First Names

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(C)Copyright 2018, C. Burke.

Either it's a fat hamster or it's ironic.




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Spread Sheets

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(C)Copyright 2018, C. Burke.

I needed to work on my delivery and wording and context ... and then I gave it to the kids.

What are the girls talking about? We'll find out really soon with (x, why?) School Life.




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Rocks Rock!

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(C)Copyright 2018, C. Burke.

And as a math teacher, I can appreciate a good complement.




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Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

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June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


10. A game spinner is divided into 6 equally sized regions, as shown in computations. the diagram below.
For Miles to win, the spinner must land on the number 6. After spinning the spinner 10 times, and losing all 10 times, Miles complained that the spinner is unfair. At home, his dad ran 100 simulations of spinning the spinner 10 times, assuming the probability of winning each spin is 1/6. The output of the simulation is shown in the diagram below.
Which explanation is appropriate for Miles and his dad to make?
1) The spinner was likely unfair, since the number 6 failed to occur in about 20% of the simulations.
2) The spinner was likely unfair, since the spinner should have landed on the number 6 by the sixth spin.
3) The spinner was likely not unfair, since the number 6 failed to occur in about 20% of the simulations.
4) The spinner was likely not unfair, since in the output the player wins once or twice in the majority of the simulations.

Answer: 3) The spinner was likely not unfair, since the number 6 failed to occur in about 20% of the simulations.
Since the number 6 didn't show up in 20% of the simulations, it is not unreasonable that it wouldn't occur in 10 spins of a spinner, even if it seems to be unlikely.

11. Which binomial is a factor of x⁴ - 4x² - 4x + 8?
1) x - 2
2) x + 2
3) x - 4
4) x + 4

Answer: 1) x - 2
If you graph the function, it has two zeroes, at (approximately) x = 1.13 and 2. So (x - 2) is a factor.

Alternatively, you could calculate to see if there would be a remainder. Luckily, the first choice is the answer.

12. Given that sin²θ + cos²θ = 1 and sin θ = - SQRT(2)/5, what is a possible value of cos θ?

Answer: 2) -0.15x³ - 0.02x² + 28x - 120
If sin θ = -SQRT(2)/5, sin²θ = (-sqrt(2)/5)² = 2/25.
This means that cos²θ = 23/25, and cos θ = SQRT(23/25), which is +Sqrt(23)/5.

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A Question?

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(C)Copyright 2018, C. Burke.

Anyone? Anyone? Bueller? Bueller?

More than just a little semi-autobiographical.




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Imaginary

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(C)Copyright 2018, C. Burke.

I wonder if he could imagine asking a girl to the pizza parlor after school ....

I actually thought about having the new girl like Vaughn who likes Missy (who seemed indifferent) because that would create ...

A love triangle. What could be more mathematical than that?




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Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


7. The solution to the equation 4x² + 98 = 0 is
1) + 7
2) + 7i
3) + 7*SQRT(2)/2
4) + 7i*SQRT(2)/2

Answer: 4) + 7i*SQRT(2)/2
This isn't the difference of squares. It has a sum, so when we move it to the other side of the equation, you have to take the square root of a negative number. That means an i in the answer.

4x² + 98 = 0
4x² = -98
x² = -98/4
x² = (-1)(2)(49)/(4)
x = +SQRT((-1)(2)(49)/(4))
x = + 7i*SQRT(2)/2

8. Which equation is represented by the graph shown below?

1) y = 1/2 cos 2x
2) y = cos x
3) y = 1/2 cos x
4) y = 2 cos 1/2x

Answer: 1) y = 1/2 cos 2x
At x = 0, the graph is at 0.5, or 1/2, so this eliminates choices 2 and 4, which would have amplitudes of 1 and 2, respectively. The cycle repeats at 1 pi, instead of 2 pi, so the answer is choice 1.

