MPM1D - Practice Mastery Test #6

Transcription

1 Name: Class: Date: ID: A MPMD - Practice Mastery Test #6 Multiple Choice Identify the choice that best completes the statement or answers the question.. Calculate 0% of 00. a. b. 0 c. 000 d. 00. Seyran's quiz scores out of 0 were 7, 0, 8, 0, and 9. The mean of these scores is a. 9 b. 8.8 c. 0 d. 8. Which of the following are equal to 9? i) ( ) ii) Ê ˆ iii) a. i only b. ii only c. iii only d. i and iii e. ii and iii 4. The fraction of the whole rectangle shaded below (in lowest terms) is a. 6 b. 4 c. d.. 4 a. -4 b. c. d Express 6 as a power of 4 a. 4 4 b. 4 6 c. 8 d. 8 Ê 7. ˆ =?? a. 6 b. c. d If the expression illustrated below is simplified as far as possible, the answer would be: a. x x + b. x + x + c. x + x + d. x + x +

2 Name: ID: A 9. Simplify x + x + x a. 6x 6 b. x 6 c. 6x d. x 0. Simplify Ê x ˆ Ê x ˆ Ê x ˆ a. 8x 6 b. 6x c. 8x 8 d. 6x 6. Simplify 6x x a. 4x b. 4x c. 4x d. 6x x. Simplify 6x x a. 4x b. 6x x c. 4x d. x. Simplify w w w + w a. w w b. w w 4 c. w + w 4 d. w 4. Sara earned $0 in hours. At the same rate, how much would Sara earn in hours? a. $8 b. $0 c. $48 d. $. Scott ran 0 km in 40 minutes. At the same rate, how long would it take Scott to run 8 km? a. min b. 0 min c. 6 min d. 4 min 6. A taxi charged $8 for a 7 km drive. At the same rate, how far will they drive you if the charge is $60? a. km b. 6 km c. 8 km d. 0 km 7. The graph below shows the temperature of a cup of coffee in a cool room. Use the graph to estimate the temperature after minutes. a..7 C b. 0. C c. 8. C d..6 C

3 Name: ID: A 8. State the slope of the staircase shown. a. b. c. d. 9. State the slope of the staircase shown. a. b. c. 0. State the slope of the staircase shown. d. a. 4 b. c. 4 d.. The slope of the line segment through A(-,) and B(,-) is a. b. c. d.

4 Name: ID: A. The coordinates of points D and E in the graph shown are a. (-6,4) and (-,0) b. (-6,4) and (0,-) c. (4,-6) and (-,0) d. (4,-6) and (0,-). Line segments with slopes,,, 0, -, -, -, and undefined are shown. The line segments with slopes and undefined are: a. a and c b. d and e c. g and e d. d and c 4. Which of the following diagrams illustrates (x - )? a. b. c. d.. Simplify -(-x + ) as far as possible. a. x + b. x c. x d. x - 6. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to solve the equation? a. add x to both sides b. add to both sides c. subtract x from both sides d. divide both sides by 7. If x - =, then x = a. 4 b. 0 c. 9 d. 7 4

5 Name: ID: A 8. If x - 4 =, then x = a. - b. 4 c. d If x =, then x = a. b. c. 7 d If =, then x = x + a. -4 b. - c. d.

6 MPMD - Practice Mastery Test #6 Answer Section MULTIPLE CHOICE. ANS: B Remember that "of" can be translated as multiplication. 0% of 00 = = 0 Another way to do this is to note that % means out of 00. So, % of 00 is. 0% of 00 is 0 = 0.. ANS: B The sum of the numbers is 44. The mean is 44 = 8.8. ANS: B ( ) = -(-)(-) = -9 Ê ˆ = ( ) = -(-9) = 9 In this case the negative is 'atttached' to the before it is squared, so ( ) means (-)(-) which is equal to 9. With the negative outside the bracket, the answer is -9. The expression inside the brackets is (same as iii). Order of operations tells us to square the number before attaching the negative sign. The number inside the brackets works out to be -9, and with the negative outside the bracket, the answer is 9. Only ii is ANS: C The unshaded area is a 4 by 4 rectangle with 6 squares, so the shaded part must be out of 48 squares. If this is reduced, we get.. ANS: C 4 = 9 4 = To subtract fractions, get a common denominator () by multiplying the numerator and denominator of the first fraction by and then the numerator and denominator of the second fraction by. Now that we have a common denominator, subtract the numerators and keep the same base.

7 6. ANS: A 6 = = 4 4. OR... evaluate your choices and compare to the question - but eliminate c and d because they are not powers of ANS: A Ê ˆ = 6... When you take the power of a power, multiply the exponents and keep the same base. 8. ANS: A The large squares represent x terms (white are positive, shaded are negative), the long thin rectangles are x-tiles and the small squares are unit tiles. One of the positive x tiles is cancelled by the negative x tile to leave one positive x tile. The positive x tile is cancelled by one of the negative x-tiles to leave one negative x tile. Two of the + tiles are eliminated by the two - tiles, to leave us with one positive x tile, one negative x tile, and one + tile. The resulting expression is x x ANS: C If we illustrate x + x + x, we can think of addition as just "together with". The diagram for x + x + x is which is the same as 6x 0. ANS: A There Ê is no written operation between the terms in brackets. This means it is multiplication. So, x ˆ Ê x ˆ Ê x ˆ is the same as x x x. We already know that x is the same as x and x is the same as x x, so x x x could be written as x x x x x x. Rearranging, we get x x x x x x which is 8x 6. You can also remember the laws of exponents - to multiply powers with the same base, (in this case x, add the exponents and leave the base unchanged, so Ê x ˆ Ê x ˆ Ê x ˆ is the same as x x x, which is x x x. = 8 and x x x is equal to x + + or x 6, so the answer is 8 x 6 or just 8x 6.

