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 II: Each correct answer will receive 2 credits. Partial credit is available.


31. The length and width of the base of a rectangular prism are 5.5 cm and 3 cm. The height of the prism is 6.75 cm. Find the exact value of the surface area of the prism, in square centimeters.

Answer:

The exact value means don't round any of the decimals.

The surface area of a rectangular prism is the area of the top and bottom, and the front and the back, and the left and the right. The opposite faces will have the same area. You can do this in parts or you can use the formula:

SA = 2LW + 2LH + 2WH

= 2(5.5)(3) + 2(5.5)(6.75) + 2(3)(6.75) = 147.75

32. Casey purchased a pack of assorted flower seeds and planted them in her garden. When the first 25 flowers bloomed, 11 were white, 5 were red, 3 were blue, and the rest were yellow. Find the empirical probability that a flower that blooms will be yellow.

Answer:

The remaining flowers of the first 25 are yellow: 11 + 5 + 3 = 19 and 25 - 19 = 6.

The empirical probability that a flower is yellow is 6/25.

33. Express in the simplest form: (x² - 1) / (x² + 3x + 2)

Answer:

(x² - 1) / (x² + 3x + 2)

((x + 1)(x - 1)) / ((x + 1)(x + 2))

(x - 1) / (x + 2)

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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