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EPISD 9 th Grade TEKS Tech Cards [ TEKS 8.14C : 2004 #48 ] STUDENT EXPECTATION Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. Objective 10 2008 Which point on the grid satisfies the conditions x ≥ 5 and y < −1? A W B X C Y D Z

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Academic Vocabulary: point horizontal line vertical line Answer: A TEKS 8.14C (Objective 10) Step 1 Step 2 Step 3 First, plot the points Draw a vertical line to represent x>5 hold right arrow and scroll to the right until you get to x=5 Only points x and w are at or to the right of the vertical line Draw a horizontal line to represent y<-1 hold down arrow and scroll down until you get to y=-1 Point x is not below the line y= -1 but point w is. Thus, letter A is the answer.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.3B : 2004 #43 ] STUDENT EXPECTATION The student l ooks for patterns and represents generalizations algebraically. Objective 2 2008 Sue wants to write an expression that will always produce an even integer. Which of the following will always produce an even integer for any given integer, n? A2n + 1 B2n – 1 Cn + 2 D2n

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Academic Vocabulary: expression integer even integer table of values Answer: D TEKS A. 3B (Objective 2) Step 1 Step 2 Step 3 Input the first expression using x instead of n. Your calculator should display a screen like the one below. Look at the table of values. 2n +1 Did your expression produce even integers? NO Repeat the process for the rest of the expressions. You may input all expressions at the same time as shown below Look and compare the tables of values. The last expression, Y4, is the only one that produces even integers for any given integer x. Therefore, letter D is the correct answer.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.2A : 2003 #7 ] STUDENT EXPECTATION The student identifies [and sketches] the general forms of linear, y=x, and quadratic, y=x², parent functions. Objective 2 2008 Which is the best representation of the function y = x?

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Academic Vocabulary: function parent function equation Answer: B TEKS A.2A (Objective 2) Step 1 Step 2 Step 3 Begin by graphing the given equation, y=x. It is easy to see that letter B, the linear parent function, is the correct answer. Guide students to come up with examples for the rest of the answer choices. Some examples are shown below: A) y = 5 C) y =|x| D) y = 0.5x²

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EPISD 9 th Grade TEKS Tech Cards Which equation describes a line that has a y-intercept of 5 and a slope of ½ ? [ TEKS A.6D : 2004 #10 ] STUDENT EXPECTATION The student graphs and writes equations of lines given characteristics such as two points, a point and a slope, or a slope and y–intercept. Objective 3 2008 F y=5 + ½ x G y=(5+x) ½ H y=5x + ½ J y=(5x + 1) ½

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Academic Vocabulary: equation line y-intercept slope ordered pair Answer: F TEKS A.6D (Objective 3) Step 1 Step 2 Step 3 Input the first answer choice into the calculator Notice how the first answer choice, F, includes the ordered pair (0, 5) on the table of values. Therefore, the y-intercept of that line is 5. Similarly, answer choices G, H, and J do not include the point (0, 5) as shown below. Thus, the y-intercept for those lines cannot be 5 and those three answers can be eliminated. Delete the three wrong answers from the and find the slope for the first line to ensure the answer is correct The slope is dy/dx =.5 = 1/2

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.6C : 2003 #18 ] STUDENT EXPECTATION The student investigates, describes, and predicts the effects of changes in m and b on the graph of y=mx+b Objective 3 2008 The graph of a line that contains the points (–1, −5) and (4, 5) is shown to the right. Which best represents this line if the slope is doubled and the y-intercept remains constant?

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Academic Vocabulary: line point slope y-intercept Answer: G TEKS A.6C (Objective 3) Step 1 Step 2 Step 3 Plot the given points (-1, -5) and (4, 5) using the function Find the slope and y-intercept of the equation of the line that passes through those two points: Double the original slope (2x2=4) and let the y-intercept (0, -3) remain the same. Then, graph the new line: y=4x-3. The new line is steeper and has the same y-intercept as the original one. Thus, the correct answer is G. So, b=-3 m=2 doubled constant steeper

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.6A : 2004 #19 ] STUDENT EXPECTATION The student develops the concept of slope as rate of change and determines slopes from graphs, tables, and algebraic representations. Objective 3 2008 What is the slope of the linear function shown in the graph?

