Download California Standards Practice Test

California Standards Practice Test
Algebra 1
Choose the correct answer for each.
1. State the name of the property illustrated. (3 + 9) + 4 = (9 + 3) + 4
A. Associative Property
C. Closure Property
2. Simplify
300
A. 100 3
3. Simplify
B. Distributive Property
D. Commutative Property
B. 10 3
C. 30 10
D. 30
B. 7
C. 10
D.
C. x = -1 or x = 4
D x= -1 or x=3
25  3 8
A. 33
33
4. What is the solution for this equation?
2x  3 = 5
A. x = -4 or x = 4
B. x = -4 or x = 3
5. Which is the simplified version of 7x – 4(x – 8) = 56?
A. 11x + 32 = 56
B. 3x – 8 = 56
C. 3x – 32 = 56
D. 3x + 32 = 56
6. Solve
3(x + 5) = 2x + 35
Step 1: 3x + 15 = 2x + 35
Step 2: 5x + 15 = 35
Step 3:
5x = 20
Step 4:
x=4
Which is the first incorrect step in the solution shown above?
A. Step 1
B. Step 2
C. Step 3
D. Step 4
7. Which value could x be if -2 < x + 2  4
A. -4
B. 3
C. -3
D. 4
8. The total cost (c) in dollars of renting a sailboat for n days is given by the equation
c = 120 + 60n.
If the total cost was $360, for how many days was the sailboat rented?
A. 2
B. 4
C. 6
D.8
9. What is the y-intercept of the graph of 4x + 2y = 12?
A. -4
B. -2
C. 6
D. 12
10. Which inequality is shown on the graph below?
A. y <
1
x 1
2
B. y 
1
x 1
2
C. y >
1
x–1
2
D. y 
1
x-1
2
11. Which point lies on the line defined by 3x + 6y = 12?
A. (0, 2)
B. (0, 6)
C. (1, 3)
D. (2, 2)
12. What is the equation of the line that has a slope of 4 and passes through the
point (3, -10)?
A. y = 4x – 22
B. y = 4x + 22
C. y = 4x – 43
D. y = 4x + 43
13. The equation of line l is y = 6x - 4, and the equation of line q is y = 6x + 7.
Which statement about the two lines is true?
A Lines l and q have the same y-intercept.
B Lines l and q are parallel.
C Lines l and q have the same x-intercept.
D Lines l and q are perpendicular.
14. What is the solution to this system of equations?
y = -3x – 2
7x + 2y = -3
A
(6, 2)
B (1, -5)
C no solution
D (1, 5)
C
D
15. Solve the linear system:
3x + 2y = 8
5x + 2y = 12
A
(-2, 7)
B (2, 1)
(1, 2)
(2, 4)
16. Which system of inequalities represents the graph below?
3
x5
4
A.
3
y  x4
2
y
3
x5
4
B.
3
y  x4
2
y
3
x5
4
C.
3
y  x4
2
y
3
x5
4
D.
3
y  x4
2
y
5x 3
17. Simplify:
10 x 8
A. 2x5
B.
1
2x5
18. Simplify: (3x2 – 5x – 7) - (x2 – 5x + 3)
A. 2x4 - 10
B. 2x2 – 10
C
1
5x 5
C. 2x2 - 10x – 4
D.
x5
5
D. 2x2 – 4
19. What is the factored form of 5x2 + 15x + 10?
A. 5(x + 2)(x + 1)
20. What is
21. Simplify:
A.
D.(5x + 2)(x + 5)
B.
x2
3x
C.
1
3
D. x2 – x – 2
7 x( x  1)
4( x  2)
D.
7x2  7x
x2  4
 3
4x  8
x  2x 2  x
7 ( x  2)
4( x  1)
22. Simplify:
A.
C.(5x + 5)(x + 2)
x 2  4x  4
reduced to lowest terms?
3x  6
x2
3
A.
B. (5x + 1)(x + 2)
B.
7 ( x  2)
4( x  1)
C.
B.
7x  3
( x  3)( x  2)
C.
7 x( x  1)
4( x  2)
3
7x

x3 x2
10 x
x 1
31x  6
( x  3)( x  2)
D.
7 x 2  24 x  6
( x  3)( x  2)
23. If x2 – 2x – 24 = 0, which of the following could be the value of x?
A. 6
B. 4
C. 10
D. -6
24. If x2 + 6x = 10, which of the following could be the value of x?
A. 3 + 19
B. 3 - 19
C. -3 + 19
D. 4
25. Karen can complete the job in 6 hours. It takes Carlos 7 hours to complete the job.
How long will it take them to complete the job if they work together?
3
A. 13 hours
B. 1 hour
C. 6.5 hours
D. 3
13
26. Andy’s average driving speed for a 4-hour trip was 45 miles per hour. During the
first three hours he drove 40 miles per hour. What was his average speed for the last hour
of his trip.
A. 50 mph
B. 60 mph
C. 65 mph
D. 70 mph
27. Which relation is a function?
A. {(8, 2), (-3, -1), (8, -2)}
C. {(0, 3), (7, 0), (5, 0)}
B. {(-5, 2), (-9, -1), (-9, -2), (7, 4)}
D. {(10, 6), (6, -3), (8, 0)}
28. Find the domain of the function graphed:
A. D = {x is a real number}
C. D = {x > 0}
B. D = { x < 3}
D. D = { x > 3}
29. Toni is solving this equation by completing the square.
ax2 + bx + c = 0 (where a  0)
Step 1:
Step 2:
Step 3:
ax2 + bx = -c
b
c
x2  x  
a
a
?
Which should be Step 3 in the solution?
c b
A. x 2    x
b a
B. x 
b
b
c b
 
C. x  x 
a
2a
a 2a
b
c  b 
 b 
D. x  x        
a
a  2a 
 2a 
2
b
c

a
ax
2
2
2
30. Which is one of the solutions to the equation 2x2 – x – 4 = 0?
A.
1
 33
4
B. 
1
 33
4
C.
1  33
4
31. The graph of the equation y  x 2  2 x  3 is shown below.
For what value or values of x is y  0 ?
A x  1 only
B x  3 only
C x  1 and x  3
D x  1 and x  3
32. What are the roots of the function shown?
A x
3
2
B y
3
2
C x= 3
1
2
D (1, 0) and (5, 0)
D.
 1  33
4
33. How many times does the graph of y = x² - 11x + 24 intersect the x-axis?
A. none
B. one
C. two
D. three
34. The height of a triangle is 4 inches greater than twice its base. The area of the
triangle is 168 square inches. What is the base of the triangle?
A. 7 in.
B. 8 in.
C. 12 in.
D. 14 in.
35. Which number serves as a counterexample to the statement below:
All positive integers are divisible by 2 or 3.
A. 100
B. 57
C. 30
36. Consider the following:
3(2x – 4) = 18
6x – 12 = 18
Distributive property
6x = 30
______________________
x=5
multiplication property of equality
What is the missing justification?
A. Addition property of equality
C. Commutative property
B. Associative property
D. Additive Identity
D. 25