Standard 6.0

1. Standard 6.0 19. What is the y-intercept of the graph of 4x + 2y = 12 • - 4 • - 2 • 6 • 12

2. Answer • 1st, place the standard form equation in point slope intercept form (y = mx + b). By doing this, “b” will be your answer to the question. 4x + 2y = 12 4x – 4x +2y = 12 – 4x 2y/2 = -4x/2 + 12/2 y = -2x + 6 • -2 = m or the slope, and 6 = b or the y-intercept. The y-intercept is your answer. • ∴ the answer is “c”

3. Standard 6.0 • Which inequality is shown on the graph below? • y < ½ x – 1 • y ≤ ½ x – 1 • y > ½ x – 1 • y ≥ ½ x – 1

4. 1st, eliminate two answers with what you know. If the slope is a solid line then the inequality must be ≥ or ≤ . Regular > and/or < are represented by dotted lines. • You are left with “b” and “d”. Look at which side of the line is shaded. If the area is shaded below the line, then y is less than or equal to (y≤ ), if shaded above the line then y is greater than or equal to (y≥). In this case, it is shaded above. • ∴ y ≥ ½ x – 1, so your answer is “d”

5. Standard 6.0 • Which best represents the graph y = 2x – 2?

6. 1st, eliminate what you know. The equation is in point slope form (y= mx + b). 2 = m or your slope. Since it is positive, the line goes from low left to high right. This eliminates “b” and “c” • Next, - 2 = b or your y intercept (where the line crosses the y-axis. In this case, “a” has the slope crossing the y-axis at (0,-2) while “d” has it crossing at (0,2). Knowing that you are looking for is – 2, you have your answer. • ∴ “a” is your answer.

7. Standard 7.0 • Which point lies on the line defined by 3x + 6y = 2. • (0, 2) • (0, 6) • (1, - 1/6 ) • (1, - 1/3 )

8. The best and easiest way to solve this problem is to insert the numbers for x and y. Remember, the numbers given are (x, y). a) 3(0) + 6(2) = 2 12 ≠ 2 b) 3(0) + 6(6) = 2 36 ≠ 2 • ∴ “c” is your answer. c) 3(1) + 6(- 1/6) = 2 3 – 1 =2 d) 3(1) + 6(- 1/3) = 2 3 – 2 ≠ 2

9. Standard 7.0 • What is the equation of the line that has a slope of 4 and passes through the point (3, – 10)? • y = 4x – 22 • y = 4x + 22 • y = 4x – 43 • y = 4x + 43

10. a) -10 = 4(3) – 22 -10 = 12 – 22 -10 = -10 b) -10 = 4(3) + 22 -10 = 12 + 22 -10 ≠ 32 • 1st, don’t get distracted by the slope of 4 comment for you already know (4x) • Simply plug (x , y) or (3, -10) into equations. c) -10 = 4(3) – 43 -10 = 12 – 43 -10 ≠ -21 d) -10 = 4(3) + 43 -10 = 12 + 43 -10 ≠ 55 • ∴ the answer is “a”

11. Standard 7.0 24. The data in the table show the cost of renting a bicycle by the hour, including a deposit. • If hours, h, were graphed on the horizontal axis and cost, c, were graphed on the vertical axis, what would be the equation of a line that fits the data? a) c = 5h b) c = 1/5h + 5 c) c = 5h + 5 d) c = 5h – 5

12. b) 15 = 1/5 (2) + 5 15 ≠ 52/5 • 1st remember that horizontal axis is the x-axis and the vertical axis is the y-axis. • Looking at the chart, pick one pair and plug into the equation. • ∴ the answer is “c”. a) 15 = 5(2) 15 ≠ 10 c) 15 = 5(2) + 5 15 = 10 + 5 15 = 15 d) 15 = 5(2) – 5 15 = 10 - 5 15 ≠ 5

13. Standard 8.0 25. The equation of line l is 6x + 5y = 3, and the equation of line q is 5x – 6y = 0. Which statement about the two lines is true? • Lines l and q have the same y - intercept • Lines l and q are parallel • Lines l and q have the same x intercept • Lines l and q are perpendicular.

14. Looking at the slope, to determine if a line is parallel or perpendicular you look at the slope (m) in the equation. In this case, the slopes are an inverse with an opposite sign. If this is the case, the lines are perpendicular. 6x + 5y = 3 6x – 6x + 5y = 3 – 6x 1/5 • 5y = -6/5 x + 3/5y = -6/5x + 3/5 • 1st, place both equations in slope intercept form. • - 5x – 6y = 0 5x – 5x – 6y = 0 -5x -1/6 • - 6y = -5x • - 1/6 y = 5/6x

15. Standard 8.0 26. Which equation represents a line that is parallel to y = - 5/4 x + 2? • y = - 5/4 x + 1 • y = - 4/5x + 2 • y = 4/5 x + 3 • y = 5/4 x + 4

16. Do not waste time on this problem. The problem is already in point slope form ( y = m x + b ) and the “m” or slope is what you need. • The problem asked for parallel lines . When comparing lines and their equation, the quickest way to determine if they are parallel is if they have the same slope or “m” in the above equation. • ∴ the answer is “a”.

