Ethen Choy's High School Portfolio
10th Grade (2019-2020)
Math 4 Honors
Ms. Kristina Lupher
Identify the holes, intercepts, HA, VA, and SA, then graph.
Multiply and simplify.
Divide and simplify.
Add and simplify.
Subtract and simplify.
Solve the inequality.
Completely factor x^2+6x+8
= (x+4)(x+2)
Completely factor 3x^2+4x-7
= (3x+7)(x-1)
Completely factor
= x^2(x-7) – 3(x-7)
= (x^2-3)(x-7)
Completely factor 2x^4-28x^2+90
= 2(x^4-14x^2+45)
= 2(x^2-9)(x^2-5)
= 2(x+3)(x-3)(x^2-5)
Completely factor.
= 2x^4-28x^2+90
= 2(x^4-14x^2+45)
= 2(x^2-9)(x^2-5)
= 2(x+3)(x-3)(x^2-5)
x=-3, 3, +-sqrt 5
Rewrite in vertex form.
Find a polynomial function with the given zeros: 0, 2 mult 2
Divide with Long Division
Divide with Synthetic Division
Use the Rational Roots Theorem to find all possible roots and then solve.
Domain – the span of all the x-values of a function
Range – the span of all the y-values of a function
x-intercept(s) – the point(s) where a function touches the x-axis
y-intercept – the point where a function touches the y-axis
Horizontal asymptote(s) – the imaginary line(s) where the domain of a rational function approaches on both sides but never touches.
Vertical asymptote – the imaginary line(s) where the range of a rational function approaches above and below but never touches.
Local minimum – the point where a positive even polynomial’s vertex is, where the function does not go any lower.
Local maximum – the point where a negative even polynomial’s vertex is, where the function does not go any higher.
End behavior – the direction, attributes, and/or limit of a function as it goes left or right.
The height of a passenger on an escalator is modeled as
where t is the time in seconds after the passenger has boarded the escalator on the second floor and h is the height in feet above the first floor.
This means it takes the passenger 16 seconds to reach the first floor (0 feet).
This means the passenger is 12 feet above the first floor when he/she first gets on the escalator. Likewise, this also means that the second floor is 12 feet above the first floor.
Find the inverse of the following function:
Find f(g(x)) and its domain if:
and:
Find what h(x) decomposes into if:
and:
A sequence expressed in the form of an operation that is performed on the previous term of the sequence to find the next. To use a recursive sequence, the previous term must be given to calculate any following terms.
Example: Find the first 4 terms of the recursive sequence below.
A sequence expressed in the form of an equation in terms of n, where n is the term’s position in the sequence. This method of expressing a sequence does not require any previous terms to find following terms; it only requires you have the position of the term (n) you are looking for and the first term of the sequence.
Example: Find the first 4 terms of the explicit sequence below.
Example: Find the 4th term of an Arithmetic sequence with a first term of 7 and a common difference of -4.
Example: Find the sum of the first 10 terms of an Arithmetic sequence with a first term of 7 and a common difference of -4.
Example: Find the 6th term of a Geometric sequence with a first term of 2 (a1) and a common ratio of 3 (r).
Example: Find the 6th term of a Geometric series with a first term of 2 (a1) and a common ratio of 3 (r).
A cybersecurity technician has a starting salary $106,000. Per his contract with the company, he is given a 5% raise each year. If he works for 20 years, how much will he have earned total by the end?
a1 = 106,000 because the salary starts at $106,000
r = 105% or 1.05 because the salary increases by 5% each year
n = 20 because the technician is working 20 years
A convergent series has an r value with an absolute value less than 1, meaning the sequence will get closer and closer to 0 as it progresses. This means you can calculate the sum of the series to the infinite term, as there will be a finite sum.
For example, the geometric series in the previous question has an r value of 1/2 (|1/2|<1), because its terms are getting closer and closer to 0 (in this case, smaller and smaller)
On the other hand, a divergent series has an r value with an absolute value greater than 1, meaning the sequence will get farther and farther away from 0 as it progresses. Because of this, you cannot find the sum to an infinite term as the sequence has no limit to how large its terms it can get.
For example, this geometric series has an r value of 2 (|2|>1), which means the terms will get larger and larger, farther and farther away from 0, meaning there is no real way to find an infinite total of the series since there is no limit to how high it will go.
Find the sum using the correct sequence formula.
Expand completely.
Find the 3rd term in expansion of
