Algebra 1 FINAL EXAM REVIEW Spring Semester Material (by chapter)

Size: px

Start display at page:

Download "Algebra 1 FINAL EXAM REVIEW Spring Semester Material (by chapter)"

Timothy Lang
5 years ago
Views:

1 Name: Per.: Date: Algebra 1 FINAL EXAM REVIEW Spring Semester Material (by chapter) Your Algebra 1 Final will be on at. You will need to bring your tetbook and number 2 pencils with you to the final eam. The final eam will cover the entire year. Re-review the material from the fall semester as well. Do not lose this packet. Replacement packets will cost $$$. 1

2 What You Must Memorize For Final 1) Quadratic Formula: = b ± b2 4ac 2a 2) Standard Form: a 2 + b + c = 0 3) Perfect Squares from 0 to 169: 0, 1, 4, 16, 4) Discriminant: b 2-4ac ) Complete the Square: 2 + 6) Direct Variation: y=k ) Inverse Variation: 8) Verte: 9) Pythagorean Theorem: a 2 + b 2 = c 2 10) X and Y Intercepts: To find y-intercept, set s equal to zero. To find, -intercepts, set y equal to zero and solve for. 2

3 Chapter *** show your work wherever applicable for full credit *** Match each of the following polynomials with its special term name y a) trinomial b) binomial c) monomial Add or subtract the following polynomials. 4. (8t 2 10t + 2) + (8t + 13). ( 2 + 1) ( ) 6. ( ) ( ) 7. (3n 3 + n 2 n 4) + (n 3 4n ) Write in decimal form (standard notation) Write in scientific notation ,

4 Simplify the following. Leave all answers with positive eponents (2w 2 4 ) (a 4 ) y (3b) y d d 26. df f y t 4 v 3 21t 2 v 6 Multiply or Divide. Epress your answers in scientific notation. 28. ( )( )

5 Multiply (4 9) ( + 6) (1 3 10) Multiply the following. Use your choice of methods, but show your work!! 33. ( + 9)( 6) 36. ( 6)( 8) 34. ( + 3)(4 + ) 37. (7 + 3)(7 2) 3. (3 1)(8 + 1) 38. ( )( + )

6 Chapter 6 Factor out the largest possible monomial a + 10b c 4 6c 2 1c Factor completely (remember they are not always ready to go ) y 2 1y t 2 + 8t m m y 42y 2 Factor the following differences of squares completely a m

7 Factor the following perfect square trinomials completely m m y 3 16y y Factor completely (remember they are not always ready to go ). 4. 3y 2 20y n n 2 6n Solve for the given variable. 7. (a )(a + 2) = 0 8. ( 3) = 0 9. y y 24 = 0 7

8 Chapter 10 Multiply or Divide Add or Subtract ( 7) (8 12) 67. (12 + 4) (4 + 3) Simplify Completely y y

9 70. 3a + 9b 12a y 2 + 3y 3y 2 + 6y a 2 14b 2 21a 21b 73. b 2 10b + 21 b 2 11b + 28 Multiply m 2 4 m 4m 2 m + 2 9

10 Divide y Add or Subtract w 2 + w w 3 9 w 3 8. (4 + 2) (7 6) (3 + 1) (3 + 1) 10

11 m m 1 3 m(m 1) 89. 2u uv 3 v u 2 v a a a b b 6 11

12 Chapter Estimate which two integers each square root is between: a) 73 is between and b) 13 is between and 9. Simplify (show work): a) 180 b) 22 c) 2 y 3 d) 196b 96. Simplify to find (show work): a) 81 2 b) c) d) e) 3 f) ( + ) 97. Find the missing side length for each triangle (show your steps): a) b) u v 12

13 98. Solve (show work): a) = 1 b) = To hang a math poster in his office, Mr. Zito leaned a 10 foot ladder against the wall, placing the bottom of the ladder on the floor 3 feet away from the wall. How high up on the wall was the ladder? (Show work. A labeled picture is also required) Chapter Write the quadratic formula. Solve the following using the QUADRATIC FORMULA. Complete all blanks = 8 (standard form) a = substitution b = c = solution(s) for : 13

14 = -2 2 (standard form) a = substitution b = c = solution(s) for : 103. Write the formula for the discriminant For questions 7, the blanks provided are for the following information: a) Substitute values for a, b, & c into the discriminant formula. b) Find the discriminant. c) Tell how many solutions the quadratic has = 3 a) d = (substitution) b) d = (simplified) c) (# of solutions) = 3 2 a) d = (substitution) b) d = (simplified) c) (# of solutions) = 8 16 a) d = (substitution) b) d = (simplified) c) (# of solutions) 14

15 107. Solve each of the following using the zero-product property. SHOW WORK. a) ( + 10)( + 24) = 0 b) (2 6)( + 2) = 0 c) ( + 18) = 0 d) (4 16)( + 9) = Solve each of the following equations by factoring: SHOW WORK. a) = 0 b) = Complete the square for the following: a) b) u 2 26u 110. Solve using any method you want show work!! a) 2 49 = 0 b) = 4 1