17. Standard 9.0 { 2x≥ y – 1 2x – 5y≤10 27. Which graph best represents the solution to this system of inequalities.

18. You want to place it into point slope intercept form (y = mx + b). • Remember, if you have a negative “y” at the end, you will need to switch the direction of the sign. • 2x ≥ y -1 2x -5y ≤ 10 • 2x +1 ≥ y -5y ≤ -2x +10 • y≤ 2x + 1 y ≥ 2/5 x – 2 • Use the y-intercept (b) to determine the line. First slope is less than 1 or colored in below the line. The second is greater than or above. The common highlighted area is your answer. ∴ the answer is “c”

19. Standard 9.0 { y = - 3x – 2 6x + 2y = -4 • What is the solution to this system of equations? • ( 6, 2 ) • ( 1, -5 ) • no solution • infinitely many solutions

20. First, eliminate what you can. Look at the first answer (6,2), if you plug the 6 into y = - 3x – 2 it would be impossible to solve, so “a” is ruled out. • Try the second answer. If you notice it works for both equations, so you can eliminate “c” or no solutions. • Now look at the equations. If you noticed, they form the same line. If they are the same line, then they have infinite number of solutions. ∴ although “b” is one solution the answer is “d” for any point on the slope is a solution.

21. Standard 9.0 { x + 3y = 7 x + 2y = 10 • Which ordered pair is the solution to the system of equations below? • ( 7/2 , 13/4 ) • ( 7/2 , 17/5 ) • ( -2 , 3 ) • ( 16 , -3 )

22. When finding the solution, remember that it must work for both equations. • Suggestion, since fractions take longer when solving, try the whole numbers first. • For this problem, “d” is your answer. Replace x and y with the ordered pair (16, -3). • x + 3y = 7 x + 2y = 10 • 16 + 3 (-3) = 7 16 + 2 (-3) = 10 • 16 – 9 = 7 16 – 6 = 10 • 7 = 7 10 = 10

23. Standard 9.0 30. Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have? • 27 • 40 • 56 • 73

24. 1st find out how many quarters go into $14.05. Divide 14.05 by .25 which equals 56.2. ∴, “c” and “d” are eliminated for being too high. Remember you have a total of 100 coins. • Down to two, use logic or just multiply .25 times 27 and times 40. Simply, you need to finish with a .05. This should tell you that multiples of 10 will not work. .25 • 40 = 10 or $10. You have no nickel or .05 thus, it eliminates choice “b” • ∴ “a” is your only logical choice.

25. Standard 10 31. • 2x4 b) c) d)

26. 1st remember to look at like terms and treat them like separate problems. You can do this since both the numerator and denominator are being multiplied. • Reduce • After reducing your like terms, combine your answers by multiplication to solve. • ∴ your answer is “b”.

27. Standard 10.0 • (4x2 – 2x + 8) – (x2 + 3x – 2) • 3x2 + x + 6 • 3x2 + x + 10 • 3x2 – 5x + 6 • 3x2 – 5x + 10

28. 1st, always remember that a subtraction sign or negative sign in front of ( ) means all signs change within the ( ) that follows • After changing the signs, you want to set it up like an addition problem. Line up your like terms and add. CAUTION, make sure you do the 1st step correctly!!! • 4x2 – 2x + 8 • (+) – x2 – 3x + 2 • 3x2 – 5x + 10 • ∴ your answer is “d”

29. Standard 10.0 • The sum of two binomials is 5x2 – 6x. If one of the binomials is 3x2 – 2x, what is the other binomial? • 2x2 – 4x • 2x2 – 8x • 8x2 + 4x • 8x2 – 8x

30. 1st, remember the word “sum” is the answer to an addition problem. • In this type of problem, you need to subtract to find the missing expression. • The expression after “is” (or equal) will be on top. WATCH OUT OF THE SIGNS!!!!! • 5x2 – 6x 5x2 – 6x • (-) 3x2 – 2x (+) - 3x2 + 2x • 2x2 – 4x 2x2 – 4x • ∴ your answer is “a”

31. Standard 10.0 • Which of the following expressions is equal to (x + 2) + (x – 2)(2x + 1) • 2x2 – 2x • 2x2 – 4x • 2x2 + x • 4x2 + 2x