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Academic Vocabulary: slope linear function equation slope-intercept form y-intercept Answer: B TEKS A.6A (Objective 3) Step 1 Step 2 Step 3 Write linear equations in slope intercept form for all answer choices using the y-intercept (0, 14) and adjust the window to match the one on the graph. A) -7/4 x + 14 B) -4/7 x +14 C) 4/7 x + 14 D) 7/4 x +14 Graph all equations A) Similarly, B) C) D) Notice how only the graph from answer choice B matches with the given one. Therefore, the correct answer is B.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.6C : 2006 #12 ] STUDENT EXPECTATION The student investigates, describes, and predicts the effects of changes in m and b on the graph of y=mx+b Objective 3 2008 The graph of a linear function is shown on the coordinate grid below. If the y-intercept is changed to (0, 5) and the slope becomes −4, which statement best describes the relationship between the two lines when they are graphed on the same coordinate grid? A The y-intercepts are 1 unit apart, and the lines are parallel. B The y-intercepts are 1 unit apart, and the lines intersect at (1, 1). C The y-intercepts are 1 unit apart, and the lines are perpendicular. DThe y-intercepts are 1 unit apart, and the lines intersect at (1, 0).

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Academic Vocabulary: linear function coordinate grid y-intercept slope relationship Answer: B TEKS A.6C (Objective 3) Step 1 Step 2 Step 3 First, find the equation of the given line using two points. y = - 5 x + 6 If the slope changes from -5 to -4 and the y-intercept from (0, 6) to (0, 5), the new equation will be y= -4x + 5. Graph both equations. The lines are not parallel nor perpendicular. Therefore, A and C cannot be the correct answers. So, we need to find where the lines intersect. Since the lines intersect at (1, 1), the correct answer is B parallel intersect

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.5C : 2006 #15 ] STUDENT EXPECTATION The student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions. Objective 3 2008 The table below shows various values for x and y. Which equation best describes the relationship between x and y? F y = −3x + 5 G y = −5x – 7 H y = −x + 17 J y = 3x + 41

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Academic Vocabulary: equation relationship table of values ordered pair Answer: F TEKS A.5C (Objective 3) Step 1 Step 2 Step 3 First, input the equations into the calculator using the function Look at the tables of values for all equations: Check the first ordered pair (-6, 23) from the original table. As you can see, that point is included in all four tables. Continue checking the rest of the ordered pairs. Only Y1 includes all points from the table. Thus, letter F is the correct answer.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.6A : 2006 #17 ] STUDENT EXPECTATION The student develops the concept of slope as rate of change and determines slopes from graphs, tables, and algebraic representations. Objective 3 2008 What is the slope of the line that contains the coordinate points (8, −3) and (−2, 7)? A) -1 B) -9/11 C) -5/3 D) -2/5

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Academic Vocabulary: Slope line coordinate points equation Answer: A TEKS A.6A (Objective 3) Step 1 Step 2 Step 3 Guide students to write the slope formula, which can be found in their formula chart: m =y2-y1 x2-x1 Identify the x and y values of the given points: (8, −3) (−2, 7) Calculate y2-y1: =10 Calculate x2-x1: =-10 Find the slope: So, m=-1 Extend by finding the equation of the line that goes through the given points and has the obtained slope. x1 y1 x2 y2 Graph the equation

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.6A ] STUDENT EXPECTATION The student develops the concept of slope as rate of change and determines slopes from graphs, tables, and algebraic representations Objective 3 2008 Find the slope of the given line. A 9 B 3 C D -3

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Academic Vocabulary: slope line parallel Answer: B TEKS A.6A (Objective 3) Step 1 Step 2 Step 3 Begin by plotting two points from the graph (0, 2) and (-2, -4) If letter A is the correct answer, then the slope of the line must be 9. So, we can graph the equation y=9x and see if such line passes through the points or seems parallel to the line that would go through those points. It doesn't. Thus, letter A is not the correct answer If we continue this process, we can see that letter B is the right answer (Look at the graphs below). B) y=3x C) y=1/3 x D) y= -3x

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.3B : 2004 #42 ] STUDENT EXPECTATION Given situations, the student looks for patterns and represents generalizations algebraically. Objective 3 2008 What are the x- and y-intercepts of the function graphed below? A (4, 0) and (5, 0) B(4, 0) and (0, 5) C (0, 4) and (5, 0) D(0, 4) and (0, 5)

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Academic Vocabulary: x-intercept y-intercept function line points Answer: B TEKS A.3B (Objective 3) Step 1 Step 2 Step 3 Find the equations of the lines passing through the given points in the answer choices and graph them: We continue the same process using the rest of the answer choices A) (4,0) & (5,0) B) (4,0) & (0,5) C) (0,4) & (5,0) D) (0,4) & (0,5) We can see that letter B is correct because: 1) The graphs match 2) (4,0) is the x-intercept on the graph, and 3) (0,5) is the y-intercept on the graph.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.6D : 2003#44 ] STUDENT EXPECTATION The student graphs and writes equations of lines given characteristics such as two points, a point and a slope, or a slope and -intercept. Objective 3 2008 Which linear function includes the points (–3, 1) and (–2, 4)? Af(x) = 3x + 10 B f(x) = ⅓ x + 2 C f(x) = 3x − 6 Df(x) = −3x + 1

