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Mastery Grade 10 Sept 11 A Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ 1. Select the table of values for the equation 3x + 2y = -2 a. b. c. d. 2. Solve 2x + 3y = -4 for x a. b. c. d. 3. Simplify a. c. d. b. ____ 4. Simplify ____ a. b. c. d. 2 5. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to solve the equation? ____ ____ a. add 4 to both sides b. add 2 to both sides c. add 3x to both sides d. divide both sides by 3 a. d. 6. b. 7. The graph of x - y = 1 is c. a. Line 2 b. Line 5 c. Line 1 d. Line 4 e. Line 3 ____ 8. Simplify a. 4x b. c. d. ____ 9. Express 23.1 as a percentage. a. 2310% b. 231% c. 0.0231% d. 0.231% ____ 10. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to solve the equation? a. divide both sides b. add x to both sides c. add 2 to both sides d. subtract 2x from by 2 both sides ____ 11. A line has equation 3x + 2y = 5. Its y-intercept is a. b. ____ 12. Simplify 3x + 2y -1 -2x -y -3 a. x + y - 2 b. x +y - 4 c. d. c. x - 3y - 2 d. x + 3y - 4 ____ 13. Which of the following diagrams illustrates that a. ____ 14. The graph of y = -2 is b. ? c. d. a. Line 4 b. Line 2 c. Line 1 ____ 15. 40% of _____ is 80. a. 50 b. 200 c. 32 ____ 16. A line has equation 3x - 2y = 5. Its slope is a. b. d. Line 5 e. Line 3 d. 0.5 c. d. ____ 17. The graph of x + 6y = 6 is a. Line 4 b. Line 3 c. Line 2 ____ 18. If x = -4, then evaluate a. 4 b. -20 ____ 19. If x = -3, then evaluate a. -15 b. 15 ____ 20. Solve 3x - 2y = 4 for x a. b. ____ 21. Which of the following diagrams illustrates that d. Line 5 e. Line 1 c. 12 d. -12 c. 39 d. 21 c. d. ? a. b. c. d. ____ 22. A line has equation 2x - 3y = 5. Its x-intercept is a. b. c. d. ____ 23. The graph of y=-1 is a. Line 3 b. Line 4 c. Line 5 ____ 24. The number marked on the number line is a. b. -2.5 d. Line 2 c. -1.5 e. Line 1 d. ____ 25. The graph of 2x - y = -1 is a. Line 1 b. Line 3 c. Line 2 d. Line 5 e. Line 4 ____ 26. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to solve the equation? a. add 2x to both sides ____ 27. Simplify a. b. subtract 2x from both sides c. divide both sides by -2 d. add x to both sides b. c. d. ____ 28. The graph of y = - x + 3 is a. Line 4 b. Line 2 c. Line 3 d. Line 1 e. Line 5 ____ 29. a. b. c. d. a. b. c. d. ____ 30. Mastery Grade 10 Sept 11 A Answer Section MULTIPLE CHOICE 1. ANS: D If x = -2 and y=2 then 3x + 2y = 3(-2) + 2(2) = -6 + 4 = -2 If x = 0 and y=-1 then 3x + 2y = 3(0) + 2(-1) = 0 + (-2) = -2 Each of these points is on the line. If x = 4 and y=-7 then 3x + 2y = 3(4) + 2(-7) = 12 - 14 = -2 is correct. PTS: 1 2. ANS: A Add -3y to both sides to isolate 2x Divide both sides by 2 to isolate x Divide each term by 2 PTS: 1 3. ANS: A The illustration of If we combine what we can, we get PTS: 1 4. ANS: D is as follows: or just . means If we were simply dividing 6 by 3, we would ask how many groups of 3 are there in 6, or what multiplied by 3 is 6? In this case, we ask "what multiplied by is ?" or " how many groups of are there in ?". We can easily see that is 2 groups of from the drawing below. This means that . Another way to say this is that . Another way to approach this question is to express any powers as multiplication and remember that multiplication and division are inverse operations (i.e., they undo each other). So ... which is equivalent to is the same as or just 2. PTS: 1 5. ANS: B The basic strategy for solving an equation is to get the x's on one side and the units on the other side by adding (or subtracting) the same thing to/from both sides. You would normally decide on the side of the equation the x's should be on first. It is easier to try to make sure the x's are positive as well, so we usually try to eliminate x's from the side of the equation that has the smallest number of x's (i.e., if both are positive, big the smaller one to eliminate, if one is negative and one is positive, eliminate the negative one, and if