This quarter, I will take the course "Calculus for social sciences." Here's the description:

"Introduction to differential and integral calculus with applications to modeling in the biological sciences," and "study of differential and integral calculus with differential and integral calculus with applications. Introduction to mathematical modeling with differential equations. Calculus of several variables including an introduction to partial derivatives."

What pre-calculus do I need to know? I bought a quick review book, here's the table of contents. if someone could point out which things I should know, that would be incredibly helpful:

Chapter 2: Functions.

- Relations vs. Functions

- Functions Graphs and transformations

- Combining functions

- inverse functions

Chapter 3: Polynomial and Rational Functions.

- Factoring

- Solving quadratic EQs

- Polynomial division

- Important root-thereoms

- Calculating roots

- Finding rational asymptotes & the "the leading coeficcient test."

Chapter 4: Exponential and Logarithmic Functions.

- Exponential and logarithmic functions

- Properties of Logs.

- Solving Ex. and Log. functions

- Exponential word problems.

Chapter 5: Trigonometry.

- Measuring angles

- Unit circle

- Right triangle trig.

- Oblique triangle trig

- Graphs of sin and cosine

- Other trig function graphs

- inverse trig functions

Chapter 6: Analytic Trigonometry.

- Trig identities

- Proving trig identities

- Solving trig identities

- sum and difference identities

- Additional identities

- Oblique triangle laws

- Calculating triangle area.

- Given side-angle-side

Chapter 7: Vectors and the Trigonometry of Complex Numbers.

- vectors in the coordinate plane

- Dot products

- complex numbers and trig

- roots and powers of complex numbers

Chapter 8: Analytic Geometry.

- conic sections

- circles, parabolas, ellipses,

- hyperbolas

- identifying conic sections

- parametric equations

- polar coordinates

Chapter 10: Additional Topics.

- Binomial expansion

- Ordered number lists.

If someone could help me out that would be awesome, currently Im spending my whole winter breaking reviewing pre-calculus

## What pre-calculus needed for this calculus class?

**Moderators:** gmalivuk, Moderators General, Prelates

### Re: What pre-calculus needed for this calculus class?

Often times classes like those avoid trig functions. So I would say to put most of your study effort towards chapter 2,3 and 4. And then possibly review a bit of the vector material from chapter 7.

- Yakk
- Poster with most posts but no title.
**Posts:**11129**Joined:**Sat Jan 27, 2007 7:27 pm UTC**Location:**E pur si muove

### Re: What pre-calculus needed for this calculus class?

What do you actually know? I'll ask some questions.

Polynomials:

1a) If I say f(x) = (x^2-1)^2 / (x^2 -2x +1). Evaluate f(1), f(3), f(5), and f(7).

1b) Let g(x) = (x+1)^2. Evaluate g(1), g(3), g(5) and g(7).

1c) Let h(x) = f(x)-g(x). Calculate h(100) without using a calculator. Justify your answer. Note that there are better and worse justifications.

1d) Which of these polynomials has a real root? If so, how many real roots does it have?

x^2 + 2x +1

x^2

x^2 - 5x +10

x^2 - 2x +1

x^2 - 7

(you should be able to do this in your head)

Inverses:

2) Let d(x) = 2x+1. Let e(x) = d(x)*d(x). Express d^-1(e(x)) in a pretty form.

Exponential:

3a) Calculate log

3b) Let 1000 = 3^x. Find x to zero decimal places without a calculator (paper allowed). Find x to two decimal places with a calculator.

3c) Every year, the nation's GDP grows by 5% in real, inflation-adjusted dollars, and inflation is 2% (both are annual percentage rates). The government budget is 30% of the size of the economy, and it has a debt equal to 100% of the economy's size. If it stops borrowing any additional money, and just pays off interest, keeping the dollar value of the debt constant, how many years will it be until the debt is below the government budget? How many years before it falls below 10% of the government's budget?

What if it borrows money at a rate that allows the debt to grow at the rate of inflation?

What if it borrows money so that the debt grows by 3% per year?

---

Your ability to answer the above, or not, might give us a good idea of where you are at.

Polynomials:

1a) If I say f(x) = (x^2-1)^2 / (x^2 -2x +1). Evaluate f(1), f(3), f(5), and f(7).

1b) Let g(x) = (x+1)^2. Evaluate g(1), g(3), g(5) and g(7).

1c) Let h(x) = f(x)-g(x). Calculate h(100) without using a calculator. Justify your answer. Note that there are better and worse justifications.

1d) Which of these polynomials has a real root? If so, how many real roots does it have?

x^2 + 2x +1

x^2

x^2 - 5x +10

x^2 - 2x +1

x^2 - 7

(you should be able to do this in your head)

Inverses:

2) Let d(x) = 2x+1. Let e(x) = d(x)*d(x). Express d^-1(e(x)) in a pretty form.

Exponential:

3a) Calculate log

_{4}( 2^100 ) in your head.3b) Let 1000 = 3^x. Find x to zero decimal places without a calculator (paper allowed). Find x to two decimal places with a calculator.

3c) Every year, the nation's GDP grows by 5% in real, inflation-adjusted dollars, and inflation is 2% (both are annual percentage rates). The government budget is 30% of the size of the economy, and it has a debt equal to 100% of the economy's size. If it stops borrowing any additional money, and just pays off interest, keeping the dollar value of the debt constant, how many years will it be until the debt is below the government budget? How many years before it falls below 10% of the government's budget?

What if it borrows money at a rate that allows the debt to grow at the rate of inflation?

What if it borrows money so that the debt grows by 3% per year?

---

Your ability to answer the above, or not, might give us a good idea of where you are at.

One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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