Example Items. Mathematical Models w/applications

Transcription

1 Example Items Mathematical Models w/pplications Mathematical Models w/pplications Example Items are a representative set of items for the P. Teachers may use this set of items along with the test blueprint as guides to prepare students for the P. On the last page, the correct answer, content SE and SE justification are listed for each item. The specific part of an SE that an Example Item measures is NOT necessarily the only part of the SE that is assessed on the P. None of these Example Items will appear on the P. Teachers may provide feedback regarding Example Items. (1) ownload the Example Feedback Form and it. The form is located on the homepage of ssessment.dallasisd.org. OR () To submit directly, click Example Feedback after you login to the ssessment website. First Semester ode #: 1311

2 P Formulas Mathematical Models with pplications Perimeter and ircumference Square: P 4s ircle: r d Rectangle: P w rea Square: = s Triangle: 1 bh Rectangle: = l w = bh Regular Polygon: 1 ap 1 Parallelogram: = bh Trapezoid: ( b1 b ) h 1 Rhombus: d1d = bh ircle: = r Lateral Surface rea Prism: L = Ph Pyramid: L 1 P ylinder: L = rh one: L = rl Total Surface rea 1 Prism: S = Ph + Pyramid: S P ylinder: S = rh + r one: S = rl + r Sphere: S = 4r Volume Rectangular Prism: V = l wh ube: V = s 3 Prism: V = h Pyramid: V 1 h 3 ylinder: V = r h V = h one: 1 1 V h V r h Sphere: V r 3 inomial Probability: Permutations: inomial oefficients: n x P( x) p q x n! npr ( n r)! n r n r nx Probability Geometric Probability: ombinations: n1 Pn ( x) q p n r n! ( n r)! r!

3 P Formulas Mathematical Models with pplications oordinate Geometry Midpoint: x1 x y1 y M, istance: d ( x x1) ( y y 1) Slope of a Line: y y1 m y m x x x 1 Slope-Intercept Form of a Line: y = mx + b Point-Slope Form of a Line: y y1 = m(x x1) Standard Form of a Line: x + y = Quadratic Equation: ax bx c 0 Quadratic Formula: x a b b 4ac Equation of a ircle: (x h) + (y k) =r Trigonometry Pythagorean Theorem: a b c Special Right Triangles: Trigonometric Ratios: To onvert egrees to Radians, Multiply by: sin opp hyp x, x 3, x x, x, x radians 180 cos adj hyp To onvert Radians to egrees, Multiply by: tan opp adj 180 radians Personal Finance PV Simple Interest: I = prt Present Value: r ompound Interest: P1 n nt Future Value: FV i Future Value of Ordinary nnuity: FV P N 1 1 i Future Value of an nnuity ue: mortization Payment: nnual Percentage Rate: 1 1 FV P 1 i i i mt PV N 1 1 i 7i PR 3 Pn ( 1) i( n1) i N FV r 1 n nt t (1 r) 1 r

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5 EXMPLE ITEMS Math Models, Sem 1 1 The diagram represents the Great Pyramid in Egypt. The volume of the Great Pyramid is 18,069,333 royal cubits cubed. If a royal cubit is approximately 1 meter, what is the volume of the Great Pyramid in cubic meters? 1,19,333 m 3,58,667 m 3 4,517,333 m 3 9,034,667 m 3 Two students conducting an experiment dropped a ball from the top of a 0-meter building. The height of the ball, in meters, is modeled by the function ht () 0 5 t, where t is the time, in seconds, since the ball was dropped. What is the approximate height of the ball 1.5 seconds after it is dropped? 8.75 feet 15 feet feet 0 feet allas IS - Example Items

6 EXMPLE ITEMS Math Models, Sem 1 3 The model of a new cell tower is shown. If the real tower is built with a scale of 6 inches to 5 feet, how far up the tower will the support wire reach? 75.0 feet 6.5 feet 50.0 feet 37.5 feet 4 oyle s Law states that the pressure and volume of a gas are inversely proportional while temperature and mass remain constant. gas has a pressure of 1.6 atm and volume of 5. L. If the volume of the gas changes to.6 L while the temperature and mass remain constant, what is the new pressure of the gas? 0.1 atm 0.8 atm 3. atm 6. atm allas IS - Example Items

7 EXMPLE ITEMS Math Models, Sem 1 5 The graph represents a musical note being played. Which graph represents the same note being played at a louder volume? allas IS - Example Items

8 EXMPLE ITEMS Math Models, Sem 1 6 n airplane is sighted at 30 angle from an airport as it descends for a landing. The pilot reports an altitude of 17,000 feet. pproximately how far is the airplane from the airport? 9,815 feet 19,630 feet 9,445 feet 34,000 feet 7 lex has a picture he wants to enlarge. The original picture is 8 inches wide and 10 inches high. The picture and the enlargement are similar. If the width of the enlargement is 0 inches, what is its height? Record the answer and fill in the bubbles on the grid provided. e sure to use the correct place value. allas IS - Example Items

9 EXMPLE ITEMS Math Models, Sem 1 8 The table shows data collected by a scientist over a five-week period during a hot, rainy summer. Week Number, x Number of Mosquitoes per Square Mile, f(x) ,350 4,05 5 3,038 ased on the data in the table, which function best models f(x), the number of mosquitoes per square mile, and x, the number of weeks since the scientist began collecting data? f( x) 00x 400 f( x) 51x f( x) 5() x f( x) 400(1.5) x 9 The data in the table represents the radioactive decay of a 90-gram sample of Strontium-90. Number of Years mount of Strontium-90 Remaining (grams) fter 70 years, approximately how much Strontium-90 will remain? 10 grams 17 grams 1 grams 33 grams 10 lake is approximately in the shape of a rectangle. If the length of the lake is about 4 miles and the width of the lake is about 1.75 miles, approximately how far would a boat travel diagonally across the lake? 3.6 miles 4.4 miles 5.3 miles 9.5 miles allas IS - Example Items

10 EXMPLE ITEMS Math Models, Sem 1 11 Logan purchased a used pick-up truck for $18,500. The table shows the value of the truck as it depreciates overtime. Number of Years of Ownership Value of Truck ($) 0 18, ,650 14,800 If the value of the pick-up truck continues to depreciate at this same rate, what will be the value of Logan s truck after 7 years? Record the answer and fill in the bubbles on the grid provided. e sure to use the correct place value. 1 sphere with a diameter of 8 inches is used as a model for a sculpture that is to be built in a local park. The scale is such that inches in the model represents 18 inches in the actual sculpture. What is the approximate surface area of the actual sculpture? 16,86 in 4,07 in 1,810 in 1,018 in allas IS - Example Items

11 EXMPLE ITEMS Math Models Key, Sem 1 Item# Key SE SE Justification 1 M.6 Use scale factors with three-dimensional objects to demonstrate proportional changes in volume. M.5 Use quadratic functions to model motion. 3 M.6 Use similarity to describe mathematical patterns and structure in architecture. 4 M.5 Use proportionality and inverse variation to describe physical laws such as oyle s Law. 5 M.7 Use trigonometric functions to model periodic behavior in music. 6 M.6 Use trigonometric ratios to calculate distances as applied to fields. 7 5 M.7 Use similarity to describe mathematical patterns and structure in photography. 8 M.9F Use regression methods available through technology to model exponential functions. 9 M.5 Use exponential models available through technology to model decay. 10 M.6 Use the Pythagorean Theorem to calculate distances M. 1 M.7 Use rates and linear functions to solve problems involving personal finance and. Use scale factors with three-dimensional objects to demonstrate proportional changes in surface area.