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Objective 10 2008 EPISD 9th Grade TEKS Tech Cards Which point on the grid satisfies the conditions x ≥ 5 and y < −1? A B C D W X Y Z [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. Step 1 First, plot the points TEKS 8.14C (Objective 10) Academic Vocabulary: • point • horizontal line • vertical line Step 2 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 Step 3 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. Answer: A Objective 2 2008 EPISD 9th Grade TEKS Tech Cards 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? A B C D 2n + 1 2n – 1 n+2 2n [TEKS A.3B : 2004 #43] STUDENT EXPECTATION The student looks for patterns and represents generalizations algebraically. Input the first expression TEKS A. 3B using x instead of n. (Objective 2) Look at the table of values. Your calculator should Academic Vocabulary: display a screen like the • expression one below. Step 1 • integer • even integer • table of values 2n +1 Did your expression produce even integers? NO Step 2 Repeat the process for the rest of the expressions. You may input all expressions at the same time as shown below Answer: D Step 3 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. Objective 2 2008 EPISD 9th Grade TEKS Tech Cards Which is the best representation of the function y = x? [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. Step 1 Begin by graphing the given equation, y=x. TEKS A.2A (Objective 2) Academic Vocabulary: • function • parent function • equation It is easy to see that letter B, the linear parent function, is the correct answer. Step 2 Guide students to come up with examples for the rest of the answer choices. Some examples are shown below: Answer: B A) y = 5 Step 3 C) y =|x| D) y = 0.5x² Objective 3 2008 EPISD 9th Grade TEKS Tech Cards Which equation describes a line that has a y-intercept of 5 and a slope of ½ ? F y=5 + ½ x G y=(5+x) ½ H y=5x + ½ J y=(5x + 1) 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. Step 1 Input the first answer choice into the calculator TEKS A.6D (Objective 3) Academic Vocabulary: • equation Notice how the first • line answer choice, F, • y-intercept includes the ordered • slope pair (0, 5) on the table of values. Therefore, • ordered pair the y-intercept of that line is 5. Step 2 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. Step 3 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 Answer: F Objective 3 2008 EPISD 9th Grade TEKS Tech Cards 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? [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 Step 1 Plot the given points (-1, -5) and (4, 5) using the function TEKS A.6C (Objective 3) Academic Vocabulary: • line • doubled • point • constant • slope • steeper • y-intercept Step 2 Find the slope and y-intercept of the equation of the line that passes through those two points: Answer: G So, b=-3 m=2 Step 3 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. Objective 3 2008 EPISD 9th Grade TEKS Tech Cards What is the slope of the linear function shown in the graph? [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. Step 1 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 Step 2 A) Academic Vocabulary: • slope • linear function • equation • slope-intercept form • y-intercept Graph all equations Similarly, B) Step 3 C) TEKS A.6A (Objective 3) D) Notice how only the graph from answer choice B matches with the given one. Therefore, the correct answer is B. Answer: B Objective 3 2008 EPISD 9th Grade TEKS Tech Cards 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. D The y-intercepts are 1 unit apart, and the lines intersect at (1, 0). [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 Step 1 First, find the equation of the given line using two points. TEKS A.6C (Objective 3) Academic Vocabulary: •linear function • parallel •coordinate grid • intersect y = - 5 x + 6 •y-intercept •slope •relationship 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. Step 2 Step 3 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 Answer: B Objective 3 2008 EPISD 9th Grade TEKS Tech Cards The table below shows various values for x and y. Which equation best describes the relationship between x and y? F G H J y = −3x + 5 y = −5x – 7 y = −x + 17 y = 3x + 41 [TEKS A.5C : 2006 #15 ] STUDENT EXPECTATION The student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions. Step 1 First, input the equations into the calculator using the function TEKS A.5C (Objective 3) Academic Vocabulary: • equation • relationship • table of values • ordered pair Step 2 Look at the tables of values for all equations: Answer: F Step 3 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. Objective 3 2008 EPISD 9th Grade TEKS Tech Cards What is the slope of the line that contains the coordinate points (8, −3) and (−2, 7)? A) B) C) D) -1 -9/11 -5/3 -2/5 [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. Step 1 TEKS A.6A Guide students to write the (Objective 3) slope formula, which can be found in their formula chart: m =y2-y1 x2-x1 Academic Vocabulary: Identify the x and y values of the given • Slope points: (8, −3) (−2, 7) • line x1 y1 x2 y2 Calculate y2-y1: Calculate x2-x1: Step 2 =10 =-10 • coordinate points • equation 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. Step 3 Graph the equation Answer: A Objective 3 2008 EPISD 9th Grade TEKS Tech Cards Find the slope of the given line. A 9 B 3 C D -3 [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 Step 1 Begin by plotting two points from the graph (0, 2) and (-2, -4) TEKS A.6A (Objective 3) Academic Vocabulary: • slope • line • parallel Step 2 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 Step 3 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 Answer: B Objective 3 2008 EPISD 9th Grade TEKS Tech Cards What are the x- and y-intercepts of the function graphed below? A B C D (4, 0) and (5, 0) (4, 0) and (0, 5) (0, 4) and (5, 0) (0, 4) and (0, 5) [TEKS A.3B : 2004 #42 ] STUDENT EXPECTATION Given situations, the student looks for patterns and represents generalizations algebraically. Step 1 Find the equations of the lines passing through the given points in the answer choices and graph them: A) (4,0) & (5,0) TEKS A.3B (Objective 3) Academic Vocabulary: • x-intercept • y-intercept • function • line • points Step 2 We continue the same process using the rest of the answer choices B) (4,0) & (0,5) Step 3 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. Answer: B Objective 3 2008 EPISD 9th Grade TEKS Tech Cards Which linear function includes the points (–3, 1) and (–2, 4)? A B C D f(x) = 3x + 10 f(x) = ⅓ x + 2 f(x) = 3x − 6 f(x) = −3x + 1 [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. Step 1 Begin by plotting the given points (-3, 1) and (-2, 4). TEKS A.6D (Objective 3) Academic Vocabulary: • linear function • point • equation Step 2 Graph each function to examine which one passes through the plotted points. Answer: A A. f(x) = 3x + 10 y = 3x + 10 Step 3 Similarly: B. y = ⅓ x + 2 C. y= 3x − 6 D y= −3x + 1 Thus, the correct answer is letter A. Objective 4 2008 EPISD 9th Grade TEKS Tech Cards 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? A B C D 4 5 9 10 [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. Step 1 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 TEKS A.7B (Objective 4) Academic Vocabulary: • graph • linear equation • true statement A 1 represents a true statement. Therefore, A is the correct answer. Step 2 However, to confirm that A is the right choice, we must test the rest of the answer choices: B) x=5 Notice how the calculator produced a 0 for this choice. Thus, this answer cannot represent the correct value for x. Step 3 C) x=9 D) x=10 Similarly, Answer: A Objective 10 2008 EPISD 9th Grade TEKS Tech Cards 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 B C D $70.50 $124.50 $156.00 $187.50 [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 Step 1 Begin by writing an equation that describes the situation: C = 39 d + 0.09 m C Total Cost d Number of days TEKS 8.14B (Objective 10) Academic Vocabulary: • equation • given values • solution m Miles driven Step 2 Store the given values for d and m: Answer: D Step 3 Enter the equation and find a solution: Therefore, the correct answer is letter D. Objective 6 2008 EPISD 9th Grade TEKS Tech Cards 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) [TEKS 8.7D: 2003#43 ] STUDENT EXPECTATION The student will locate and name points on a coordinate plane using ordered pairs of rational numbers Step 1 Adjust the window to match the one on the given grid: TEKS 8.7D (Objective 6) Academic Vocabulary: • point • coordinate • grid • ordered pair Step 2 Plot the ordered pairs for each answer choice: A) Answer: D Similarly, B) Step 3 C) D) The answer choice that shows a point representing the post office is letter D. Objective 4 2008 EPISD 9th Grade TEKS Tech Cards Which inequality best describes the graph shown below? A B C D y ≥ −2x y ≥ −x − 2 y ≥ −2x − 2 y≥x–2 [TEKS A.7A ] STUDENT EXPECTATION The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems. Step 1 A) Graph each inequality: TEKS A.7A (Objective 4) B) Academic Vocabulary: • inequality • table of values • intercepts Step 2 C) D) Answer: C You can eliminate answer choices A and D Step 3 Check the tables of values for choices B and C: B) C) Choice C does include the intercepts (-2, 0) and (0, -2). Thus, C is the correct answer. Objective 1 2008 EPISD 9th Grade TEKS Tech Cards Which inequality best describes the graph shown below? F G H J y > − ¾x + 5 y < − 4⁄3 x + 5 y < − ¾x + 5 y > − 4⁄3 x + 5 [TEKS A.1D : 2006 #5 ] STUDENT EXPECTATION The student represents relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. Step 