8 . ANS: A We can think of 6x x as 6x + ( x ). These are 'like terms', so they can be 'combined' to get 4x. You may have not looked at diagrams for x yet - but it is possible to illustrate this question as follows: Two of the positive x solids eliminate the two negative x solids. The answer is 4x.. ANS: B We can think of 6x x as 6x + ( x ). These are NOT 'like terms', so they cannot be 'combined'. You may have not looked at diagrams for x yet - but it is possible to illustrate this question as follows: The diagram helps to understand that these terms cannot be combined.

9 . ANS: C The illustration of w w w + w is as follows: If we combine what we can, we get or just w + w ANS: A In one hour she would earn $0 =$6/h, so in hours she would earn h $6/h = $8 h. ANS: A He runs at a rate of 40min = 4 min/km, so to run 8km, it would take him 4 min/km 8km = min. 0km 6. ANS: A The taxi charged $8 for 7 km. The rate is $8 7km = $4/km. If they will charge $60, then the distance = $60 $4 / km = km. 7. ANS: D Each division on the vertical axis is 6. C (since there are 4 divisions for ). Following up from minutes on the horizontal axis, and then across to the vertical axis, we get a point about a quarter of the way between 0 and 6. so a reasonable answer is.6 (one quarter of 6. is.6 ). 8. ANS: A Slope = rise run = = 4

10 9. ANS: C Slope = rise run = 0. ANS: D Slope = rise run =. ANS: B Slope = rise run = ( ) = =. ANS: A D is located at -6 on the x-axis and 4 on the y-axis and E is at - on the x-axis and 0 on the y-axis.. ANS: B For a slope of, the only line segments with positive slope are b, d, and h (go up to the right), and of these d has the smallest slope. For an undefined slope, the run is 0 (so that slope would be some number 0 which is undefined), so the only choice is e. Another way to think about this one is that we know its either c or e, but c has slope 0 - think flat ski hill ANS: A (x - ) means three multiplied by (x - ) or groups of (x - ). We want a diagram that shows us (x - ) twice. The correct answer is squares are "-'s",. The long white rectangles are each x, while the small shaded

11 . ANS: D The first thing to note is that while order of operations tells us we should simplify inside the bracket first, there is nothing we can do to add -x +. These are not like terms. It is clear if you draw it,, that they cannot be 'combined'. So, we need an approach that allows us to bypass order of operations to find an equivalent expression. -(-x + ) can be thought of in two different ways: the negative in front of the bracket means the 'opposite' of the stuff in the bracket. So... if you picture the stuff in the bracket: and then flip everything to find the 'opposite', you get or x -. the negative in front of the bracket is equivalent to -(-x + ). Now - must be multiplied by each term inside the bracket. I.e., -(-x) + (-)() = x + (-) = x - If you have learned how to multiply using tiles, you can picture this as follows:, again, with answer x 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 -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 - to both sides to eliminate the + on the left, OR add + to both sides to eliminate the - on the right. So the algebraic solution should look like one of the following: x + = + x x + = + x x + = + x x + = + x x + + x = + x + x = + x + = + x + = x = x. = x x =. x + x = + x x x + = x + = x = x = x =. x + = + x x = + x x x = + x x x = x = x =. x + + = + x + x + = x x + + x = x + x = x = x. = x x =. 6

12 7. ANS: A Since this is multiple choice, the easiest thing to do might be to just check each of the answers (avoiding the fraction at first!). We discover that x=4 satisfies the equation; i.e., (4) - =. Another way is to think... something - is equal to. This means that x must be equal to. If X something is, then the number must be 4. Of course, an algebraic solution is possible: x = x + = + x = x = 8. ANS: C Since this is multiple choice, the easiest thing to do might be to just check each of the answers (avoiding the fraction at first!). We discover that x=- satisfies the equation; i.e., (-) - 4 =. x = 4 Another way is to think... something - 4 is equal to. This means that x must be equal to 6. If X something is 6, then the number must be. Of course, an algebraic solution is possible: x 4 = x = + 4 x = 6 x = 6 x = 7

13 9. ANS: C Since this is multiple choice, the easiest thing to do might be to just check each of the answers (avoiding the fraction at first!). We discover that x=7 satisfies the equation; i.e., (7) =. Another way is to think... something divided by is equal to. This means that x - must be equal to, and x=7. Of course, an algebraic solution is possible: x = Ê x ˆ = ( ) x = x + = + x = 7 0. ANS: A Since this is multiple choice, the easiest thing to do might be to just check each of the answers (avoiding the 6 fraction at first!). We discover that x=-4 satisfies the equation; i.e., ( 4) + =. Another way is to think... 6 divided by something is equal to -. This means that x + must be equal to -, and x=-4. Of course, an algebraic solution is possible. In this case, having the variables in the denominator makes an algenraic solution quite a bit more difficult (and grade 9 students do NOT have to know how to do this algebraically). However, one possible algebraic solution is shown below. 6 x + = Ê 6 ˆ (x + ) = (x + ) x + ( ) 6 = (x + ) 6 (x + ) = = x + = x + 4 = x x = 4 8