Download ALGEBRA INDIVIDUAL

ALGEBRA 1 INDIVIDUAL
March 27, 2010 Statewide Invitational
Choose the letter of the best answer. If your answer is not present, choose E. NOTA which means “None of
These Answers”.
1. If f(x) is a linear function and g(-7) = 7, g(-5) = 2. Find g(0).
A. -13
B. -10.5
C. 6.5
D. 22
E. NOTA
2. The sum of two consecutive odd integers is 80. What is the negative difference between these two
numbers?
A. -1
3. Evaluate
B. -2
C. 0
D. 2
E. NOTA
(x98 y29z85 )
when x = 1, y = 2, z = 1.
(x- 2 y33z80 )
A. 16
B. 4
C.
1
4
D.
1
16
E. NOTA
4. Which of the following is considered a prime factorization?
A. 21326374
B. 22334471
C. 2432519
D. 23315271
E. NOTA
5. What is the slope of the line passing through (2, 5) and (8, 2)?
A. -
1
2
B. −1
C.
1
2
D. 2
E. NOTA
For 6 − 7, use the following line: 4x + 10y = 16.
6. What is the y-intercept of the line given above?
A. (8/5, 0)
B. (0, 4)
C. (4, 0)
D. (0, 8/5)
E. NOTA
D. (0, 8/5)
E. NOTA
7. What is the x-intercept of the line given above?
A. (8/5, 0)
B. (0, 4)
C. (4, 0)
8. Matt has five test scores of 87, 92, 98, 95, and 78. What is the sum of Matt’s average test score and the third
triangular number?
A. 91
B. 96
C. 100
D. 105
E. NOTA
9. (8, 5) , (−1, −13), and (4, k) are all points on the same line. What is the value of k?
A. -5
B. -3
C. 0
D. 3
E. NOTA
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10. Let F=12!, M= 2!, H= 10!, and S=0!. Find the value of (FM/HS).
A. 264
B. 240
C. 132
D. 120
E. NOTA
11. What is the slope of the line perpendicular to the line passing through points (2, 5) and (8, 2)?
A. 1
B. -2
C. -½
D. 2
E. NOTA
12. How many roots does the equation x2 −5x + 6=0 have?
A. 2
B. 1
C. 0
D. Cannot be determined
E. NOTA
13. Find the prime factorization of 2010.
A. 213151(67)1
B. 213151(61)1
14. Given the linear system
C. 223151(67)1
D. 213152(67)1
E. NOTA
find xy + xy2.
3x +4y = −5
6x + 2y = 20
A. 125/3
15. Simplify
A.
B. 125
C. 150
D. 100/3
E. NOTA
10
x2
+ 2
x+ 2
x - 4
x2 - 10x - 20
x2 - 4
B.
x2 + 10x - 20
x2 - 4
C.
æx2 + 10x + 20 ÷
ö
÷
D. - ççç
÷
2
÷
è x - 4
ø
x2 + 10x + 20
x2 - 4
E. NOTA
16. What is the distance between the two points (4, 5) and (8, 3)?
A. 4
B. 5
C. 4 5
D. 2 5
E. NOTA
17. If x2(15!) = 16!, then x = ?
A. 16
B. 15
C. +4 or -4
D. 2
E. NOTA
18. Solve the inequality: −8x < 24.
A. x>-3
B. x>-2
C. x<-3
x<-2
E. NOTA
19. If x is 7 more than 1/3 a number and x is 3 less than 2 times the same number, then what is x?
A. 9
B. 5
C. 7
D. 12
E. NOTA
20. If (x + y)2 = 18 and xy = 6, what is: x2 + y2?
A. 12
B.
18
C. 6
D.
6
E. NOTA
21. The sum of three consecutive even integers is 90. What is the product of these three integers?
A. 26880
B. 24300
C. 21840
D. 17472
E. NOTA
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22. The product of two consecutive even integers is 24. What is the sum of these two integers?
A. 24
B. 12
C. 10
D. 6
E. NOTA
23. Factor completely: x4 − 16
A. (x2 + 4)(x2 − 4)
B. (x2 + 4)(x − 2)(x + 2)
C. (x − 2)(x2 + 2x + 4)
D. (x + 2)2(x − 2)2
E. NOTA
24. Solve for x: 5 + (2)(3) + 32 − 9 + 3 − 5 = 2x
A. 18
B. 12
C. 9
D. 6
E. NOTA
25. Vishan has an average of 88% on four math tests. What does he need on his next math test in order to
increase his average to 90%?
A. 102
B. 100
C. 98
D. 96
E. NOTA
26. Nadine has 45 pencils. On day 1, she puts one aside for herself. On day two, she puts one aside for herself and
gives one to Jacquelyn. For each day after that she gives herself a pencil, a pencil to each person that she has
already given a pencil, and one to a new person. On what day will Nadine give away her last pencil?
A. 8
27.
B. 9
C. 10
D. 11
E. NOTA
C. 12/5
D. 4
E. NOTA
625(3−x) = 5(x−3). What is x?
A. 6
B. 3
28. Which property of addition does the following example exhibit?
A(y + z) = A(z + y)
A. Commutative
B. Associative
C. Distributive
D. Identity
E. NOTA
29. The midpoint of the segment containing (6,10) and (20, 8) is (x, y). What is the value of xy?
A. 143
B. 132
C. 128
D. 117
E. NOTA
30. What are the roots of the equation 3x2 − 14x − 5 = 0?
A. -1/3, −5
B. 1/3, 5
C. -1/3, 5
D. −3, 5
E. NOTA
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