both are negative, eliminate the one that is the 'most' negative.) In this case, there is a +3x on the left and a +x on the right, so we choose to eliminate the +x by adding -x to both sides. While this is probably the best strategy, it would also be acceptable to eliminate the 3x from the left side by adding -3x to both sides, or adding 2 to both sides to eliminate the -2 on the left, OR add -4 to both sides to eliminate the +4 on the right. The only correct answer listed is c. add 2 to both sides. So the algebraic solution should look like one of the following: PTS: 1 6. ANS: B To multiply fractions, just multiply the numerators and denominators to get . PTS: 1 7. ANS: C We know the x-intercept is 1 (if we let y=0, we get x=1) and the y-intercept is -1 (if we let x=0, we get y=-1), so it must be Line 1 We also could have solved for y and used slope and y-intercept to identify the line. PTS: 1 8. ANS: D We can think of as may have not looked at diagrams for Two of the positive . These are 'like terms', so they can be 'combined' to get yet - but it is possible to illustrate this question as follows: solids eliminate the two negative solids. The answer is . You . PTS: 1 9. ANS: A 23.1 means or . Therefore, 23.1 is 2310%. Another way to do this is to use the fact that 100% is the same as the number 1. We know that if we multiply a number by 1 we don't change its value, so 23.1 = 23.1 100%. Multiplying the 23.1 by the 100 we get 2310% (the decimal place moves 2 units to the right when you multiply by 100). PTS: 1 10. ANS: B The basic strategy for solving an equation is to get the x's on one side and the units on the other side by adding (or subtracting) the same thing to/from both sides. You would normally decide on the side of the equation the x's should be on first. It is easier to try to make sure the x's are positive as well, so we usually try to eliminate x's from the side of the equation that has the smallest number of x's (i.e., if both are positive, big the smaller one to eliminate, if one is negative and one is positive, eliminate the negative one, and if both are negative, eliminate the one that is the 'most' negative.) In this case, there is a -x on the left and a +x on the right, so we choose to eliminate the -x by adding +x to both sides. While this is probably the best strategy, it would also be acceptable to eliminate the +x from the right side by adding -x to both sides, or adding -2 to both sides to eliminate the +2 on the left, OR add +3 to both sides to eliminate the -3 on the right. So the algebraic solution should look like one of the following: PTS: 1 11. ANS: A 3x + 2y = 5 2y = 5 - 3x Isolate y by subtracting 3x from both sides. Divide both sides by 3 Simplify or Comparing with y = mx + b, we see that the y-intercept,b, is . PTS: 1 12. ANS: B The illustration of 3x + 2y -1 -2x -y -3 is below. Note that x and y tiles are similar ... just different lengths: or just x + y - 4. . Simplifying, we get PTS: 1 13. ANS: C The corrct answer is It has 4 out of 6 or . shaded on the left It also has 3 out of 6 or shaded on the top. The overlapping area is 12 squares out of the 36 or . This diagram shows that . PTS: 1 14. ANS: A We know the y-coordinate of every point on the line is -2, so it must be line 4. PTS: 1 15. ANS: B If 40% of the unknown number is 80, then 10% of the number would be 20 (divide both parts by 4). This means that 100% of the number is 200 (multiply both parts by 10), and 100% of the number IS the number! The number is 200. This question is equivalent to 40 out of 100 is the same as 80 out of _____. Once you understand this meaning, it is easy to see that the answer is 200. PTS: 1 16. ANS: C 3x - 2y = 5 3x - 5 = 2y Isolate y by adding 2y to both sides and subtracting 5 from both sides. Divide both sides by 2 Simplify or Comparing with y = mx + b, we see that the slope, m, is . PTS: 1 17. ANS: C We know the x-intercept is 6 (if we let y=0, we get x=6) and