Std 9.0 What two equations are represented in the grid? 15. Std 12.0 ... Std 15.0 Plane A leaves Los Angeles for New York at 500 miles per hour. At th...
Garden Grove Unified School District Algebra 1P Q4 Benchmark Review 2008-09
1. Std 2.0 What is the simplified form of (3x 5y 6 ) 2 ? 2. Std 2.0 Simplify 4(2x 2 y 3 ) 3 3. Std 2.0 What is the reciprocal of 1.4? 4. Std 2.0 What is the reciprocal of (x + y)? 5. Std 2.0 Simplify:
3
64a 6 b12
6. Std 2.0 Simplify: 100x 5y 2 7. Std 2.0 Simplify ab 2 ! a 3b 3 + 3a 4 b 5
Ê ˆ Ê 1 1ˆ 8. Std 2.0 Using fractional exponents, what is the simplified form of 3 x 2 y Á x 3 y 6 ˜ ? Ë ¯Ë ¯ 9. Std 9.0 What is the solution of this system of equations? 1 y= x+9 3 y= x+ 3 Ïx - y = 4 10. Std 9.0 Solve the linear system: Ì Ó x + 2y = 19
1 Ï Ôy ! 2 x + 2 11. Std 9.0 Which graph represents the solution of this system of inequalities? Ì Ôy £ - 3 x + 6 2 Ó
Algebra 1P Q4 Benchmark Review 2008-09
Ï 3x + 2y = 10¸ 12. Std 9.0 The solution of Ì ˝ is (a, b). What is a + b? Ó x + 4y = 10 ˛
Ï x + 3y = 2 13. Std 9.0 Solve for x and y: Ì Ó- x + 2y = 3
14. Std 9.0 What two equations are represented in the grid? y
x
15. Std 12.0 Gabriela did the following problem on her quiz. Simplify:
Step 1:
Step 2:
x 2 + 4x - 5 3x 3 + 18x 2 + 15x x 2 + 4x - 5
3x 3 + 18x 2 + 15x x 2 + 4x - 5 3x(x 2 + 6x + 5)
x 2 + 4x - 5
=
=
3x(x 2 + 6x + 5) (x + 5)(x - 1) 3x(x + 5)(x + 1)
Step 3:
(x + 5)(x - 1) x-1 = 3x(x + 5)(x + 1) 3x(x + 1)
Step 4:
x-1 -1 = 3x(x + 1) 3(x + 1)
In which step does the first error occur? Explain.
Algebra 1P Q4 Benchmark Review 2008-09
16. Std 12.0 In order to simplify denominator?
17. Std 12.0 Simplify
2x 2 - 9x - 5 6x 2 + 5x + 1
, what is the common factor of the numerator and the
2x 2 + x - 3 x 2 + 3x - 4
18. Std 12.0 What is the simplified form of
4x 2 + 28x x 2 + 4x - 21
?
3x 2 + 6x
19. Std 12.0 Factor and simplify:
3x 2 + x - 10
20. Std 13.0 What is the area of the rectangle shown?
4x + 1 2 5x - 2 3 21. Std 13.0 Find the product of 22. Std 13.0 Gerri has have?
3n + 2 4n - 1 CDs and Armon has CDs. Together, how many CDs do they 2 5n
23. Std 13.0 Find the sum of
24. Std 13.0 Simplify:
x +1 2x and 5 3
x +1 2x + 3 and . 3x 5
x 2 + 6x + 9 x2 - 9
!
x 2 + 3x 2x 2 - 6x
25. Std 14.0 Sonia is solving x 2 - 12x = -10 by completing the square. What is the first step?
26. Std 14.0 What are the solutions of 3x 2 - 7x - 6 = 0 ?
Algebra 1P Q4 Benchmark Review 2008-09
27. Std 14.0 Factor and solve: 2x 2 - 7x - 15 = 0 28. Std 14.0 What is the solution of 5x 2 = x ? 29. Std 14.0 Solve: 2x 2 + x = 0 30. Std 15.0 Ellen and Sahra want to plant a garden. If Ellen worked alone, it would take her 4 hours to complete the job. If Sahra worked alone, it would take her 2 hours to complete the job. How many hours would it take them to plant the garden if they worked together? 31. Std 15.0 Judie can clean her room in 60 minutes. If her sister helps her, it takes them 36 minutes to complete the job working together. How long does it take her sister to clean the room alone? 32. Std 15.0 Plane A leaves Los Angeles for New York at 500 miles per hour. At the same time, Plane B leaves New York for Los Angeles at 750 miles per hour. The distance from LA to New York is approx. 2,500 miles. How many miles will Plane A travel when the two planes cross paths? 33. Std 15.0 Michelle rode her bike from her home to her grandma’s house and then walked back home. The total travel time was 1 hour. If she averaged 6 miles per hour on the bike and 3 miles per hour walking, how far is it from her home to her grandma’s house? 34. Std 15.0 A acid solution of 100 quarts is 20% acid. Approximately how many quarts of a 60% acid solution needs to be added to obtain a 30% acid solution? 35. Std 15.0 How many ml of pure water must be added to 60 ml of a 20% salt solution to make a 12% salt solution? 36. Std 20.0 What are the solutions of the equation 2x 2 - x - 2 = 0 ? 37. Std 20.0 What are the roots of the equation? 3x 2 + x - 5 = 0 38. Std 20.0 Describe the roots of the following equations: A. n2 + 5n - 2 = 0 B. n2 + 5n + 7 = 0 C. n2 + 2n + 1 = 0 39. Std 20.0 What is the solution set of x 2 - 6x + 2 = 0 ? 40. Std 20.0 What are the roots of x 2 - 4x - 1 = 0 ? 41. Std 20.0 What are the zeros of f (x) = x 2 - 3x - 7 ? 42. Std 20.0 Find the x-intercepts of the graph of f (x) = x 2 - 2x - 2 . Algebra 1P Q4 Benchmark Review 2008-09
Garden Grove Unified School District Algebra 1P Q4 Benchmark Review 2008-09 Answer Key 1. 9x10 y12 5 3. 7
2. 32x 6 y 9 1 4. x+ y
5. 4a 2 b 4
6. 10x 2 y x
7. 4a 4 b 5
1
8. xy 2 10. (9,5) 12. 4 1 14. y = x + 1 and y = - x - 2 2 16. 2x + 1
