June 2014 NY Integrated Algebra Regents, Thread 1

Today, Friday, was both the Integrated Algebra and the Geometry Regents exams. Integrated Algebra is over as I type this (although it won't be posted until later, after all extended time and conflict rooms have completed). I taught more Algebra students than Geometry students this year and the Algebra examis the one required for graduation, so I'll start my review with this test.

Part 1 was "fair" to use a term that a student or two used. Most of the ones I saw in the hallway after the exam, returning their calculators as I was resetting a box of them for the next exam, said that they think they did well. Only one said she'd done poorly, and I hope (and I believe) that she's wrong because I know how intelligent she really is. She's underestimating herself. I hope.

Keep in mind that I had to type all of this. There was no cutting and pasting involved, so I left out most of the "choices", and illustrations will have to wait. Given all that then, without further ado....

NOTE: Thread 2, with the rest of the questions, is here.

June 2014 Integrated Algebra Regents

1. The product of 6x³y³ and 2x²y is

Multiply the coefficients, add the exponents, and don't forget that the exponent on the last y is 1. 12x⁵y⁴

2. Which set of data is qualitative?

My class (as I'll speak of them often) just went over this on an old exam. Qualitative is descriptive, like the swimmer's favorite swimsuit colors.

3. It takes a snail 500 hours to travel 15 miles. At this rate, how many hours will it take the snail to travel 6 miles.

Simple proportion: 500/15 = x/6 (or similar). Cross-multiply and get 200 hours, which is 2/5ths of 500.

4. The equation y = ax² + bx + c is graphed on the set of axes below. [GRAPH OMITTED] Based on the graph, what are the roots of the equation ax² + bx + c?

The roots of the equation are where the parabola crosses the x-axis. As you can see plainly from the graph (if you happen to have the test in front of you) is that it crosses at 1 and 5.

5. When solving for the value of x in the equation 4(x - 1) + 3 = 18, Aaron wrote the following lines on the board [ILLUSTRATION TO BE ADDED LATER]
Which property was used incorrectly when going from line 2 to line 3?

They made it easier by telling you where the mistake would be. Aaron didn't distribute the 4, writing - 1, instead of - 4.

6. What is the solution of 4x - 30 > -3x + 12?

Add 3x to both sides. Add 30 to both sides. You get 7x > 42. That becomes x > 6.

7. A local government is planning to increase the fee for use of a campsite. If a survey were taken, which group woulb be most biased in their opposition to the increase?

Even if you didn't cover "bias", it should be obvious that of the groups listed, the ones who would be against the tax are the campers.

8. An example of an algebraic equation is

They ask one of thee every test. An equation has an equal sign, an expression does not. 5x = 7 is an equation, even if its solution is a fraction. (That doesn't matter, but I'm sure it bothered someone.)

9. What is the value of x in the solution of the system of equations 3x + 2y = 12 and 5x - 2y = 4?

Add the two equations together and y is eliminated. 8x = 16, so x = 2.

10. What is the slope of a line that passes through the points (-2. -7) and (-6, -2)?

Change in y divided by change in x. (-2 - -7) / (-6 - -2), which is - (5 / 4).

11. Which notation is equivalent to the inequality -3 < x < 7?

As I've told my students, if you don't remember which is ( and which is [, the first thing you need to realize is that the two symbols have to be different. So you've eliminated two choices. The second thing to ask yourself is this: which is more likely to be the square bracket -- less than or less than or equal to?

The correct answer is (-3, 7].

12. What is the value of the expression 3a² - 4|a| + 6 when a = -3?

Simple substitution. Don't forget parentheses around the (-3) when squaring it on your calculator! 3(9) - 4(3) + 6 = 27 - 12 + 6 = 21

13. Which relation is a function?

In a function, the x values can not be repeated. The y values can be repeated. Option 1 is correct. {(2, 1), (3, 1), (4, 1), (5, 1)}

14. When 6x² - 4x + 3 is subtracted from 3x² - 2x + 3, the result is

"Subtracted from". You need to do 3x² - 6x², which gives -3x². The answer is -3x² 2x . The +3 and +3 cancel out.

