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Name: ______________________ Class: _________________ Date: _________ ID: A CC Geometry Pretest ____ 1. Write the exponential expression 3x A. 3 B. 8 8 C. 3 3 8 in radical form. (N.RN.2) x3 D. 3 3x 3 3 3 8 8 x3 E. I don’t know. x8 Simplify the expression. (N.CN.2) ____ 2. (i)(−7i) A. –7i B. 7i C. –7 D. 7 E. I don’t know. Simplify the sum. (A.APR.1) ____ 3. (2u 3 + 6u 2 + 3) + (2u 3 – 7u + 6) A. 9 – 7u + 6u 2 + 4 u 3 B. 4u 3 + 6u 2 – 7u + 9 C. 0u 3 + 6u 2 – 7u + 9 ____ D. 0u 3 – 7u 2 + 6u – 9 E. I don’t know. 4. A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years. 2 White-sided jackrabbits: 9.7x − 0.8x + 2.3 2 Black-tailed jackrabbits: −1.1x + 7.7x + 5.4 What polynomial models the total number of white-sided and black-tailed jackrabbits? 2 A. −8.6x + 6.9x − 7.7 2 B. 8.6x + 6.9x + 7.7 2 C. 8.6x − 6.9x − 7.7 2 D. 8.6x − 6.9x + 7.7 E. I don’t know. 1 Name: ______________________ ID: A Simplify the product using the distributive property. (A.APR.1) ____ 5. (3h − 7)(3h − 6) 2 A. 9h − 3h − 42 2 B. 9h − 39h + 42 2 C. 9h + 3h − 42 2 D. 9h + 39h + 42 E. I don’t know. What are the coordinates of the vertex of the graph or table? Is it a maximum or minimum? (F.IF.4) ____ 6. A. (–2, –4); maximum B. (–4, –2); maximum C. (–4, –2); minimum D. (–2, –4); minimum E. I don’t know. 2 Name: ______________________ ____ ID: A 7. X 0 –1 –2 –3 –4 Y 1 –2 –3 –2 1 A. (–2, –3); maximum B. (–4, 1); minimum C. (–2, –3); minimum D. (1, 0); maximum E. I don’t know. 3 Name: ______________________ ____ ID: A 2 8. What are the solutions of the equation 2x = 2? Use a graph of the related function.(F.IF.4) A. C. There are no real number solutions. B. There are two solutions: –1 and 1. D. I don’t know. There are two solutions: –1 and 1. 4 Name: ______________________ ID: A Graph the function and identify the domain and range. (F.IF.5) ____ 9. y = 0.5x2 A. C. domain: ÊÁË −∞, ∞ ˆ˜¯ È range: ÍÍÎ 0, ∞ ˜ˆ¯ domain: ÊÁË −∞, ∞ ˆ˜¯ ˘ range: ÊÁË −∞, 0 ˙˙˚ B. D. I don’t know. domain: ÊÁË −∞, ∞ ˆ˜¯ È range: ÍÍÎ 0, ∞ ˜ˆ¯ 5 Name: ______________________ ID: A What is the graph of the function? (F.IF.7a) ÔÏÔ 1 ÔÔ x, Ô ____ 10. f(x) = ÔÔÌ 3 ÔÔ ÔÔ 2 ÔÓ x + 2, A. B. for x > 0 for x ≤ 0 C. D. I don’t know. Factor the quadratic equation in order to determine the zeros of the function. (F.IF.8, A.SSE.3a) 2 ____ 11. x − 9x + 18 = 0 A. 3, 6 B. –3, –6 C. 3, –6 D. –3, 6 E. I don’t know. 6 Name: ______________________ ID: A ____ 12. Do the equation and graph below share a vertex? If so, what is it? (F.IF.9) 2 f(x) = x − 6x + 4 1 1 A. yes, ( , −1 ) 2 2 B. yes, (1, –1) C. yes, (3, –5) D. no E. I don’t know. Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence. (F.BF.1a, A.CED.1) ____ 13. a 1 = −4, a 2 = 8, a 3 = −16 A. a n = −4 ⋅ (−2) n − 1 ; –64 D. a n = −4 ⋅ (2) n ; –64 B. a n = −4 ⋅ (−2) n ; 128 E. I don’t know. C. a n = −2 ⋅ (−4) n − 1 ; –512 7 Name: ______________________ ID: A 2 Graph each function. How is each graph a translation of f(x) = x ? (F.BF.3) 2 ____ 14. y = (x + 3) + 4 A. C. f(x) translated down 4 unit(s) and translated to the left 3 unit(s) B. f(x) translated down 4 unit(s) and translated to the right 3 unit(s) D. I don’t know. f(x) translated up 4 unit(s) and translated to the left 3 unit(s). 8 Name: ______________________ ____ 15. Find the inverse of f(x) = 5x − 3. (F.BF.4) −1 x−3 A. f ( x) = −5 −1 x+3 B. f ( x) = 5 −1 x+3 C. f ( x) = −5 ID: A −1 D. f ( x) = −5x + 3 E. I don’t know. Find the vertex of each parabola by completing the square. (A.SSE.3b) 2 ____ 16. x − 6x + 8 = y A. (–3,– 6) B. (–3,1) C. (–1, 3) D. (3,–1) E. I don’t know. Solve the equation using square roots. (A.REI.4b) ____ 17. 2x A. B. C. 2 − 98 = 0 –49, 49 − 7, 7 –7, 7 D. no real number solutions E. I don’t know. Solve the equation by completing the square. Round to the nearest hundredth if necessary. (A.REI.4b) 2 ____ 18. x + 8x = −15 A. 5, –3 B. –5, 3 C. 5, 3 D. –5, –3 E. I don’t know. ____ 19. Find the solutions of the equation. (N.CN.7) 1 2 x −x+5 = 0 2 A. 1 ± 9i B. −1 ± 9i C. 1 ± 11 i D. −1 ± 11 i E. I don’t know. 9 Name: ______________________ ID: A What are the solutions of the system? Solve by graphing. (A.REI.7) 2 ____ 20. y = x − 3x + 3 y = 2x − 3 A. The solutions of the system are (2, 1) and (3, 3). B. C. 3 3 The solution of the system is ( , ). 2 4 D. I don’t know. The system has no solution. 10 Name: ______________________ ____ 21. The dashed-lined figure is a dilation image of ID: A ABC with center of dilation P (not shown). Is D (n, P) an enlargement, or a reduction? What is the scale factor n of the dilation? (G.SRT.1) A. reduction; n=2 B. reduction; 1 n= 4 C. enlargement; n=2 D. reduction; 1 n= 2 E. I don’t know. ____ 22. Suppose S and T are mutually exclusive events, P(S) = 20%, and P(T) = 22%. Find P(S or T). A. 440% D. 2% B. 42% E. I don’t know. C. 4.4% 11 Name: ______________________ ID: A ____ 23. On St. Patrick’s Day, you took note of who was coming into your restaurant wearing green. The two-way frequency table shows the results of your survey. What is the probability that a randomly chosen customer will be a female wearing green? Round to the nearest thousandth. Wearing Green Yes No Totals Male Female Totals 36 44 80 83 68 151 119 112 231 A. 0.393 B. 0.190 C. 0.370 D. 0.294 E. I don’t know. ____ 24. In a survey of a town, 56% of residents own a car, 21% of residents own a truck, and 4% of residents own both a car and a truck. What is the conditional probability that a person who owns a car also owns a truck? Round to the nearest whole number. A. 44% D. 7% B. 17% E. I don’t know. C. 19% 12 Name: ______________________ ID: A ____ 25. Which is a correct two-column proof? Given: r Ä s Prove: ∠b and ∠h are supplementary. A. B. C. State me nts R e asons 1. r Ä s 1. Given 2. ∠b ≅ ∠c 2. Vertical Angles 3. ∠d and ∠h are supplementary. 