Final+Study+Guide

**Algebra 1B - Second Semester Exam Study Sheet Short Answer Graph the inequality. 1. y < 4x − 1 What is the solution of the system? Use elimination. 2. 2x + 4y = –14 x – 4y = 17 3. 2x – 2y = –8 x + 2y = –1 What is the graph of the system? 4. y ≤ −x − 1 y ≥ 2x + 4 What is the solution of the system? Use substitution. 5. y = x + 2 y = 3x What is the solution of the system? Use a graph. 6. y = 2x – 4 y = 2x – 3 2 Which inequality represents the graph? 7. What is the solution of the equation? 8. −7p − 2 = − 3(−4p − 2) + 7(4 − 3p) What are the solutions of the equation? 9. 3z2 + 8z + 4 = 0 10. z2 − 3z − 54 = 0 Simplify the product. 11. 8p(–3p2 + 6p – 2) 12. (5h − 5)(2h + 7) 13. (3k + 4)(2k2 – 5k – 4) What is a simpler form of each product? 14. (3m + 8)2 Solve the equation using square roots. 15. x2 − 81 = 0 3 Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 16. 2 – 11x2 – 8x + 6x2 Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. 17. x2 − 22 = −x Graph the function. Identify the vertex and axis of symmetry. 18. f(x) = x2 + 3x + 2 What is the factored form of the expression? 19. 12x2 + 17x + 6 20. 6w7 + 15w3 21. 25b2 – 9 22. d2 + 10d + 25 23. x2 – x – 42 Simplify the expression. 24. (–7x – 5x4 + 5) – (–7x4 – 5 – 9x) 25. (2w2 – 8w – 8) – (7w2 + 6w – 4) 26. (3u3 + 3u2 + 4) + (4u3 – 3u + 5) 27. The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle. 28. The total cost to rent a row boat is $17 times the number of hours the boat is used. How long can you rent the boat for $221? 29. Angela and Neil are going to the movies. They each bought a medium popcorn, and Neil got a small soft drink. Angela had a $20 gift certificate to put toward the cost, and Neil paid the rest, which came to $ 14.90. A movie ticket costs $11.00 and a medium popcorn costs $5.50. How much does a small soft drink cost at the theater? 4 30. A square painting is surrounded by a frame. The outside edges of the frame are x inches in length and there is a 3-inch border between the painting and the frame. What is the total area of the border? 31. If an object is dropped from a height of 144 feet, the function h(t) = −16t2 + 144 gives the height of the object after t seconds. When will the object hit the ground? ** **Answer Section ** **SHORT ANSWER ** 1. ANS: DIF: L3 OBJ: 6-5.1 To graph linear inequalities in two variables NAT: CC A.CED.3| CC A.REI.12| A.4.d STA: AL A1.2c 2. ANS: (1, –4) DIF: L3 OBJ: 6-3.1 To solve systems by adding or subtracting to eliminate a variable NAT: CC A.REI.5| CC A.REI.6| A.4.d STA: AL A1.8a 3. ANS: (–3, 1) DIF: L3 OBJ: 6-3.1 To solve systems by adding or subtracting to eliminate a variable NAT: CC A.REI.5| CC A.REI.6| A.4.d STA: AL A1.8a **ID: A ** 2 4. ANS: DIF: L3 OBJ: 6-6.1 To solve systems of linear inequalities by graphing NAT: CC A.REI.12| A.4.d STA: AL A1.8a 5. ANS: (1, 3) DIF: L2 OBJ: 6-2.1 To solve systems of equations using substitution NAT: CC A.REI.6| A.4.d STA: AL A1.8a 6. ANS: no solutions DIF: L3 OBJ: 6-1.2 To analyze special systems NAT: CC A.REI.6| A.4.d STA: AL A1.8a 7. ANS: //y // < 5 //x // − 5 DIF: L3 OBJ: 6-5.1 To graph linear inequalities in two variables NAT: CC A.CED.3| CC A.REI.12| A.4.d STA: AL A1.2c **ID: A ** 3 8. ANS: //p // = 18 DIF: L3 OBJ: 2-4.1 To solve equations with variables on both sides NAT: CC A.CED.1| CC A.REI.1| CC A.REI.3| A.4.a| A.4.c STA: AL A1.7c 9. ANS: − 2  3 , –2  DIF: L4 OBJ: 9-4.1 To solve quadratic equations by factoring NAT: CC A.SSE.3.a| CC A.CED.1| CC A.REI.4.b| CC F.IF.8.a| N.5.c| A.4.a STA: AL A1.11a 10. ANS: 9, –6 DIF: L3 OBJ: 9-4.1 To solve quadratic equations by factoring NAT: CC A.SSE.3.a| CC A.CED.1| CC A.REI.4.b| CC F.IF.8.a| N.5.c| A.4.a STA: AL A1.11a 11. ANS: –24 //p // 3 + 48 //p // 2 – 16 //p // DIF: L3 OBJ: 8-2.1 To multiply a monomial by a polynomial NAT: CC A.APR.1| N.5.c| A.3.c| A.3.e STA: AL A1.6 12. ANS: 10 //h // 2 + 25 //h // − 35 DIF: L3 OBJ: 8-3.1 To multiply two binomials or a binomial by a trinomial NAT: CC A.APR.1| A.3.e 13. ANS: 6 //k // 3 – 7 //k // 2 – 32 //k // – 16 DIF: L3 OBJ: 8-3.1 To multiply two binomials or a binomial by a trinomial NAT: CC A.APR.1| A.3.e 14. ANS: 9 //<span style="font-family: 'TimesNewRoman,Italic'; font-size: 11.5pt;">m // 2 + 48 //<span style="font-family: 'TimesNewRoman,Italic'; font-size: 11.5pt;">m // + 64 DIF: L3 OBJ: 8-4.1 To find the square of a binomial and to find the product of a sum and difference NAT: CC A.APR.1| A.3.e 15. ANS: –9, 9 DIF: L2 OBJ: 9-3.1 To solve quadratic equations by graphing and using square roots NAT: CC N.Q.2| CC A.CED.1| CC A.CED.4| CC A.APR.3| CC A.REI.4.b| N.2.c| A.1.e| A.1.h| A.4.a| A.4.g STA: AL A1.9a| AL A1.11a **<span style="font-family: 'TimesNewRoman,Bold';">ID: A ** 4 16. ANS: –5 //<span style="font-family: 'TimesNewRoman,Italic';">x // 2 – 8 //<span style="font-family: 'TimesNewRoman,Italic';">x // + 2; quadratic trinomial DIF: L3 OBJ: 8-1.1 To classify, add, and subtract polynomials NAT: CC A.APR.1| A.3.c| A.3.e 17. ANS: –5.22, 4.22 DIF: L3 OBJ: 9-6.1 To solve quadratic equations using the quadratic formula NAT: CC N.Q.3| CC A.CED.1| CC A.REI.4.a| CC A.REI.4.b| A.4.a 18. ANS: axis of symmetry: //<span style="font-family: 'TimesNewRoman,Italic'; font-size: 11.5pt;">x // = − 1.5 vertex: (–1.5, –0.25) DIF: L3 OBJ: 9-2.1 To graph quadratic functions of the form y = ax^2 + bx + c NAT: CC A.CED.2| CC F.IF.4| CC F.IF.7.a| CC F.IF.9| CC F.BF.3| A.1.e| A.2.a| A.4.a  19. ANS: (4 //<span style="font-family: 'TimesNewRoman,Italic';">x // + 3)(3 //<span style="font-family: 'TimesNewRoman,Italic';">x // + 2) DIF: L3 OBJ: 8-6.1 To factor trinomials of the form ax^2 + bx + c NAT: CC A.SSE.1.a| CC A.SSE.1.b| N.5.c STA: AL A1.6 20. ANS: 3 //<span style="font-family: 'TimesNewRoman,Italic';">w // 3 (2 //<span style="font-family: 'TimesNewRoman,Italic';">w // 4 + 5) DIF: L3 OBJ: 8-2.2 To factor a monomial from a polynomial NAT: CC A.APR.1| N.5.c| A.3.c| A.3.e STA: AL A1.6 21. ANS: (5 //<span style="font-family: 'TimesNewRoman,Italic';">b // + 3)(5 //<span style="font-family: 'TimesNewRoman,Italic';">b // – 3) DIF: L3 OBJ: 8-7.1 To factor perfect-square trinomials and the differences of two squares NAT: CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| N.5.c STA: AL A1.6 **<span style="font-family: 'TimesNewRoman,Bold';">ID: A ** 5 22. ANS: ( //<span style="font-family: 'TimesNewRoman,Italic';">d // + 5)( //<span style="font-family: 'TimesNewRoman,Italic';">d // + 5) DIF: L3 OBJ: 8-5.1 To factor trinomials of the form x^2 + bx + c NAT: CC A.SSE.1.a| N.5.c STA: AL A1.6 23. ANS: ( //<span style="font-family: 'TimesNewRoman,Italic';">x // – 7)( //<span style="font-family: 'TimesNewRoman,Italic';">x // + 6) DIF: L3 OBJ: 8-5.1 To factor trinomials of the form x^2 + bx + c NAT: CC A.SSE.1.a| N.5.c STA: AL A1.6 24. ANS: 2 //<span style="font-family: 'TimesNewRoman,Italic';">x // 4 + 2 //<span style="font-family: 'TimesNewRoman,Italic';">x // + 10 DIF: L3 OBJ: 8-1.1 To classify, add, and subtract polynomials NAT: CC A.APR.1| A.3.c| A.3.e 25. ANS: –5 //<span style="font-family: 'TimesNewRoman,Italic';">w // 2 – 14 //<span style="font-family: 'TimesNewRoman,Italic';">w // – 4 DIF: L3 OBJ: 8-1.1 To classify, add, and subtract polynomials NAT: CC A.APR.1| A.3.c| A.3.e 26. ANS: 7 //<span style="font-family: 'TimesNewRoman,Italic';">u // 3 + 3 //<span style="font-family: 'TimesNewRoman,Italic';">u // 2 – 3 //<span style="font-family: 'TimesNewRoman,Italic';">u // + 9 DIF: L3 OBJ: 8-1.1 To classify, add, and subtract polynomials NAT: CC A.APR.1| A.3.c| A.3.e 27. ANS: length = 18 cm; width = 5 cm DIF: L2 OBJ: 6-2.1 To solve systems of equations using substitution NAT: CC A.REI.6| A.4.d STA: AL A1.8a 28. ANS: 13 hours DIF: L3 OBJ: 2-6.1 To find ratios and rates NAT: CC N.Q.1| CC N.Q.2| N.3.b| N.3.f| M.1.i| M.2.b 29. ANS: $1.90 DIF: L3 OBJ: 2-3.1 To solve multi-step equations in one variable NAT: CC A.CED.1| CC A.REI.1| CC A.REI.3| A.4.a| A.4.c STA: AL A1.7c 30. ANS: 12 //<span style="font-family: 'TimesNewRoman,Italic';">x // – 36 DIF: L3 OBJ: 8-4.1 To find the square of a binomial and to find the product of a sum and difference NAT: CC A.APR.1| A.3.e **<span style="font-family: 'TimesNewRoman,Bold';">ID: A ** 6 31. ANS: 3 s DIF: L3 OBJ: 9-1.1 To graph quadratic functions of the form y = ax^2 and y = ax^2 + c  NAT: CC A.CED.2| CC F.IF.4| CC F.IF.5| CC F.IF.7.a| CC F.IF.7.b| CC F.BF.3| A.1.e| A.2.a
 * <span style="font-family: 'TimesNewRoman,Bold'; font-size: 13pt;">Algebra 1B - Second Semester Exam Study Sheet **