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Academic Vocabulary: linear function point equation Answer: A TEKS A.6D (Objective 3) Step 1 Step 2 Step 3 Begin by plotting the given points (-3, 1) and (-2, 4). Graph each function to examine which one passes through the plotted points. A. f(x) = 3x + 10 y = 3x + 10 B. y = ⅓ x + 2 C. y= 3x − 6 D y= −3x + 1 Similarly: Thus, the correct answer is letter A.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.7B : 2004 #36 ] STUDENT EXPECTATION The student investigates methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, selects a method, and solves the equations and inequalities. Objective 4 2008 The graphs of the linear equations y = 2x – 3 and y = 3x − 7 are shown below. If 2x − 3 = 3x − 7, what is the value of x? A4 B 5 C 9 D10

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Academic Vocabulary: graph linear equation true statement Answer: A TEKS A.7B (Objective 4) Step 1 Step 2 Step 3 The correct value of x will make the equation 2x-3 = 3x -7 true. Guess and check to see which answer choice will do that. A) x=4 A 1 represents a true statement. Therefore, A is the correct answer. However, to confirm that A is the right choice, we must test the rest of the answer choices: Notice how the calculator produced a 0 for this choice. Thus, this answer cannot represent the correct value for x. B) x=5 C) x=9 Similarly, D) x=10

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EPISD 9 th Grade TEKS Tech Cards [ TEKS 8.14B: 2003 #5 ] STUDENT EXPECTATION The student uses a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness Objective 10 2008 Alonso’s family rented a car when they flew to Orlando for a 4-day vacation. They paid $39 per day and $0.09 for each mile driven. How much did it cost to rent the car for 4 days and drive 350 miles, not including tax? A $70.50 B $124.50 C $156.00 D $187.50

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Academic Vocabulary: equation given values solution Answer: D TEKS 8.14B (Objective 10) Step 1 Step 2 Step 3 Begin by writing an equation that describes the situation: C = 39 d + 0.09 m C Total Cost d Number of days m Miles driven Store the given values for d and m: Enter the equation and find a solution: Therefore, the correct answer is letter D.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS 8.7D: 2003#43 ] STUDENT EXPECTATION The student will locate and name points on a coordinate plane using ordered pairs of rational numbers Objective 6 2008 Jake made a map of his neighborhood for a school project. He placed a grid over the map. Which coordinate point best represents the post office? A (6, 12) B (12, 6) C (1.2, 0.6) D (0.6, 1.2)

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Academic Vocabulary: point coordinate grid ordered pair Answer: D TEKS 8.7D (Objective 6) Step 1 Step 2 Step 3 Adjust the window to match the one on the given grid: Plot the ordered pairs for each answer choice: A) Similarly, B) C) D) The answer choice that shows a point representing the post office is letter D.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.7A ] STUDENT EXPECTATION The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems. Objective 4 2008 Which inequality best describes the graph shown below? A y ≥ −2x By ≥ −x − 2 C y ≥ −2x − 2 Dy ≥ x – 2

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Academic Vocabulary: inequality table of values intercepts Answer: C TEKS A.7A (Objective 4) Step 1 Step 2 Step 3 Graph each inequality: B) C) D) Check the tables of values for choices B and C: B) C) A) You can eliminate answer choices A and D Choice C does include the intercepts (-2, 0) and (0, -2). Thus, C is the correct answer.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.1D : 2006 #5 ] STUDENT EXPECTATION The student represents relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. Objective 1 2008 Which inequality best describes the graph shown below? F y > − ¾x + 5 G y < − 4⁄ 3 x + 5 H y < − ¾x + 5 J y > − 4⁄ 3 x + 5

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Academic Vocabulary: inequality point shaded area corresponding values Answer: J TEKS A.1D (Objective 1) Step 1 Step 2 Step 3 Begin by selecting a point from the shaded area. For example (8, -2) Store the corresponding x and y values. Test each inequality: F) G) H) J) F and G produced a 0 (False statements!) We repeat the process for H and J, only, using a different point: H produced a false statement. Therefore, letter J is the correct answer. H) J) (5, 3)

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.11A : 2003 #10 ] STUDENT EXPECTATION The student uses [patterns to generate] the laws of exponents and applies them in problem solving situations. Objective 5 2008 Which expression describes the area in square units of a rectangle that has a width of 4x 3 y 2 and a length of 3x 2 y 3 ? A 12x 6 y 6 B12x 5 y 5 C 7x 6 y 6 D7x 5 y 5

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Academic Vocabulary: expression area square units rectangle Answer: B TEKS A.11A (Objective 5) Step 1 Step 2 Step 3 Begin by storing a value for both x and y: Find the area of the rectangle by multiplying the given expressions: A= (L)(W) A= Input all choices and compare to the value obtained in step 2: A) B) C) D) The correct answer is letter B since = width length

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.11A : 2006 #9 ] STUDENT EXPECTATION The student uses [patterns to generate] the laws of exponents and applies them in problem solving situations. Objective 5 2008 Which expression is equivalent to A 4x 9 B4x 2 C 2x 8 D 2x 4

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Academic Vocabulary: expression equivalent table of values Answer: B TEKS A.11A (Objective 5) Step 1 Step 2 Step 3 Enter the expression into the calculator using the y editor: Enter each answer choice and compare the tables of values A) B) C) D)

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EPISD 9 th Grade TEKS Tech Cards [ TEKS 8.16B : 2004 #28 ] STUDENT EXPECTATION The student validates his/her conclusions using mathematical properties and relationships. Objective 10 2008 Sean is an Algebra I student who believes that xy 2 = (xy) 2. Rudy informs Sean that this theory is not always true. Which pair of values for x and y could Rudy use to disprove Sean’s theory? F x = 0 and y = 2 G x = 1 and y = 2 H x = 2 and y = 0 Jx = 2 and y = 1

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Academic Vocabulary: pair values substitute equation Answer: J TEKS 8.16B (Objective 10) Step 1 Step 2 Step 3 Substitute the x and y values from each answer choice into each side of the equation and compare. F) x=0 and y=2 xy 2 (xy) 2 G) x=1 and y=2 H) x=2 and y=0 xy 2 (xy) 2 xy 2 (xy) 2 J) x=2 and y=1 The only choice that Rudy could use to disprove Sean is letter J. xy 2 (xy) 2

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.11A : 2004 #44 ] STUDENT EXPECTATION The student uses [patterns to generate] the laws of exponents and applies them in problem solving situations. Objective 5 2008 If y = x 3, what is equivalent to x 12 ? A y 36 B y 15 C y 9 Dy 4

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Academic Vocabulary: equation equivalent table of values Answer: D TEKS A.11A (Objective 5) Step 1 Step 2 Step 3 Input both y=x 3 and x 12 using the y editor. Input the answer choices and compare their tables of values with that of x 12 A) Similarly, B) C) D)

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EPISD 9 th Grade TEKS Tech Cards [ TEKS 8.7B : 2003 #31 ] STUDENT EXPECTATION The student uses geometric concepts and properties to solve problems in fields such as art and architecture. Objective 7 2008 A 12- by 16-foot rectangular floor will be covered by square tiles that measure 2 feet on each side. If the tiles are not cut, how many of them will be needed to cover the floor? A 192 B 96 C 48 D 14

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Academic Vocabulary: rectangular floor square tiles measure cover grid Answer: C TEKS 8.7B (Objective 7) Step 1 Step 2 Step 3 Adjust the window : Turn on the grid and graph: There are 6 “tiles” in each column and 8 “tiles” in each row. Therefore, the total number of tiles needed to cover the floor is: Thus, the correct answer is C.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.4B : 2004 #20 ] STUDENT EXPECTATION The student uses the commutative, associative, and distributive properties to simplify algebraic expressions. Objective 2 2008 Simplify the algebraic expression 3(x + 3) − 2(x + 3). Ax + 3 B x − 3 C −6x 2 − 54 D6x 2 + 3

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Academic Vocabulary: simplify algebraic Expression Answer: A TEKS A.4B (Objective 2) Step 1 Step 2 Step 3 Input the expression using the and graph: Graph all choices: Similarly, A B C D Notice how letter A is the only answer which graph matches the original one. Thus, letter A is the correct answer.

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EPISD 9 th Grade TEKS Tech Cards [ TEKS A.6E : 2006 #19 ] STUDENT EXPECTATION The student determines the intercepts of linear functions from graphs, tables, and algebraic representations. Objective 3 2008 Which of the following ordered pairs is the x-intercept or the y-intercept of the function 2x − y = 8? F (8, 0) G (0, 4) H (4, 0) J (0, 8)

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Academic Vocabulary: ordered pair x-intercept y-intercept function solve Answer: H TEKS A.6E (Objective 3) Step 1 Step 2 Step 3 Find the x-intercept: Substitute a 0 for y2x-0=8 Solve: The x-intercept is at x=4, or (4, 0) Substitute a 0 for x2(0)-y=8 Solve similarly. Continue to use x when you input the expression into the calculator Find the y-intercept: Scroll up until you see y1=y2 So, The x-intercept is (4, 0), and The y-intercept is (0, -8) Therefore, the correct answer is letter H.

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