Master Pre-Calculus: Tackle Challenging Problems 7 and 24 from Math.unb.ca

[Stratosphere]

I am just starting to get into calculus, I have just self taught my self pre-calculus from another textbook, however when searching online to see if I am ready to proceed into calculus I found that 2 questions have me stumped. Is this a problem? The problems I am talking about are located here: http://www.math.unb.ca/ready/paper.pdf the ones I am confused about are numbers 7. and 24.

 

[Coto]

You will find that these types of questions will pop up a few times in calculus.

Number 7 is just a simplifying type problem. For example, solve for a:

$$x+a = 5$$

would be:

$$a = 5 - x$$.

Of course, the equations they give you are a little bit harder to solve.

For number 14 you want to find all numbers that satisfy those equations. For example, solve:

$$x^2 - 4 = 0$$

That is, find all x such that the above equation holds. Well you would find:

$$x^2 = 4 \implies x = \pm 2$$.

Again, the sample problems are harder than this, and draw on techniques that you should have learned.

 

[Coto]

As a hint for #14. All the equations given are equations of parabolas. The question translates into finding the x-intercepts.

 

[Mentallic]

Coto you misread the OP. He asked for #7 and #24 :tongue:

Stratosphere: For #7 it is basically getting you to touch up on your algebraic manipulation skills. You're given an equation and must solve for one variable.

If you don't remember how to do this very well, these are some examples of the rules you'll need to use:

$$\frac{a}{b}+\frac{c}{d}=x \rightarrow \frac{ad+bc}{bd}=x \rightarrow ad+bc=bdx$$

$$ab+ac=x \rightarrow a(b+c)=x \rightarrow a=\frac{x}{b+c}$$

$$ax^2+bx+c=0 \rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

and of course there will be simple adding/subtracting and multiplying/dividing which you'll need to use as well. This should have you set.

 

[Mentallic]

Coto you misread the OP. He asked for #7 and #24 :tongue:

Stratosphere: For #7 it is basically getting you to touch up on your algebraic manipulation skills. You're given an equation and must solve for one variable.

If you don't remember how to do this very well, these are some examples of the rules you'll need to use:

$$\frac{a}{b}+\frac{c}{d}=x \rightarrow \frac{ad+bc}{bd}=x \rightarrow ad+bc=bdx \rightarrow a=\frac{bdx-bc}{d}$$

$$ab+ac=x \rightarrow a(b+c)=x \rightarrow a=\frac{x}{b+c}$$

$$ax^2+bx+c=0 \rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

and of course there will be simple adding/subtracting and multiplying/dividing which you'll need to use as well. This should have you set.


As for #24, do you know the distance formula? You are told the distance from P(x,y) and A(-1,1) and 3 times the distance from P(x,y) and B(2,-1). Can you form an equation using the distance formula to show this? You will have an equation in 2 variables which, if you simplify by squaring and re-arranging etc. will give you the equation of the curve.

 

[Stratosphere]

Thanks a lot for the help there, I feel kinda dumb about not realizing number 7.