Algebra I AIR Test. Mar 12-10:36 AM

Transcription

1 Algebra I AIR Test Mar 12-10:36 AM Test blueprint with important areas: Numbers, Quantities, Equations, and Expressions 33-41% Polynomials, expressions, create/solve/re-arrange equations, write systems of equations, explain how to solve equations, solve inequalities Functions 41-50% What is a function, function notation, interpret functions/applications of/context, represent and solve equations and inequalities graphically Statistics 18-22% Rate of change/slope, intercept/constant, compute and interpret correlation coefficient with calculator, correlation versus causation Mar 14-8:41 AM 1

2 Formula Sheet Many formulas that you will need on the AIR test are not included on the provided formula sheet! Mar 14-8:54 AM Mar 14-8:58 AM 2

3 Mar 12-11:03 AM Technology-Enriched Questions Some questions will have you plot points, graph, fill-in-the-blank and select multiple answers! Read the questions carefully! Mar 14-9:03 AM 3

4 Mar 14-9:01 AM Mar 14-9:05 AM 4

5 (8 1 x 3 ) 2/3 8 2/3 x 3*2/3 4x 2 Use calculator: 8 ^ 2 3 ENTER 4 3 * (exponent on x) Mar 12-11:38 AM (b): FAR from the center of the city is towards the top of the graph, so it doesn't make sense that all rents go down the farther you get, except $1275, if this is the correct answer. It isn't correct! Change in rent (c): each time rent would go UP 1275 because positive, so isn't the correct answer because the dots are going down. Change in distance (d): look at scale on x axis. At 1275 we'd probably be something negative (doesn't make sense, not correct). Mar 12-11:04 AM 5

6 TI-84 STAT, Edit for lists. Type Time values in L 1, Distance in L 2. STAT, CALC, 1-var stats, run for L 1 and L 2 separately. L 1 (time) stats: x = 10 (mean) med = 10 delete outlier 10, re-run stats. x = 10 med = 10 Range: high - low Mean: add up all values, then divide by how many values there are Median: when numbers are in order, the middle number. When there are two numbers, add the two numbers and divide by 2. Mar 12-11:18 AM Mean time: 10 Median: 10 w/o outlier: 10 : 10 Mean distance: 4.06 Median: 3.7 w/o outlier: 3.37 :3.7 Do same for L 2 --run 1-var test with data as is, then delete outlier (11.0) and re-run stats! Percent is part total/whole. The part we want is 20. Total: = = 0.4, but percent means per * 100 = 40% Mar 12-11:17 AM 6

7 How to reason: lowest dots cluster around 20 (rules out a and c). From there, must use slope, rise run y = mx + b When graphing lines: 1. plot y-intercept 2. from y-intercept, follow slope rise run m is slope b is y-intercept (where the line crosses the y-axis) Mar 12-11:34 AM *need best answer! positive (goes up from left to right) close to 1, strong relationship negative (goes down from left to right) close to -1 strong relationship Mar 12-11:35 AM 7

8 with x, marble-related 3x + 8 must be bucket (only weighing marbles and the bucket) marbles Mar 12-12:43 PM total = cost per pound plus fixed fee f(x) = 4.99 x Mar 12-11:39 AM 8

9 f(12) means everywhere there is x, plug in 12 f(12) = 2/3 * (can type in calculator as 2 3 * ) = 24/3 + 3 = = 11 Mar 12-11:37 AM Each point (x, y), take and plug each point into equation y = 1/2x + 3/4 Can use calculator to help! A. 1/2 = 1/2 * 0 + 3/4 1/2 = 0 + 3/4, 1/2 = 3/4 NO B. 3/4 = 1/2*0 + 3/4 3/4 = 0 + 3/4, 3/4 = 3/4 YES C. 0 = 1/2*3/4 + 3/4 0 = 3/8 + 3/4 NO D. 1/2 = 1/2*3/4 + 3/4 1/2 = 3/8 + 3/4 NO E. 1 = 1/2 * 1/2 + 3/4 1 = 1/4 + 3/4, 1 = 4/4 = 1 YES Mar 12-11:37 AM 9

10 Identify what Fred did wrong, does not equal 46! If having a hard time doing so, start from beginning and do it yourself to try and get it. Fred did not combine correctly. 24x - 56 = -6x x - 56 = -6x x +6x 30x - 56 = x = x = 18/30 = 3/5 (can type in calculator, get 0.6, MATH 1:Frac ENTER ENTER) Mar 12-11:16 AM FOIL (First, Outer, Inner, Last) (2x 2 + 3)(x + 4) 2x x 2 * x 2x 3 2x 2 * 4 +8x 2 3 * x +3x 3 * x +4 2x 3 +8x 2 +3x +12 2x 3 +8x 2 +3x+12 Mar 12-11:35 AM 10

11 9x 4 - y 2 3x 2 *3x 2 - y*y use formula sheet shortcut, (x + a)(x - a) (3x 2 + y)(3x 2 - y) 9x 4 - y 2 3*3*x 2 *x 2 y*y (3) 2 (x 2 ) 2 (y) 2 (3x 2 ) 2 - (y) 2 Mar 12-11:36 AM p + g = 2.5 total pounds peaches and grapefruit! pounds peaches pounds grapefruit Mar 12-11:36 AM 11

12 MATRIX 2nd x -1 > >EDIT 1: [A] 2 x QUIT 2nd MODE MATRIX 2nd x -1 >> EDIT 2: [B] 2 x QUIT 2nd MODE Use MATRIX to put in calculator: [A] -1 [B] ENTER [ ] as answer, meaning l=150 and u = 200 Sales (money): 35l + 25u = 10,250 Number of tickets: l + u = 350 Shortest route: Use coefficients to set up matrix, use calculator to solve. (see left) Can also use substitution: l + u = 350 -u -u l = u 35l + 25u = (350 - u) + 25u = u + 25u = u = Mar 12-11:39 AM -10u = u = 200 l + u = 350 l = 350 l = 150 year 1: 150*2 = 300 year 2: 300 * 2 which is 150*2*2 = 600 year 3: 600*2 which is 150*2*2*2 = 1200 Every year another *2, which is where you get 2 x Mar 12-11:37 AM 12

13 Graph on TI-84: use y=, type in -x 2 +4/3x+1/4, push GRAPH. 1.5 seconds (see below) Where grasshopper jumps Mar 12-11:38 AM Where he lands 2nd, TRACE 2: zero ENTER ENTER Use > to move cursor past landing point. ENTER, ENTER Zero x = 1.5, y = 0 Graph on TI-84 calculator y=, input -x 2 +14x-40, GRAPH Look at x values between 6 and 8. a. Increase = goes up, true between 6 and 7 b. No, because it goes down (decreases) c. Rate of change= slope (slant). Goes up and down symmetrically, so average (add both together, divide) would be zero. It is like is zero. d. Constant = doesn't change. Not the case. e. False. One is positive, one is negative. Mar 12-11:38 AM 13

14 Using the calculator, you can graph using y= (as explained in the previous questions), then use 2nd TRACE 3: minimum ENTER use cursor to trace to the right of the minimum ENTER, ENTER minimum value x = 2, y = 3 (2, 3) Can also use knowledge of vertex form, a(x - h) 2 + k, where (h, k) is vertex. Mar 12-11:40 AM 5 g(x) = f(x) + h If we look at x = 0, g(0) = f(0)+h We see f(0) = 0 on the graph. So, g(0) = 0 + h We also know g(0) is 5 from the graph. So, instead of g(0), we replace with 5. 5 = 0 + h h must equal 5. Mar 12-12:43 PM 14

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