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PSSA - Math

PSSA - Math. Targeted Review of Major Concepts. The Guess & Check Strategy.

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PSSA - Math

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  1. PSSA - Math Targeted Review of Major Concepts

  2. The Guess & Check Strategy The main advantage to taking a multiple choice test is that the correct answer is right in front of you…you simply have to find it. Remember, sometimes the “most mathematical” way to get the answer may not be the easiest! Plug your answer choices into the calculator until you find the one that works!! Example: What value of k makes the following true? (53)(25) = 4(10k) • 2 • 3 • 4 • 6

  3. Use the Calculator!!! Don’t be afraid to use the calculator to help answer questions. Remember, you can solve any equation simply by entering each half into Y= and finding where the two graphs intersect. You can enter data into your calculator by using the STAT button and going to EDIT. This is especially helpful for finding mean, median, and quartiles (1-VAR Stats). The same process can also be used for lines of best fit (LinReg)

  4. The Formula Sheet Please be aware that you are permitted the useof the formula sheetprovided – it is very important that you familiarize yourself with this formula sheet ahead of time! Some important formulas on the sheet: Slope, Equations of lines, Area/Volume, Distance, Midpoint

  5. y = mx + b • Slope-intercept form of a linear function • m is the slope • b is the y-intercept • ax + by = c can easily be converted to this form • Know the positive and negative y-axis • Know slope relationships Y = 2x + 1 Y = -3x - 4 2x + 3y = 19 3y = -2x + 19 y = (-2/3)x + (19/3)

  6. Slope • Slope is the rate of change • Difference in y / Difference in x • Parallel Lines – Same slopes • Perpendicular line – Opposite Reciprocal slopes

  7. Functions • Domain – Inputs (x’s) • Range – Outputs (y’s) • A relation is a function whenever each x is paired with exactly one y. • [ (1,2) (3,5) (-4, 8) (2,5) ]– Function • [ (3,4) (9,1) (5,2) (3,6) ]– Not a Function since the 3 is paired with two different y’s

  8. Systems of Equations Terminology Inconsistent (Parallel - same slope) Consistent & Independent (Intersect with one solution) Consistent & Dependent (Lines Coincide – Same Line) y = 2x + 4 y = 2x - 3 y = 2x + 4 y = -3x – 3 y = 2x + 4 y = 2x + 4

  9. Exponent Rules • When multiplying, we add exponents. • When dividing, we subtract exponents. • When raising a power to a power, we multiply exponents. • Negative exponents can be rewritten as positive exponents by using the reciprocal.

  10. Finding Maximum or Minimum Values Example: Find the maximum height of a projectile whose height at any time, t, is given by h(t) = 160 + 480t – 16t2 Strategy: • Enter the function of the Y= screen of calculator • Graph and adjust window to view the function • Use 2nd “TRACE” – option 3 or 4 to find desired value

  11. Percentages…Percentages ! • A percentage indicates a part of the whole • Percentages can be expressed as fractions and decimals as well • 75% = .75 = ¾ • 25% = .25 = ¼ • 10% = .10 = 1/10 REMEMBER: = P IS OF 100

  12. Proportions If 60 out of 370 people surveyed preferred Doritos over Tostitos, how many people out of 2400 would you expect to prefer Doritos? 60 x = 370 2400 370 x = 144,000 x = 389.19 = 389

  13. Direct Variation • When y varies directly as x, this means that y always equals the same number multiplied by x, that is: y = kx, where k is the constant of variation. • k can always be found by taking (y/x) ! Example: When traveling at 50 mph, the number of miles traveled varies directly with the time driven. Find the miles traveled in 4.5 hours. y = 50x y = 50(4.5) y = 225 miles

  14. Inverse Variation When y varies inversely as x, this means that the x multiplied by the y will always equal the same number, that is xy = k, where k is the constant of variation. (x)(y) = k (2)(36) = 72 So, k = 72 (6)(y) = 72 Therefore, y = 12 workers Example: The number of hours it takes to paint a room varies inversely as the number of workers according to the chart above. How long would it take 6 workers to complete the room?

  15. Exponential Functions y = ax Growth The independent variable (x) is found in the exponent of the function y = 2x Example from PSSA: What does the graph of y = 2(.25x) look like? y = 2(-x) Decay

  16. Families of Functions y = x Linear function (Line) y = x2 Quadratic Function (Parabola) y = x3 Cubic Function

  17. Mean – Median - Mode • Meanis the sum of the data divided by the total number in the data set • Median is the middle data point – average the middle two if the set has an even number • Mode is the data point which occurs most All three of these can be interpreted as the average. Remember that the median is unaffected by really large or small data values. But, the mean can be drastically affected by such values. Your graphing calculator can calculate the mean and the median quite easily ! STAT, CALC, 1: 1-VAR STATS

  18. Box and Whisker Plots • Lower quartile (Q1) – middle of the lower half of the data (25% mark) • Upper quartile (Q3) – middle of the upper half of the data (75% mark) • Range = Max – Min • IQR = Q3 – Q1

  19. Linear Regression The process of “fitting” a linear function, y = mx + b to a particular data set This process is most efficiently and effectively carried out on a graphing calculator STAT, CALC, 4:LinReg

  20. Positive vs. Negative Correlation • A positive correlation in a set of data points is indicated by a positively sloping (up left to right) line • A negative correlation is indicated by a negatively sloping (down left to right) line • Some data display no correlation Positive Negative None

  21. The Pythagorean Theorem This theorem applies to all right triangles and can be used to find the missing measure of a side of the right triangle. Remember, that “c” is always the side opposite the right angle. C2 = A2 + B2

  22. Sum of the Interior Angles of a Polygon • Triangle = 180° • Quadrilateral = 360 ° • Any other polygon 180 (n – 2) Where “n” is the number of sides of the polygon Exterior angles always add up to 360 °

  23. Angle Relationships • Vertical angles are congruent (1 and 3, 2 and 4) • Linear Pairs are supplementary (add up to 180°.

  24. When lines are parallel, • Corresponding angles are congruent(Ex. 1 and 5, 4 and 8) • Alt. int. angles are congruent (Ex. 3 and 6, 4 and 5) • Alt. ext. angles are congruent (Ex. 1 and 8, 2 and 7) • Same-side int. are supplementary(3 and 5, 4 and 6) • Same-side ext are supplementary(1 and 7, 2 and 8)

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