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Algebra II Practice Test CH1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Write the set in set-builder notation. ____ a. ÏÔ x| − 3 ≤ x < 4 ¸Ô c. ÏÔ x| − 3 < x < 4 ¸Ô ÔÌÓ Ô˝˛ ÔÌÓ Ô˝˛ b. [–3, 4) d. [–3, 4] 2. What statement can be determined from the diagram? ____ a. Every square is a rhombus. c. No parallelogram is a rhombus. b. Every rhombus is a square. d. No parallelogram is a square. 3. Which example shows that the Associative Property does not hold for division? a. (24 ÷ 3) ÷ 2 ≠ 24 ÷ (3 ÷ 2) c. 81 ÷ 3 ÷ 3 ≠ 81 ÷ (3 ÷ 3) 18 ÷ (3 ÷ 6) ≠ 18 ÷ (6 ÷ 3) b. d. (48 − 12) − 4 ≠ 48 − (12 − 4) ____ 4. Simplify the expression a. 5 7 b. ____ 2 25 49 5. Simplify a. b. 35 5 7 35 50 . 98 c. 25 49 d. 5 7 7 by rationalizing the denominator. 5 c. 7 5 d. 7 5 ____ ____ ____ ____ 2 2 6. Simplify the expression s − 3s + t + 5s . a. 5s2 − 3s + t b. 3s2 + t c. 2s2 + t d. 6s2 − 3s + t 7. Murphy’s motorcycle gets 55 miles per gallon of gas on the highway and 45 miles per gallon in the city. The motorcycle holds 8 gallons of gas. Write and simplify an expression for the total number of miles Murphy can travel if he has a full tank of gas but uses 2 gallons on the highway and the rest in the city. a. 10x + 36; 270 miles c. 36x + 10; 110 miles b. 10x + 36; 380 miles d. 36x + 10; 420 miles 8. Write the expression (5xy)4 in expanded form. a. (5xy)(5xy)(5xy)(5xy) c. 20xy b. (5xy) + (5xy) + (5xy) + (5xy) d. 4(5xy)(5xy)(5xy)(5xy) 9. Give the domain and range of the relation. x 2 8 0 –3 ____ y 5 17 0 –5 a. D: {–3, 0, 2, 8}; R: {–5, 0, 5, 17} b. D: {–5, 0, 5, 17}; R: {–3, 0, 2, 8} c. D: {2, 8, –3, 5, 17, –5}; R: {0} d. D: {–3, 2, 8}; R: {–5, 5, 17} 10. Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through. a. Yes, the relation is a function. b. No, the relation is not a function. (0, 4) and (0, –4) ____ ____ ____ 11. Which is an element of the range of the graphed function? a. 3 c. 4 b. 2 d. 0 12. For f(x) = −5x − 2, evaluate f(5). a. 23 c. –27 b. –15 d. –32 13. Use a table to perform a vertical stretch of f(x) = x by a factor of 3. Graph the transformed function on the same coordinate plane as the original function. a. c. b. ____ d. 14. In the deep ocean, the length of a wave in meters is related to the period of the wave in seconds. Graph the relationship between wave period and wavelength and identify which parent function best describes it. (Hint: Although time cannot be negative, the negative portion of this function has been provided for you.) Wave period (sec) –1 1 2 3 5 a. Wavelength (m) 1.56 1.56 6.24 14.04 39 Linear c. parent function Quadratic parent function b. ____ Cubic d. Square- parent function root parent function 15. For which function is 3 NOT an element of the range? a. y = −2x + 4 c. y = 3 5 b. y = x d. y = −(−x)2 Numeric Response 16. By the Pythagorean Theorem, the length d of a diagonal of a rectangle is given by d = Find the length of diagonal MO to the nearest tenth. 17. What is the value of 3x(y − 6)2 when x = 9 and y = 3? Matching Match each vocabulary term with its definition. a. principal root b. radicand c. radical symbol d. power e. like radical terms l2 + w 2 . f. rationalize the denominator g. cube root ____ ____ 18. a method of rewriting a fraction by multiplying by another fraction that is equivalent to 1 in order to remove radical terms from the denominator 19. the positive square root of a number, indicated by the radical sign ____ ____ ____ 20. the symbol used to denote a root 21. radical terms having the same radicand and index 22. the number or expression under a radical sign Match each vocabulary term with its definition. a. domain b. x-axis c. range d. relation e. dependent variable f. independent variable g. y-axis h. function ____ ____ ____ ____ ____ 23. 24. 25. 26. 27. a type of relation that pairs each element in the domain with exactly one element in the range a set of ordered pairs a variable whose value depends on the value of the input, also known as the output of a function the set of output values of a function or relation the set of input values of a function or relation Algebra II Practice Test CH1 Answer Section MULTIPLE CHOICE 1. ANS: A Use inequalities to rewrite the set in set-builder notation. Use a less than or equal sign when the endpoint is included in the set (closed circle) or a less than sign if the endpoint is not included in the set (open circle). Feedback A B C D Correct! Use set-builder notation, not interval notation. The left endpoint should be included in the set. Use set-builder notation, not interval notation, and do not include the right endpoint in the set. PTS: 1 DIF: Average REF: Page 9 OBJ: 1-1.3 Translating Between Methods of Set Notation NAT: 12.1.1.d TOP: 1-1 Sets of Numbers 2. ANS: A Since the region representing squares is entirely within the region representing rhombi, every square is a rhombus. Feedback A B C D Correct! According to the diagram, some rhombi are not squares. According to the diagram, some parallelograms are rhombi. According to the diagram, some parallelograms are squares. PTS: 1 DIF: Advanced NAT: 12.1.5.f TOP: 1-1 Sets of Numbers 3. ANS: A This example, (24 ÷ 3) ÷ 2 ≠ 24 ÷ (3 ÷ 2), shows that the Associative Property does not hold for division. In the Associative Property, numbers are regrouped. Feedback A B C D Correct! This example shows the Commutative Property, not the Associative Property. In the Associative Property, numbers are regrouped. The question asks for an example using division, not subtraction. PTS: 1 DIF: Advanced TOP: 1-2 Properties of Real Numbers 4. ANS: D NAT: 12.1.5.e 50 = 98 2 ⋅ 25 = 2 ⋅ 49 25 = 49 25 = 5 49 7 Feedback A B C D First divide out any factors common to the numerator and the denominator. Factor the numerator and the denominator. Divide out any common factors and look for perfect square factors. Take the square root of the numerator and the denominator. Correct! PTS: OBJ: TOP: 5. ANS: 1 DIF: Basic REF: Page 22 1-3.2 Simplifying Square-Root Expressions 1-3 Square Roots A 7 = 5 = = 7 5 ÊÁ ÁÁ ÁÁ ÁË 35 25 35 5 5 5 ˆ˜ ˜˜ ˜˜ ˜¯ NAT: 12.5.3.c Multiply by a form of 1 to get a perfect-square radicand in the denominator. Simplify the denominator. Feedback A B C D Correct! A quotient with a square root in the denominator is not simplified. Rationalize the denominator by finding the appropriate form of 1 to multiply by. First, multiply by a form of 1 to get a perfect-square radicand in the denominator. Then, simplify the denominator. PTS: OBJ: TOP: 6. ANS: 1 DIF: Average REF: Page 23 1-3.3 Rationalizing the Denominator 1-3 Square Roots D 2 Identify like terms. s − 3s + t + 5s2 2 Combine like terms. 6s − 3s + t NAT: 12.5.3.c Feedback A B C D A term that is written without a coefficient has a coefficient of 1. Combine only the like terms. Combine only the like terms. Correct! PTS: 1 DIF: Basic REF: Page 28 OBJ: 1-4.3 Simplifying Expressions NAT: 12.5.3.c TOP: 1-4 Simplifying Algebraic Expressions 7. ANS: B Let x be the number of gallons used on the highway, so 8 − x is the remaining number of gallons to be used in the city. 55x + 45(8 − x) = 55x + 360 − 45x = 10x + 360 Distribute 45. Combine like terms. Substitute 2 for x, as this is given as the number of gallons used on the highway. 10(2) + 360 = 380 Feedback A B C D Calculate for total gas used. Correct! The trip includes both city and highway travel. Be sure to clearly define your variable for either city or highway gallon use. PTS: 1 NAT: 12.5.2.b 8. ANS: A (5xy)4 = (5xy)(5xy)(5xy)(5xy) DIF: Average REF: Page 29 OBJ: 1-4.4 Application TOP: 1-4 Simplifying Algebraic Expressions The base is 5xy and the exponent is 4. 5xy is a factor 4 times. Feedback A B C D Correct! Use the base as a factor, not as an addend. Write the base four times. Write the base four times. PTS: 1 DIF: Basic REF: Page 34 OBJ: 1-5.5 Writing Exponential Expressions in Expanded Form NAT: 12.1.1.f TOP: 1-5 Properties of Exponents 9. ANS: A The domain is the set of all x-values. The range is the set of all y-values. Feedback A B C D Correct! The domain is the set of all x-values. The range is the set of all y-values. The domain includes only the x-values. The domain is the set of all x-values. PTS: 1 DIF: Basic REF: Page 44 OBJ: 1-6.1 Identifying Domain and Range NAT: 12.5.1.g TOP: 1-6 Relations and Functions KEY: domain | range | function | relation 10. ANS: B If any vertical line passes through more than one point on the graph of a relation, the relation is not a function. This relation is not a function. A vertical line at x = 0 would pass through (0, 4) and (0, –4). Feedback A B A vertical line can pass through more than one point on this graph. Correct! PTS: 1 DIF: Basic REF: Page 46 OBJ: 1-6.3 Using the Vertical-Line Test NAT: 12.5.1.e TOP: 1-6 Relations and Functions 11. ANS: D The range is the set of y-coordinates on the graph. According to the graph, the range is y < 1. Feedback A B C D The range includes only the y-coordinates on the graph. The range includes only the y-coordinates on the graph. The range includes only the y-coordinates on the graph. Correct! PTS: 1 DIF: Advanced TOP: 1-6 Relations and Functions 12. ANS: C f(x) = −5x − 2 f(5) = −5(5) − 2 f(5) = −27 NAT: 12.5.1.g Substitute 5 for x. Simplify. Feedback A B C D Substitute the value of x in the function, and then simplify. Substitute the value of x in the function, and then simplify. Correct! Substitute the value of x in the function, and then simplify. PTS: OBJ: KEY: 13. ANS: 1 DIF: Basic 1-7.1 Evaluating Functions function | input | output | evaluate D REF: Page 51 NAT: 12.5.2.b TOP: 1-7 Function Notation Stretching a function vertically means y-coordinates will change and move away from the x-axis, relative to the original function. Use a table to determine points for the stretched function. x 1 –1 0 2 y 1 –1 0 2 3y 3 –3 0 6 Feedback A B C D To stretch the function multiply each y-coordinate by 3. To stretch the function multiply each y-coordinate by 3. A vertical stretch should move the y-values farther from the x-axis. Correct! PTS: OBJ: TOP: 14. ANS: 1 DIF: Average REF: Page 61 1-8.3 Stretching and Compressing Functions 1-8 Exploring Transformations C NAT: 12.5.2.d The graph is most like a parabola, so the graph resembles the shape of the quadratic parent function. Feedback A B C D The negative data mirrors the positive side of the graph. The negative portion of the cubic function curves down, but data shows a curve upwards. Correct! The square root function curves in the opposite direction that the data indicates. PTS: 1 NAT: 12.5.1.h DIF: Average REF: Page 69 OBJ: 1-9.3 Application TOP: 1-9 Introduction to Parent Functions 15. ANS: D 3 is NOT an element of the range of a function if no value of x returns the value 3. If y = 3, then the range is only the number 3 and 3 is an element of the range. If y = x5, then the range is all real numbers and 3 is an element of the range. If y = −2x + 4, then the range is all real numbers and 3 is an element of the range. If y = −(−x)2, then for any value of x, y ≤ 0. To see this clearly, make a table. x values y values −2 −1 0 1 2 2 2 2 −(2) = −4 −(1) = −1 −(0) = 0 2 −(−1) = −1 −(−2)2 = −4 Thus, 3 is NOT an element of y = −(−x)2 . Feedback A B C D The range of the function is all real numbers and includes the given number. The range of the function is all real numbers and includes the given number. The range of the function is exactly the given number. Correct! PTS: 1 DIF: Advanced NAT: 12.5.1.d TOP: 1-9 Introduction to Parent Functions NUMERIC RESPONSE 16. ANS: 10.8 PTS: 1 17. ANS: 243 DIF: Advanced NAT: 12.5.3.c TOP: 1-3 Square Roots PTS: 1 DIF: Average NAT: 12.5.3.c TOP: 1-4 Simplifying Algebraic Expressions MATCHING 18. ANS: TOP: 19. ANS: TOP: 20. ANS: TOP: 21. ANS: TOP: 22. ANS: TOP: F PTS: 1-3 Square Roots A PTS: 1-3 Square Roots C PTS: 1-3 Square Roots E PTS: 1-3 Square Roots B PTS: 1-3 Square Roots 1 DIF: Basic REF: Page 22 1 DIF: Basic REF: Page 21 1 DIF: Basic REF: Page 21 1 DIF: Basic REF: Page 23 1 DIF: Basic REF: Page 21 23. ANS: TOP: 24. ANS: TOP: 25. ANS: TOP: 26. ANS: TOP: 27. ANS: TOP: H PTS: 1 1-6 Relations and Functions D PTS: 1 1-6 Relations and Functions E PTS: 1 1-7 Function Notation C PTS: 1 1-6 Relations and Functions A PTS: 1 1-6 Relations and Functions DIF: Basic REF: Page 45 DIF: Basic REF: Page 44 DIF: Basic REF: Page 52 DIF: Basic REF: Page 44 DIF: Basic REF: Page 44