3. Alternate Interior Angles 4. ∠e ≅ ∠h 4. Vertical Angles 5. ∠b and ∠h are supplementary. 5. Same-Side Interior Angles State me nts R e asons 1. r Ä s 1. Given 2. ∠b ≅ ∠c 2. Vertical Angles 3. ∠c and ∠e are supplementary. 3. Same-Side Interior Angles 4. ∠e ≅ ∠h 4. Vertical Angles 5. ∠b and ∠h are supplementary. 5. Substitution State me nts R e asons 1. r Ä s 1. Given 2. ∠b ≅ ∠h 2. Corresponding Angles 3. ∠c and ∠e are supplementary. 3. Same-Side Exterior Angles 4. ∠e ≅ ∠h 4. Vertical Angles 5. ∠c and ∠h are supplementary. 5. Substitution D. I don’t know. 13 Name: ______________________ ID: A ____ 26. What is the missing reason in the proof? Given: ABCD with diagonal BD Prove: ABD ≅ CDB Statements 1. AD Ä BC 2. ∠ADB ≅ ∠CBD 3. AB Ä CD 4. ∠ABD ≅ ∠CDB 5. DB ≅ DB 6. ΔABD ≅ ΔCDB A. Alternate Interior Angles Theorem B. ASA C. Reflexive Property of Congruence Reasons 1. Definition of parallelogram 2. Alternate Interior Angles Theorem 3. Definition of parallelogram 4. Alternate Interior Angles Theorem 5. ? 6. ASA D. Definition of parallelogram E. I don’t know. 14 Statement Justification 1 ΔABCisisosceles; BDisanangle bisector Given 2 AB=BC Definitionof isosceles 3 <ABD≅ <CBD _____________ 4 BD=BD Reflexive Property 5 ΔABD≅ΔCBD _____________ 6 <BAD≅ <BCD CPCTC 27.Whattwophrasesfillintheblanks?G.CO.10 A.Substitution; SAS B.Definitionofbisector;SAS C.Substitution; SSA D.Definitionofbisector;SSA E.Idon’tknow 28.Whatpropertycouldbeusedtostatethatthesetrianglesaresimilar?G.SRT.3 A.ASA B.SAS C.AA D.SSS E.Idon’tknow 29.Whattheoremisprovedhere?G.SRT.5 Statement Justification 1 ΔABCisaright triangle,BDis perpendicularto AC Given 2 <BAD≅<BAD, ReflexiveProperty <BCD≅<BCD 3 ΔABC≅ΔADB, ΔABC≅ΔBDC AAProperty 4 AB/AC=AD/AB, AC/BC=BC/DC DefinitionofSimilar Triangles 5 6 7 8 A. B. C. D. E. AB2=AC*AD, BC2=AC*DC AB2+BC2= AC*AD+AC*DC AB2+BC2= AC(AD+DC) AB2+BC2=AC2 CrossMultiplication AdditionProperty Distributive Property Substitution Property TheHingeTheorem TheTrigonometricTheorem TheTriangleSimilarityTheorem ThePythagoreanTheorem Idon’tknow 30.WhatdoweknowabouttrianglesABCandDBE?G.SRT.4 A. They’resimilartriangles B. They’recongruenttriangles C. Theyhaveascalefactoroftwo D. Theyhavenorelationship E. Idon’tknow 31.WhatisthesidelengthofACgiventhatAB=12andBC=16(AssumeABCisa righttriangle)?G.SRT.8 A. B. C. D. E. 5 20 25 22 Idon’tknow 32.Usingthesametriangle,ifangleAis32degrees,whatisthemeasureofangleC? G.SRT.7 A. 148 B. 32 C. 58 D. 68 E. Idon’tknow