9. A manufacturing company has developed a cost model, C(x) = 0.15x³ + 0.01x² + 2x + 120, where x is the number of items sold, in thousands. The sales price can be modeled by S(x) = 30 − 0.01x. Therefore, revenue is modeled by R(x) = x • S(x). The company's profit, P(x) = R(x) − C(x), could be modeled by
1) 0.15x³ + 0.02x² - 28x + 120
2) -0.15x³ - 0.02x² + 28x - 120
3) -0.15x³ + 0.01x² - 2.01x - 120
4) -0.15x³ + 32x + 120

Answer: 2) -0.15x³ - 0.02x² + 28x - 120
Substitute. Multiply. Combine like terms.
P(x) = R(x) − C(x)
P(x) = x • S(x) − C(x)
P(x) = x (30 − 0.01x) - (0.15x³ + 0.01x² + 2x + 120)
P(x) = 30x − 0.01x² - 0.15x³ - 0.01x² - 2x - 120
P(x) = - 0.15x³ − 0.01x² - 0.01x² + 30x - 2x - 120
P(x) = - 0.15x³ − 0.02x² + 28x - 120

Comments and questions welcome.

More Algebra 2 problems.

Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


4. The expression 6xi³(-4xi + 5) is equivalent to
1) 2x - 5i
2) -24x² - 30xi
3) -24x² + 30x - i
4) 26x - 24x²i - 5i

Answer: 2) -24x² - 30xi
i² = -1, i³ = -1i = -i, i⁴ = i²i² =(-1)(-1) = 1

6xi³(-4xi + 5)
-24x²i⁴ + 30xi³
-24x²(1) + 30x(-i)
-24x² - 30xi

5. If f(x) = 3|x| - 1 and g(x) = 0.03x³ - x + 1, an approximate solution for the equation f(x) = g(x) is
1) 1.96
2) 11.29
3) (-0.99, 1.96)
4) (11.29, 32.87)

Answer: 2) 11.29
Eliminate choices 3 and 4 because the solution is a single number, not an ordered pair.
There are up to three possible intersections. If you graph them, you will find them at approximately -0.99, 0.5, and 11.29.

6. Given the parent function p(x) =cos x, which phrase best describes the transformation used to obtain the graph of g(x) = cos(x + a) - b, if a and b are positive constants?
1) right a units, up b units
2) right a units, down b units
3) left a units, up b units
4) left a units, down b units

Answer: 4) left a units, down b units
Inside the parentheses, plus shifts to the left and minus shifts to the right. Outside of the parentheses, plus moves the graph up and minus moves the graph down.

Comments and questions welcome.

More Algebra 2 problems.

Second Difference

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(C)Copyright 2018, C. Burke.

He is a Ranger, so he'd know his domain and take it all in Stride.
But when it comes to lines, you know they never want to stop.




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(x, why?) Mini: Making Toast

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(C)Copyright 2018, C. Burke.

The equation doesn't break any rules.
Suggested from the Cheese Stands Alone strip, except this comic doesn't really solve for toast, as toast occurs on both sides of the equation.




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Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


1. The graph of the function p(x) is sketched below.

Which equation could represent p(x)?
1) p(x) = (x² − 9)(x − 2)
2) p(x) = x³ − 2x² + 9x + 18
3) p(x) = (x²2 + 9)(x − 2)
4) p(x) = x³ + 2x² − 9x − 18

Answer: 1) p(x) = (x² − 9)(x − 2)
The zeroes are -3, 2, and 3, so the factors are (x + 3)(x - 2)(x - 3).
(x + 3)(x - 3) = x² - 9.
Choice 3 is bad because it has x² + 9, which doesn't have zeroes.
Choice 4 is bad because (3)(-2)(-3) = 18, not -18.

2. What is the solution to 8(2^{x + 3}) = 48?
1) x = ln6/ln2 - 3
2) x = 0
3) x = ln48/ln16 - 3
4) x = ln4 - 3

Answer: 1) x = ln6/ln2 - 3

8(2^{x + 3}) = 48
2^{x + 3} = 6
(x + 3)ln 2 = ln 6
x + 3 = ln6/ln2
x = ln6/ln2 - 3

3. Cheap and Fast gas station is conducting a consumer satisfaction survey. Which method of collecting data would most likely lead to a biased sample?
1) interviewing every 5th customer to come into the station
2) interviewing customers chosen at random by a computer at the checkout
3) interviewing customers who call an 800 number posted on the customers' receipts
4) interviewing every customer who comes into the station on a day of the week chosen at random out of a hat

Answer: 3) interviewing customers who call an 800 number posted on the customers' receipts
Self-selection introduces bias because those with stronger opinions are more likely to call the number. You would not get a random sample.

Comments and questions welcome.

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(x, why?) Mini: Length & Width

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(C)Copyright 2018, C. Burke.

Don't get them started on the whole base and height thing.




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