16 Chapter 12 Identify the domain and range for each. Tell if the relation is a function h: {(3, 1), (2, 4), (3, ), (4, 8)} 112. j: {(2, 7), (3, 6), (4, ), (, 4), (6, 3)} a) domain: a) domain: b) range: b) range: c) function / not a function c) function / not a function 113. k: {(1, 2), (2, 3), (3, 2), (4, 1)} 114. m: {(4, ), (4, 2), (4, 1), (4, 3), (1, 6)} a) domain: a) domain: b) range: b) range: c) function / not a function c) function / not a function Find the indicated outputs for the following functions. 11. f() = g() = f(1) = g( 2) = f( 3) = g( 1) = f(0) = g(4) = 16

17 Determine which of the following graphs represent functions y y y function / not a function function / not a function function / not a function State the domain and range for the following graphs y 121. y 122. y Domain: Domain: Domain: Range: Range: Range: Graph the following functions f() = 124. g() = h() = y y y 17

18 Graph each of the following quadratic functions, finding all indicated information f() = 2 b Verte 2a y-intercept -intercept(s) 127. f() = 2 b 2a Verte y-intercept -intercept(s) 128. f() = b 2a Verte y-intercept -intercept(s) 18

19 129. Find an equation of variation where y varies directly as for each pair of values given. a) y = 3 when = 24 b) y = 0 when = Find an equation of variation where y varies inversely as for each pair of values given. a) y = 2 3 when = 27 b) y = 4 when = 8 19

20 131. Find the Verte: f() = Write the equation in Standard Form and then identify a, b, and c. 3 2 = Solve using the quadratic formula: = Find the and y intercepts: f() = y 136. What is the Domain and the Range of a relation defined by: {(,2), (,3), (6,2), (3,1)} Function? Yes or No Domain: Domain: Range: Range: 137. Find the indicated outputs for the function: f() = for f(-2) 138. Find the equation of variation where y varies directly as, and y = 14 and = 2. 20

21 139. Find the equation of variation where y varies inversely with, and y = 14 and = ( 3) What number should be added to complete the square? X ( 2 ) 147. Find the length of side a. a

22 ANSWER KEY 17 a b or w y 9 or 28y X Page a c 36 X b t 2 2t ( 2 3) (4a+b 8) 7 8n 3 3n 2 n c(c 3 2c ) 8 80, (+2)(+7) 9 982, (y 6)(y 9) (t+3)(t+) (m 1)(m+24) (+3)( 4) ( 6y)(+7y) ( 11)(+11) (10a 12)(10a+12) 16 X 9 0 (m 2)(m+2) 22

23 ANSWER KEY 1 (+9) (m+3) y(y 2) (3y 2)(y 6) 84 (2+)( 9) 8 6 3n(6n 1)(n+2) 86 7 a= ; a= X=0 ; = Y=1 ; y= a) 8 and 9 b) 3 and 4 a) 6 ; b) 6 7 ; c) y ; d) 14 a) 4 ; b) 10 ; c) 11 7 ; d) 6 6 ; e) f) 97 a) b) 29 or a) 16 b) or = 2 & = 2 NO SOLUTION; can t have a negative inside radical b) 39 ; c) zero solutions b) 40 ; c) 2 solutions b) 0 ; c) 1 solution a) 10 & 24 ; b) 3 & ; c) 0 & 18 d) 0 & 4 & a) 4 ; b) 7 & a) +100 ; b) a) 7 & 7 ; b) 21

24 ANSWER KEY 111 a) {2,3,4} ; b) {1,4,,8} ; c) not a function 112 a) {2,3,4,,6} ; b) {3,4,,6,7} ; c) function 113 a) {1,2,3,4} ; b) {1,2,3} ; c) function 114 a) {1,4} ; b) {1,2,3,,6} ; c) not a function 11 6 ; 38 ; ; 2 ; 117 Not a function 118 Not a function 119 function 120 Domain: { 2} ; Range: {y all real numbers} 121 Domain: { 1 } ; Range: {y 1 y 4} 122 Domain: all real numbers ; Range: all real numbers 123 Graph should form a v: 124 Graph should form a v: 12 Graph should be a negative sloped line: ; verte (0,0) ; y intercept (0,0) ; intercepts (0,0) ; verte (0, ) ; y intercept (0, ) ; intercepts =,0 &, ; verte (2, 16) ; y intercept (0, 12) ; intercepts = 6 & 2 or (6,0) & ( 2,0) 129 a) 130 a) 131 ( 1, 3) ; b) y=2 ; b) = 0 a=3 ; b=2 ; c= 1 & & ; or ( 2, 0) & (,0) 13 Yes ; all real numbers; {y y {3,,6} ; {1,2,3} y= & 7 24

Algebra Final Exam Review Packet

Algebra Final Exam Review Packet Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial: