precalc

#$&*

course phy 201

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(7,17) to (10,29) will be steeper since it does not increase as much on the x axis and increases more on the y axis.

Slope = 3

Slope = 4

Confidence: 3

*********************************************

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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Because when x = 2, the first part of the expression will equal 0 and therefore the answer will be 0 when the second half is multiplied by 0. When x = -2.5, the second half of the expression equals 0 and therefore the product will be 0 when the two halves are multiplied together.

Confidence: 3

*********************************************

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

3x - 6 = 0

x = 2

x + 4 = 0

x = -4

x^2 -4 = 0

x = 2 or -2

Confidence: 3

*********************************************

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'.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The second trapezoid’s area is bigger. Although the first trapezoid is taller, the second’s length is significantly larger. Since a trapezoid area is dependent on height and length, the second’s overwhelming length makes it much larger in area than the first.

Confidence: 3

*********************************************

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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

As we move from left to right, the graph increases as the slope increases for x^2.

For 1/x the graph decreases as the slope increases.

The square root of x causes the graph to increase while the slope decreases.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

1st mo. - 22

2nd mo. - 24.2

3rd mo. - 26.42

If you raise 1.1 to the 300th power we could find the number of frogs after 300 months.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The numbers increase my multiples of ten.

Because the positive numbers are decreasing.

.0001, .00001, etc.

The values continue to increase by multiples of ten

The graph 1/x would be much steeper and much bigger than x alone.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

V = 3(5) + 9

V= 24

E= 800 x 24^2

E= 460,800

Confidence: 3

"

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

precalc

#$&*

course phy 201

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(7,17) to (10,29) will be steeper since it does not increase as much on the x axis and increases more on the y axis.

Slope = 3

Slope = 4

Confidence: 3

*********************************************

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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Because when x = 2, the first part of the expression will equal 0 and therefore the answer will be 0 when the second half is multiplied by 0. When x = -2.5, the second half of the expression equals 0 and therefore the product will be 0 when the two halves are multiplied together.

Confidence: 3

*********************************************

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

3x - 6 = 0

x = 2

x + 4 = 0

x = -4

x^2 -4 = 0

x = 2 or -2

Confidence: 3

*********************************************

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'.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The second trapezoid’s area is bigger. Although the first trapezoid is taller, the second’s length is significantly larger. Since a trapezoid area is dependent on height and length, the second’s overwhelming length makes it much larger in area than the first.

Confidence: 3

*********************************************

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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

As we move from left to right, the graph increases as the slope increases for x^2.

For 1/x the graph decreases as the slope increases.

The square root of x causes the graph to increase while the slope decreases.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

1st mo. - 22

2nd mo. - 24.2

3rd mo. - 26.42

If you raise 1.1 to the 300th power we could find the number of frogs after 300 months.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The numbers increase my multiples of ten.

Because the positive numbers are decreasing.

.0001, .00001, etc.

The values continue to increase by multiples of ten

The graph 1/x would be much steeper and much bigger than x alone.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

V = 3(5) + 9

V= 24

E= 800 x 24^2

E= 460,800

Confidence: 3

"

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

#*&!

precalc

#$&*

course phy 201

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(7,17) to (10,29) will be steeper since it does not increase as much on the x axis and increases more on the y axis.

Slope = 3

Slope = 4

Confidence: 3

*********************************************

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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Because when x = 2, the first part of the expression will equal 0 and therefore the answer will be 0 when the second half is multiplied by 0. When x = -2.5, the second half of the expression equals 0 and therefore the product will be 0 when the two halves are multiplied together.

Confidence: 3

*********************************************

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

3x - 6 = 0

x = 2

x + 4 = 0

x = -4

x^2 -4 = 0

x = 2 or -2

Confidence: 3

*********************************************

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'.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The second trapezoid’s area is bigger. Although the first trapezoid is taller, the second’s length is significantly larger. Since a trapezoid area is dependent on height and length, the second’s overwhelming length makes it much larger in area than the first.

Confidence: 3

*********************************************

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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

As we move from left to right, the graph increases as the slope increases for x^2.

For 1/x the graph decreases as the slope increases.

The square root of x causes the graph to increase while the slope decreases.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

1st mo. - 22

2nd mo. - 24.2

3rd mo. - 26.42

If you raise 1.1 to the 300th power we could find the number of frogs after 300 months.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The numbers increase my multiples of ten.

Because the positive numbers are decreasing.

.0001, .00001, etc.

The values continue to increase by multiples of ten

The graph 1/x would be much steeper and much bigger than x alone.

Confidence: 3

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

V = 3(5) + 9

V= 24

E= 800 x 24^2

E= 460,800

Confidence: 3

"

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