1 Begin by selecting a point from the shaded area. For example (8, -2) Store the corresponding x and y values. Step 2 F) Academic Vocabulary: • inequality • point • shaded area • corresponding values Test each inequality: G) Answer: J H) J) F and G produced a 0 (False statements!) Step 3 We repeat the process for H and J, only, using a different point: (5, 3) H) TEKS A.1D (Objective 1) J) H produced a false statement. Therefore, letter J is the correct answer. Objective 5 2008 EPISD 9th Grade TEKS Tech Cards Which expression describes the area in square units of a rectangle that has a width of 4x 3y 2 and a length of 3x 2y 3? A B C D 12x 6y 6 12x 5y 5 7x 6y 6 7x 5y 5 [TEKS A.11A : 2003 #10 ] STUDENT EXPECTATION The student uses [patterns to generate] the laws of exponents and applies them in problem solving situations. Step 1 Begin by storing a value for both x and y: TEKS A.11A (Objective 5) Academic Vocabulary: • expression • width • area • length • square units • rectangle Step 2 Find the area of the rectangle by multiplying the given expressions: Answer: B A= (L)(W) A= Step 3 Input all choices and compare to the value obtained in step 2: A) B) C) D) The correct answer is letter B since = Objective 5 2008 EPISD 9th Grade TEKS Tech Cards Which expression is equivalent to A B C D 4x 9 4x 2 2x 8 2x 4 [TEKS A.11A : 2006 #9 ] STUDENT EXPECTATION The student uses [patterns to generate] the laws of exponents and applies them in problem solving situations. Step 1 Enter the expression into the calculator using the y editor: TEKS A.11A (Objective 5) Academic Vocabulary: • expression • equivalent • table of values Step 2 Enter each answer choice and compare the tables of values A) B) Step 3 C) D) Answer: B Objective 10 2008 EPISD 9th Grade TEKS Tech Cards 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 G H J x = 0 and y = 2 x = 1 and y = 2 x = 2 and y = 0 x = 2 and y = 1 [TEKS 8.16B : 2004 #28 ] STUDENT EXPECTATION The student validates his/her conclusions using mathematical properties and relationships. Step 1 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 TEKS 8.16B (Objective 10) Academic Vocabulary: • pair • values • substitute • equation Step 2 G) x=1 and y=2 xy 2 (xy) 2 H) x=2 and y=0 xy 2 (xy) 2 Step 3 J) x=2 and y=1 xy 2 (xy) 2 The only choice that Rudy could use to disprove Sean is letter J. Answer: J Objective 5 2008 EPISD 9th Grade TEKS Tech Cards If y = x 3, what is equivalent to x 12 ? A B C D y 36 y 15 y9 y4 [TEKS A.11A : 2004 #44 ] STUDENT EXPECTATION The student uses [patterns to generate] the laws of exponents and applies them in problem solving situations. Step 1 Input both using the y editor. y=x3 and x12 TEKS A.11A (Objective 5) Academic Vocabulary: • equation • equivalent • table of values Step 2 Input the answer choices and compare their tables of values with that of x12 A) Step 3 B) C) D) Similarly, Answer: D Objective 7 2008 EPISD 9th Grade TEKS Tech Cards 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 B C D 192 96 48 14 [TEKS 8.7B : 2003 #31 ] STUDENT EXPECTATION The student uses geometric concepts and properties to solve problems in fields such as art and architecture. Step 1 Adjust the window : TEKS 8.7B (Objective 7) Academic Vocabulary: • rectangular floor • square tiles • measure • cover • grid Step 2 Turn on the grid and graph: Answer: C Step 3 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. Objective 2 2008 EPISD 9th Grade TEKS Tech Cards Simplify the algebraic expression 3(x + 3) − 2(x + 3). A B C D x+3 x−3 −6x2 − 54 6x2 + 3 [TEKS A.4B : 2004 #20 ] STUDENT EXPECTATION The student uses the commutative, associative, and distributive properties to simplify algebraic expressions. Step 1 Input the expression using the and graph: TEKS A.4B (Objective 2) Academic Vocabulary: •simplify •algebraic Expression Step 2 Graph all choices: Similarly, A B Step 3 C D Notice how letter A is the only answer which graph matches the original one. Thus, letter A is the correct answer. Answer: A Objective 3 2008 EPISD 9th Grade TEKS Tech Cards Which of the following ordered pairs is the x-intercept or the y-intercept of the function 2x − y = 8? F G H J (8, 0) (0, 4) (4, 0) (0, 8) [TEKS A.6E : 2006 #19 ] STUDENT EXPECTATION The student determines the intercepts of linear functions from graphs, tables, and algebraic representations. Step 1 Find the x-intercept: Substitute a 0 for y 2x-0=8 Academic Vocabulary: • ordered pair • x-intercept • y-intercept • function • solve Solve: The x-intercept is at x=4, or (4, 0) Step 2 TEKS A.6E (Objective 3) Find the y-intercept: Substitute a 0 for x 2(0)-y=8 Solve similarly. Continue to use x when you input the expression into the calculator Scroll up until you see y1=y2 Step 3 So, The x-intercept is (4, 0), and The y-intercept is (0, -8) Therefore, the correct answer is letter H. Answer: H