Algebra Problems of the Day (Integrated Algebra Regents, June 2013)

While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part III: Each correct answer will receive 3 credits. Partial credit is possible.


34. The menu for the high school cafeteria is shown below.

Determine the number of possible meals consisting of a main course, a vegetable, a dessert, and a beverage that can be selected from the menu.

Determine how many of these meals will include chicken tenders.

If a student chooses pizza, corn or carrots, a dessert, and a beverage from the menu, determine the number of possible meals that can be selected.

Answer:

There are three parts to this question and each is worth a point. Some work needs to be shown. If you just write the three numbers, you will only get 1 point total.

Part 1: Use the Counting Principle to find the number of possible meals, selecting one item from each category. That is, multiply the number of items in each column. So the total is 5 * 3 * 5 * 3 = 225.

Part 2: If we only include chicken tenders from the firt column, then we would multiply 1 * 3 * 5 * 3 = 45.

Part 3: There is one main course, two side dishes, five desserts and three beverages, so 1 * 2 * 5 * 3 = 30.

Note that if you wrote the answer as a decimal instead of a radical, you would have scored 0 points.

35.A man standing on level ground is 1000 feet away from the base of a 350-foot-tall building. Find, to the nearest degree, the measure of the angle of elevation to the top of the building from the point on the ground where the man is standing

Answer:

The distance along the ground is adjacent to the angle of elevation. The height of the building is opposite to the angle of elevation. Opposite and adjacent means that we need to use the Tangent ratio.

Tan x = opp / adj
Tan x = 350 / 1000
x = tan^-1 (350 / 1000)
x = 19.29...

The angle of elevation is 19 degrees.

Make sure the calculator is measuring degrees and not radians (which is the default).

36. Express √25 - 2√3 + √27 + 2√9 in simplest radical form.

Answer:

Take the square root of the terms which are perfect squares. Find the largest perfect square which is a factor of the other terms so you can simplify. √25 - 2√3 + √27 + 2√9
= 5 - 2√3 + √27 + 2(3)
= 5 - 2√3 + √9√3 + 6
= 5 - 2√3 + 3√3 + 6
= 11 + √3





End of Part III



More to come. Comments and questions welcome.

More Regents problems.