give me 10 questions on binomial theorem, 10 questions on quadratic functions, 10 questions on linear functions, 10 questions on piecewise functions, 10 questions about domain and range of linear, quadratic, and piecewise functions, and 10 questions that are a mix of all of the prompts previously mentioned. All the questions must be 11th grade level and able to be done without a calculator.
what is n
the exponent
what is r
the position of a specific term in the sequence
if they ask for the 5th term, r = 4
max number of terms
n+1
n choose r
n! / (n-r)! r!
find the xth term in the sequence
t(r+1) = (n choose r) (a^n-r) (b^r)
how do exponents increase
a - starts at exponenet then goes down to 0
b - starts at 0 and goes up to exponent
how do coefficients increase
(n choose 0), (n choose 1), (n choose 2), etc
the xth term in the expansion of (ax+by)^n is ____. find a and b
- identify n and r from exponents of the term
- set up equation of T(r+1) = (n choose r)
- (n choose r) x A x B = coefficient of term
- remember it is a^n-r and b^r. so now find what numbers could be a and b so that when added together = answer from pervious step
in the expansion of (ax x b)^n, find the coefficient of x^_
just go through the various (n choose r) until you find which one matches the x^_.
proofs
do LHS =
steps
steps
steps
answer = RHS
a ^ n x b^n
(a x b) ^n
parallel lines
gradeints are equal
y intercepts are diff
perpendicular lines
gradients are negative recipricol
y intecepts are diff
possibilities of system of equations
no solution = parallel
unique solution = intersection
infinite # of solutions = same line
substitution
make one equation = the other
or replace a variable
elimination
make equations have one of the same numbers but opposite signs, add them to eliminate that number
midsection
(x1 + x2/2), (y1+y2/2)
piecewise function
function with 2 or more equations for diff intervals of the domain
how to read piecewise function
equation only works when x falls into the domain that the equation is assigned to
domain
all possible x values
range
all possible y values
standard form
y intercept is found when x = 0
vertex = (h,k) - find h by doing -b/2a
zeros are found by setting function = 0 - solve via factoring or quadratic equation
line of symmetry: x =
factored form
whether a is positive or negative says whether its concave up or down
gives you the zeros (always do the parenthesis = 0 to solve for zeros)
from this, find x coordinate of vertex by doing (p+q/2)
