Algebra Problems of the Day (Integrated Algebra Regents, January 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Integrated Algebra Regents, January 2012

Part I: Each correct answer will receive 2 credits.


26. The diagram below shows right triangle LMP.

Which ratio represents the tangent of ∠PLM?

1) 3/4
2) 3/5
3) 4/3
4) 5/4

Answer: 3) 4/3

THe tangent is the ratio of the opposite side to the adjacent side. It doesn't use the hypotenuse. Since the hypotenuse of the given triangle is 5, eliminate the choices that have 5 in them. That is, Choices (2) and (4).

The side opposite angle L has a length of 4. The adjecent side has a length of 3. So the tangent is 4/3.

Unlike sine and cosine, tangent can be greater than 1.

27. Mr. Stanton asked his students to write an algebraic expression on a piece of paper. He chose four students to go to the board and write their expression.

Robert wrote: 4(2x + 5) > 17
Meredith wrote: 3y - 7 + 11z
Steven wrote: 9w + 2 = 20
Cynthia wrote: 8 + 10 - 4 = 14
Which student wrote an algebraic expression?

1) Robert
2) Meredith
3) Steven
4) Cynthia

Answer: 2) Meredith

An expression is one or more terms joined by basic operations. They won't have an equals sign or an inequality symbol. Meredith has 3 terms joined by subtraction and addition.

Choice (1), Robert wrote an inequality.

Choice (3) and (4), Steven and Cynthia wrote equations.

28. If s = (2x + t) / r, then x =

1) (rs - t) / 2
2) (rs + 1) / 2
3) 2rs - t
4) rs - 2t

Answer: 1) (rs - t) / 2

Use Inverse Operations to isolate the variable x.

s = (2x + t) / r
rs = (2x + t)
rs - t = 2x
(rs - t) / 2 = x

29. A scatter plot was constructed on the graph below and a line of best computations. fit was drawn.
What is the equation of this line of best fit?

1) y = x + 5
2) y = x + 25
3) y = 5x + 5
4) y = 5x + 25

Answer: 4) y = 5x + 25

The y-intercept of the graph is clearly 25, so eliminate Choices (1) and (3).

Each box represents 1 unit for x but 5 units for y. The rise is 5 while the run is 1. So the slope is 5. The answer is Choice (4).

30. What is the sum of 2y / (y + 5) and 10 / (y + 5) expressed in simplest form?

1) 1
2) 2
3) 12y / (y + 5)
4) (2y + 10) / (y + 5)

Answer: 2) 2

WHen you add two fractions with a common denominator, you keep the denomiator and add the two numerators by combining like terms.

2y/(y + 5) + 10/(y + 5) = (2y + 10)/(y + 5).

However, this is NOT in simplest form. If you factor 2 from wy + 10, you get 2(y + 5)/(y + 5). You can then reduce the two common factors to 1, which leaves 2.

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.

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