binomial theorem
What is the row of Pascal's triangle that corresponds to the coefficients for the expansion of (a + b)^3?
1, 3, 3, 1
What is the total number of ways to arrange the 5 letters in the word MATHS
120
What is the remainder when P(x) = x^3 - 2x^2 + 4 is divided by (x - 3)
13
multiplication is to division
as cos is to ...
arccos
or
cos inverse
What is the opposite of differentiation
integration
What is the 3rd term in the expansion of (x + 2)^4?
24x^2
What is the number of distinct committees of 3 people that can be chosen from a group of 8 candidates
56
According to Vieta's formulas, what is the product of the three roots of the cubic equation x^3 - 4x^2 + x + 6 = 0
-6
What is the negative solution to the absolute value equation |2x - 5| = 9
-2
What is this called: Σ
sigma
What is the numerical value of the constant term in the expansion of (x + (1/x))^6
20
What is the number of ways to choose a committee of 5 people from 6 men and 5 women if the committee must contain at least 3 women?
181
What is the value of k such that (x + 2) is a factor of P(x) = x^3 + kx^2 - 4
3
what determines if a function is inverse?
(2 possible answers, only need 1)
if and only if it is one-to-one
or
if it passes the horizontal line test
Who is currently living and is widely regarded as the best mathematician in the world right now
hint: their nickname is the “Mozart of Math”
terrance tao
What is the numerical value of the sum of the binomial coefficients 6C0 + 6C1 + 6C2+ 6C3 + 6C4 + 6C5 + 6C6
64
What is the number of distinct circular seating arrangements for 5 people if 2 specific individuals are not permitted to sit next to one another?
12
What is the value of the double root of the polynomial P(x) = x^3 - 3x + 2
x=1
What is the complete solution set to the non-linear inequality (x + 3)/(x - 2)≥0
x≤-3 , x>2
or in interval notation:
(-infinity, -3] U (2, infinity)
What is the major step that is used to derive the quadratic formula
completing the square
what is the highest coefficient in the expression (2x+3)^8
108,864
What is the number of ways 5 boys and 5 girls can stand in a line if all the girls must stand together
For the cubic x^3 - 7x^2 + 14x - 8 = 0, the three roots form an arithmetic progression. What is the value of the middle root
hint: roots in form (a-d,a,a+d)
a=7/3
What are the centre and radius of the circle defined by the parametric equations x = 3 + 4cost and y = -2 + 4sint
centre 3, -2
radius 4
What is the 8th problem on David Hilbert's 1900 list of 23 unsolved mathematical challenges, which concerns the non-trivial zeroes of the zeta function and remains the most famous open problem in number theory?
Riemann Hypothesis