Precalculus

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course Mth 163

Jan 13 6PM

Pre-calculus *********************************************

Question: `q001 A straight line connects the points (3, 5) and (7, 17), while another straight line continues on from (7, 17) to the point (10, 29). Which line is steeper and on what basis to you claim your result?

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Your solution:

(7,17) and (10,29) has a steeper slope based on the slope intercept form and y=mx+b form

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3

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Question: `q002. The expression (x-2) * (2x+5) is zero when x = 2 and when x = -2.5. Without using a calculator verify this, and explain why these two values of x, and only these two values of x, can make the expression zero.

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Your solution:

-2.5*2=-5 2(-2.5)+5=0

-5*0=0

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3

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Question: `q003. For what x values will the expression (3x - 6) * (x + 4) * (x^2 - 4) be zero?

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Your solution:

-4

(-4)+4=0 whatever the other numbers turn out to be when you multiply it by 0 the answer is 0

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3

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Question: `q004. One straight line segment connects the points (3,5) and (7,9) while another connects the points (10,2) and (50,4). From each of the four points a line segment is drawn directly down to the x axis, forming two trapezoids. Which trapezoid has the greater area? Try to justify your answer with something more precise than, for example, 'from a sketch I can see that this one is much bigger so it must have the greater area'.

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Your solution:

1st

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2

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Question: `q005. Sketch graphs of y = x^2, y = 1/x and y = `sqrt(x) [note: `sqrt(x) means 'the square root of x'] for x > 0. We say that a graph increases if it gets higher as we move toward the right, and if a graph is increasing it has a positive slope. Explain which of the following descriptions is correct for each graph:

As we move from left to right the graph increases as its slope increases.

As we move from left to right the graph decreases as its slope increases.

As we move from left to right the graph increases as its slope decreases.

As we move from left to right the graph decreases as its slope decreases.

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Your solution:

X^2 increase as it increases

1/x decreases as increases

Sqrt(x) increases as decreases

confidence rating #$&*:

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3

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Question: `q006. If the population of the frogs in your frog pond increased by 10% each month, starting with an initial population of 20 frogs, then how many frogs would you have at the end of each of the first three months (you can count fractional frogs, even if it doesn't appear to you to make sense)? Can you think of a strategy that would allow you to calculate the number of frogs after 300 months (according to this model, which probably wouldn't be valid for that long) without having to do at least 300 calculations?

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Your solution:

1st month 22

2nd month 24.2

Just multiply by 1.1 each month

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3

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Question: `q007. Calculate 1/x for x = 1, .1, .01 and .001. Describe the pattern you obtain. Why do we say that the values of x are approaching zero? What numbers might we use for x to continue approaching zero? What happens to the values of 1/x as we continue to approach zero? What do you think the graph of y = 1/x vs. x looks for x values between 0 and 1?

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Your solution:

You approach zero because you increasing the decimal place from hundredths to thousandsths and so on.

The next number in the sequence would be .0001

confidence rating #$&*:

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3

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Question: `q008. At clock time t the velocity of a certain automobile is v = 3 t + 9. At velocity v its energy of motion is E = 800 v^2. What is the energy of the automobile at clock time t = 5?

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Your solution:

E=460800

confidence rating #$&*:

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3

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Question: `q009. Continuing the preceding problem, can you give an expression for E in terms of t?

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Your solution:

E=800(3t+9)^2

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Self-critique (if necessary):

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Self-critique rating:

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You got most of this but not all, and you lacked sufficient detail on at least some of your solutions.

I'm going to ask you to resubmit and include the entire document.

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Many of your answers can just be copied and pasted into that document.

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