Thursday, March 23, 2017

Radical

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(C)Copyright 2017, C. Burke.

He's definitely lower than 3, but he's still more than 2.




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Wednesday, March 22, 2017

Algebra 2 Regents Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.
Previous problems can be found here

Part 1

3. When factored completely, m5 + m3 - 6m is equivalent to

(4) m(m2 + 3)(m2 - 2)
Start with: m5 + m3 - 6m
Each term has m, factor it: (m)(m4 + m2 - 6)
Factor into two binomials: What are two factors of -6 that add up to +1: +3 and -2
So it factors into m(m2 + 3)(m2 - 2).

4. If sin2(32°) + cos2(M) = 1, then M equals

(1) 32°.
The rule is: sin2x + cos2x = 1.
In this case x = 32°, so M must be 32° as well.

Geometry Regents Problems of the Day

The following problems were taken from the GEOMETRY (COMMON CORE) Regents Exam given on Thursday, January 26, 2017.
Previous problems can be found here.

Part 1

3. Given triangle ABC = triangle DEF, which statement is not always true?(

(1) BC = DF.
BC and DF are not corresponding sides. BC corresponds to EF and DF corresponds to AC. They would only be congruent if the triangles were isosceles or equilateral. We don't know whether they are or not.

4. In the diagram below, DE, DF and EF are midsegments of triangle ABC.


The perimeter of quadrilateral ADEF is equivalent to

(4) AB + AC.
FE = DB and DE = FC. So AD + DE + EF + FA = AD + FC + DB + FA.
Rearrange the terms: AD + DB + AF + FC = AB + AC.

Sunday, March 19, 2017

Algebra 2 Regents Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.

Part 1

1. Relative to the graph of y = 3sin x, what is the shift of the graph of y = 3sin(x + π/3)?

(2) π/3 left.
When the value within the parentheses is added to x, the graph shifts to the left. When the value within the parentheses is subtracted from x, the graph shifts to the right.
To move up or down, the addition or subtraction would have to take place outside the parantheses.

2. A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in weeks, and P(t) is the population of rabbits with respect to time, about how many rabbits will there be in 98 days?

(1) 56.
The starting value is 5. The base is 2. The exponent is 98 days / 4 weeks, which is 98 / 28 after converting weeks to days.
That gives a value of approximately 56.5685424949..., which is approximately 56.
(Yes, that would round up to 57, but that is not one of the choices, leaving 56 as the closest.)

Geometry Regents Problems of the Day

The following problems were taken from the GEOMETRY (COMMON CORE) Regents Exam given on Thursday, January 26, 2017.

Part 1

1. Which equation represents the line that passes through the point (-2,2) and is parallel to y = 1/2 x + 8?

(3) y = 1/2 x + 3.
A parallel line will have the same slope, 1/2, so y = 1/2 x + b.
Next, substitute the coordinates (-2, 2) in place of x and y, giving you

2 = 1/2 (-2) + b
2 = -1 + b
3 = b
so y = 1/2 x + 3

2. In the diagram below, triangle ADE is the image of triangle ABC after a reflection over the line AC followed by a dilation of scale factor (AE/AC) centered at point A.

Which statement must be true?

(2) m∠ABC = m∠ADE.
Neither reflection nor dilation changes the shape of the figure, nor the sizes of the angles, and ∠ABC and ∠ADE are corresponding angles in the two triangles.

Friday, March 17, 2017

Happy St. Patrick's Day 2017

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(C)Copyright 2017, C. Burke.

Tora Lora Torus just doesn't sound right. But now I might get Pearl Harbor comments

This St. Paddy's Day, may all your non-Irish friends be Green with envy!




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Wednesday, March 15, 2017

Sides

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(C)Copyright 2017, C. Burke.

Followed by the sound of a dagger striking . . .




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Tuesday, March 14, 2017

Pi in the Sky

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(C)Copyright 2017, C. Burke.

Next Up: Pi on Sports!

I almost went with a family trip on an airline instead. Maybe I should make a note of that for the future.




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Thursday, March 09, 2017

(x, why?) Mini: Irreplaceable

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(C)Copyright 2017, C. Burke.

Speaks for itself. I hope.




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Monday, March 06, 2017

(x, why?) Mini: Improper Fraction

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(C)Copyright 2017, C. Burke.

He's a bit mixed up.




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P = NP

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(C)Copyright 2017, C. Burke.

Seriously, it's hard to tell. I think she's just putting him on. Maybe.




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