the y-intercept is 1 (if we let x=0, we get y=1), so it must be Line 2. We also could have solved for y and used slope and y-intercept to identify the line. PTS: 1 18. ANS: B if x = -4 then = = -4 - (16) = -4 - 16 = -20 First, replace x with -4 in brackets. The brackets group the negative sign with the 4. Next, we must square -4 to get 16. Finally subtract to get -20. PTS: 1 19. ANS: D if x = -3 then = = 2(9) + 3 = 18 + 3 First, replace x with -3 in brackets. The brackets group the negative sign with the 3. Next, we must square -3 to get 9 and change subtract -3 to add +3. Multiply next and then add to get 21 = 21 PTS: 1 20. ANS: B Add 2y to both sides to isolate 3x Divide both sides by 3 to isolate x This cannot be simplified (3 would have to divide into both terms) PTS: 1 21. ANS: C The corrct answer is It has 1 out of 6 or . shaded on the left It also has 2 out of 6 or shaded on the top. The overlapping area is 2 squares out of the 36 or This diagram shows that PTS: 1 22. ANS: D 2x - 3y = 5 2x - 3(0) = 5 2x = 5 . . To find the x-intercept, let y=0 Simplify Therefore the x-intercept is . PTS: 1 23. ANS: D We know that the y-coordinate of every point on the line is -1, so it must be line 2. PTS: 1 24. ANS: B If -3 was marked on the number line we could see that the number marked is halfway between -2 and -3, so it is -2.5. If we look elsewhere on the number line we can see that is spaces is 0.5 units. The marked number spaces to the left of -2, so it is -2.5. PTS: 1 25. ANS: A We know the x-intercept is (if we let y=0, we get x= ) and the y-intercept is 1 (if we let x=0, we get y=1), so it must be Line 1. We also could have solved for y and used slope and y-intercept to identify the line. PTS: 1 26. ANS: A The basic strategy for solving an equation is to get the x's on one side and the units on the other side by adding (or subtracting) the same thing to/from both sides. You would normally decide on the side of the equation the x's should be on first. It is easier to try to make sure the x's are positive as well, so we usually try to eliminate x's from the side of the equation that has the smallest number of x's (i.e., if both are positive, big the smaller one to eliminate, if one is negative and one is positive, eliminate the negative one, and if both are negative, eliminate the one that is the 'most' negative.) In this case, there is a -2x on the left and a +x on the right, so we choose to eliminate the -2x by adding +2x to both sides. While this is probably the best strategy, it would also be acceptable to eliminate the +x from the right side by adding -x to both sides, or adding -1 to both sides to eliminate the +1 on the left, OR add +3 to both sides to eliminate the -3 on the right. So the algebraic solution should look like one of the following: PTS: 1 27. ANS: B There is no written operation between the terms in brackets. This means it is multiplication. So, is the same as . We already know that is the same as so could be written as . Rearranging, we get which is . PTS: 1 28. ANS: E We know the slope is - and the y-intercept is 3, so it must be line 5 (that is the only line with y-intercept 3). You can check the equation for two points: If x = 0, then y= - (0) + 3 If x = 2 then y = - (2) + 3 =0+3 = -3 + 3 =3 =0 The points at (0,3) and (2,0) are on the line, so it must be line 5. PTS: 1 29. ANS: C = = To subtract fractions, get a common denominator (12) by multiplying the numerator and denominator of the first fraction by 3 and then the numerator and denominator of the second fraction by 2. Now that we have a common denominator, subtract the numerators and keep the same base. PTS: 1 30. ANS: A = = PTS: 1 To add fractions, get a common denominator (15) by multiplying the numerator and denominator of the first fraction by 5 and then the numerator and denominator of the second fraction by 3. Now that we have a common denominator, add the numerators and keep the same base.