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.
16. The expression (4x3)2 / 2x is equivalent to
1) 4x4
2) 4x5
3) 8x4
4) 8x5
Answer: 4) 8x5
Multiply the exponents on top. The 4 is squared but not cubed because the three isn't assoicated with the 4. The 2 applies to everything in the parentheses.
After that, divide the numerator by 2, and subtract 1 from the exponent on top.
(4x3)2 / 2x = 16x6 / 2x = 8x5
17. In the diagram below, circle O is inscribed in square ABCD. The
square has an area of 36.
What is the area of the circle?
1) 9π
2) 6π
3) 3π
4) 36π
Answer: 1) 9π
Yes, this is an Algebra question, even if it looks like Geometry. It's an area problem. The diameter of the circle is the same length as the same of the square. Take the square root of the area of the square to find the length of one side and the diameter. Then halve that to get the radius. Finally, use the formula for the Area of a circle, A = πr2. Note: this formula is NOT in the back of the booklet because they assume you know something this basic!
The square root of 36 is 6, so d = 6. That makes r = 3, and A = π(3)2 = 9π.
18. Which point lies on the graph represented by the equation
3y + 2x = 8?
1) (-2,7)
2) (0,4)
3) (2,4)
4) (7,-2)
Answer: 4) (7,-2)
You can plug each pair in to see which works, or you can rewrite the equation in "y=" form so it can be entered into the graphing calculator, after which you can check the Table of Values.
Note that the equation has the y term first and the x second. Be careful!
3(7) + 2(-2) = 17. Eliminate Choice (1).
3(4) + 2(0) = 12. Eliminate Choice (2).
3(4) + 2(2) = 16. Eliminate Choice (3).
3(-2) + 2(7) = 8. Choice (4) is the answer.
You could have entered y = -2/3 x + 8/3 into your calculator and checked the table of values.
19. The equation of the axis of symmetry of the graph of y = 2x2 - 3x + 7 is
1) x = 3/4
2) y = 3/4
3) x = 3/2
4) y = 3/2
Answer: 1) x = 3/4
THe Axis of Symmetry is a vertical line in the middle of the parabola. All vertical lines have equations in the form of x = n, where n is a value. Immediately eliminate Choices (2) and (4).
The formula to find the equation for the Axis of Symmetry is x = -b/a, where a and b come from the standard form of a quadratic, y = ax2 + bx + c.
Therefore x = -(-3)/(2(2)) = 3/4.
Don't forget that the negative of a negative is positive. Don't forget the 2 in the formula.
20. The box-and-whisker plot below represents the ages of 12 people.
What percent of these people are age 15 or older?
1) 25
2) 35
3) 75
4) 85
Answer: 3) 75
15 is the first quartile (Q1). 25% of the data is below that number and 75% is above that number.
You cannot identify 35% or 85% of the data in a box-and-whisker plot. So those choices should have been eliminated immediately.
More to come. Comments and questions welcome.
More Regents problems.
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