)
Q13
Circle
Answer: (x-a)^2 + (y-b)^2 = r^2 r = radius of circle
Q14
Ellipse
Answer: (x^2)/(a^2) + (y^2)/(b^2) = 1
Q15
Hyperbola
Answer: (x^2)/(a^2) - (y^2)/(b^2) = 1