32. Remember your order of operations. 1st, use the distribute property to find the product of (x + 3)(2x + 1). • (x – 2)(2x + 1) 2x2 + x – 4x – 2 • 2x2 – 3x – 2 • Now take (2x2 – 3x – 2) and add it to (x + 2). 2x2 – 3x – 2 (+) x + 2 2x2 – 2x + 0 • Drop the zero and you have your answer. ∴ your answer is “a”

33. Standard 11.0 • Which is the factored form of 3a2 – 24ab + 48b2 • (3a – 8b)(a – 6b) • (3a – 16b)(a – 3b) • 3(a – 4b)(a – 4b) • 3(a – 8b)(a – 8b)

34. 1st, factor the coefficients to make easier. • 3a2 – 24ab + 48b2 has a 3 in common for each so take it out. 3(a2 – 8ab + 16b2). Now factor. Make sure to look at the second sign, if it is a plus then both signs in the ( ) are minus since the middle term has a minus 8ab. Since they are both negative numbers, what number times another can also be added together to make -8 (the answer -4) • 3(a2 – 8ab + 16b2) • 3(a – 4b)( a – 4b) • ∴the answer is “c”

35. Standard 11.0 • Which is a factor of x2 – 11x + 24? • x + 3 • x – 3 • x + 4 • x – 4

36. When you see this problem, they are asking for you to factor the expression. After factoring, they want you to look at just one of the two ( ) to determine the answer. • x2–11x+24 • (x ) (x ) • (x– ) (x– ) • (x–8) ( x–3 ) • ∴ looking at the possible answers, “b” would be your choice since (x – 3) is a factor of the expression.

37. Standard 11.0 • Which of the following shows 9t2 + 12t + 4 factored completely. • (3t + 2)2 • (3t + 4)(3t + 1) • (9t + 4)(t + 1) • 9t2 + 12t + 4

38. Like the previous question, you are factoring out the expression. You might notice the first and last are squares (9t2 = 3t • 3t)and(4 = 2 • 2). Also, notice that you have a plus (+) in front of the 4 which means your signs are the same. • 9t2 + 12t + 4 • ( 3t + 2 )( 3t + 2 ) • If you are unsure of the answer, use FOIL. • If you notice (3t + 2) is repeated which means it can be rewritten as (3t + 2)2. • ∴ the answer is “a”

39. Standard 14.0 38. If x2 is added to x, the sum is 42. Which of the following could be the value of x? • - 7 • - 6 • 14 • 42

40. Solving quadratic equation you 1st set up the problem, x2 + x = 42. There is two ways to solve this problem; trial and error (input your answers until you find one that works) or factoring. • x2 + x = 42 x2 + x = 42 • (- 7)2 + (-7) = 42 x2 + x – 42 = 0 • 49 - 7 = 42 (x + 7) (x – 6) = 0 • 42 = 42 x + 7 = 0 x – 6 = 0 • x = -7 x = 6 • - 7 is a possible answer ∴ “a” is your answer.

41. Standard 14.0 39. What quantity should be added to both sides of this equation to complete the square? x2 – 8x = 5 • 4 • – 4 • 16 • – 16

42. The key phrase is “completing the square” The quadratic equation (ax2 + bx + c = 0) is in the format (ax2 + bx = - c) needed, x2 – 8x = 5, to complete the square. • The next step is to make sure the “a” is 1, if it was not then you would have to multiply 1/a to each side. • Then, using “b” (-8) add (b/2)2 or (-8/2)2to each side. Divide – 8 by 2 then square the answer -4. At this point you can stop. After (-4)(-4) = 16 you get the answer to the question, what quantity should be added. ∴ the answer is “c” or 16.

43. Standard 14.0 40. What are the solutions for the quadratic equation x2 + 6x = 16? • - 2, - 8 • - 2, 8 • 2, -8 • 2, 8

44. Two of the three methods to find your answer in quadratic equations are below. The answer is “c”. • Factoring method: • x + 8 = 0 x – 2 = 0 • x = -8 x = 2 • Quadratic Formula: • x= -8 x = 2

45. Standard 14.0 41. Leanne correctly solved the equation x2 + 4x = 6 by completing the square. Which equation is part of her solution? • (x + 2)2 = 8 • (x + 2)2 = 10 • (x + 4)2 = 10 • (x + 4)2 = 22

46. Complete the square (until you find the equation that is part of the solution). • x2 + 4x = 6 • x2 + 4x + (4/2)2 = 6 + (4/2)2 • x2 + 4x + (2)2 = 6 + (2)2 • x2 + 4x + 4 = 6 + 4 • (x + 2)(x+2) = 10 • (x + 2)2 = 10 • At this point you can stop for since the question is not asking for a final answer. ∴ the answer is “b”.