15. The lengths of the sides of a right triangle can be

Use Pythagorean Theorem on the choices, or just recognize 9-12-15 because it gets used so often. You should recognize some of the basic Pythagorean Triples.

16. Which equation represents a line that is parallel to the y-axis?

The y-axis is x = 0. A line parallel to that would be in the form x = a. The correct answer is (1) x = 5. There is no y in the equation.

17. In right triangle ABC, shown below, AC = 12, BC = 16 and AB = 20. Which equation is not correct?

Remember SOHCAHTOA to remember which sides go with which ratios. You'll notice that tangent doesn't use the hypotenuse. The correct choice is tan B = 16/20, which is an incorrect statement.

18. Three times the sum of a number and four is equal to five times the number, decreased by two. If x represents the number, which equation is a correct translation of the statement?

Taking it one piece of the statement at a time, we get 3(x + 4) = 5x - 2. Note that the comma before "decreased by two" reinforces the fact that the previous multiplication only applies to the variable and not to the difference of the variable and 2.

19. What is the equation of the line that passes through the point (3, -7) and has a slope of -4/3?

Obviously, it has to start with y = -4/3 x. Is the y-intercept +3 or -3? Plug is 3 for x, and see which y-intercept will give you 7 for y. The answer is (2) y = -4/3 x - 3.

20. Which parabola has an axis of symmetry of x = 1?

Look at the graph. Which has a vertex where x = 1? Choice (1) does.

21. When factored completely, the expression 3x² - 9x + 6 is equivalent to

Factor out the 3 and you get x² - 3x + 2, which factors into (x - 1)(x - 2). So the answer is 3(x - 1)(x - 2).

22. The equation P = 0.0089t² + 1.1149t + 78.4491 models the United States population, P, in millions since 1900. If t represents the number of years after 1900, then what is the estimated population in 2025 to the nearest tenth of a million?

t = 2025 - 1900 = 125. Plug the equation into your calculator, and you get 356.9.

23. Which graph represents an absolute value equation?

Absolute value graphs are shaped like the letter "V" or an upside-down "V". Choice (2).

24. The expression (a / b) - (1 / 3) is equivalent to

The least common denominator between b and 3 is 3b. You have to multiply the first fraction by (3/3) and the second fraction by (b/b). This gives you (3a / 3b) - (1b / 3b), which is (3a - b) / 3b.

25. Which value of x is the solution of the equation 2(x - 4) + 7 = 3?

2x - 8 + 7 = 3
2x - 1 = 3
2x = 4
x = 2.

26. Given: M = {green, red, yellow, black} and N = {blue, green, yellow}
Which set represents M U N? (union)

The Union of two sets is every element contained in either or both sets. Don't repeat them in the final set.

{green, red, yellow, blue, black}

27. Which situation describes a correlation that is not a causal relationship?

The more miles you walk, the more calories you burn. The more hours a TV is on, the more electricity is uses. The higher the speed of a car, the fewer hours is takes to travel a given distance. The census happens every ten years and it measures the population of the country. A rise in the population does not speed up when the census takes place. When I first read the question, my first response was "What about the census taken every ten years?"

28. A school offers three classes of math and two classes of science, all of which meet at different times. What is the total number of ways a student can take a math class and a science class?

The Counting Principle! My students should've gotten this. Again, it wasn't that long ago.

The number of items in the first list times the number of items in the second list: 3 X 2 = 6.

29. The expression (x - 7) / (9 - x²) is undefined when x is

A fraction is undefined when the denominator is equal to 0 and at no other time. (The numerator doesn't matter for this.) When is 9 - x² = 0? When x = 3 or -3.

30. What is the product of (1.5 X 10²) and (8.4 X 10³) expressed in scientific notation?

Multiplying with give you 12.6 X 10⁵, but that's not scientific notation. You have to move the decimal one place to the left and raise the exponent by 1. The answer is 1.26 X 10⁶.