Algebra 2 Problems of the Day (Algebra 2/Trigonometry 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.

Algebra 2/Trigonometry Regents, January 2012

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


28. Find the solution of the inequality x² - 4x > 5, algebraically.

Answer:

Solve it like any other quadratic equation.

x² - 4x = 5
x² - 4x - 5 = 0
(x - 5)(x + 1) = 0
x - 5 = 0 or x + 1 + 0
x = 5 or x = -1

To make (x - 5)(x + 1) > 0 true, both expression would have be positive or both would have to be negative. This will have when x > 5 or x < -1.

29. Solve algebraically for x:

4 - √(2x - 5) = 1

Answer:

Use inverse operations to isolate x.

4 - √(2x - 5) = 1
-√(2x - 5) = -3
√(2x - 5) = 3
2x - 5 = 9
2x = 14
x = 7

Check: 4 - √(2x - 5) = 1
4 - √(2(7) - 5) = 1
4 - √(9) = 1
4 - 3 = 1

30.Evaluate: Summation (n=1 to 3): (-n⁴ - n)

Answer:

You can calculate each individual value and then sum them.

Substitute and sum:

term 1 = -(1)⁴ - 1 = -1 - 1 = -2
term 2 = -(2)⁴ - 2 = -16 - 2 = -18
term 3 = -(3)⁴ - 3 = -81 - 3 = -84
Sum of the 3 terms = -2 + -18 + -84 = -104.

31. Express in simplest form: CBRT( a⁶ b⁹ / -64)

Answer:

Take the cube root of -64 and divide the exponents on the two variables by 3.

a² b³ / -4 or -a² b³ / 4

More to come. Comments and questions welcome.

More Regents problems.

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