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February Regional
Algebra I Individual Test
Answer choice “E) NOTA” means that none of the above answers are correct.
1. Given the system of equations:
Ax + By = C
Dx + Ey = F
where A, B, C, D, E, and F represent the first six prime numbers respectively, find (x,y).
æ 1 4ö
3 3
B) ç , ÷
è
ø
A) (16, -9)
æ 3ö æ 4ö
C) (19, -11)
æ
æ 12 5 ö
,
è 7 7 ÷ø
E) NOTA
285
14
E) NOTA
D) ç
9 ö æ 43 ö
2. Evaluate: ç ÷ ç ÷ +19 - 32 + ç 6 × 5 + ÷ ¸ ç ÷
è 2ø è 7ø
è
4ø è 4 ø
A) -
285
14
B)
1207
301
C)
97
7
D)
3. Integers are a subset of __________ numbers.
A) Whole B) Natural
C) Irrational
D) Rational
4.
E) NOTA
x
2
+
>3
x - 2 x -1
Which of the following can be a value for 𝑥?
A)
1
2
B)
2
3
C)
5
6
D) 4
E) NOTA
5. Solve for x: 2 x + 3 = 16
A) 13, −19
B) −11
C) 5, −11
D) 13
E) NOTA
6. Hansol has taken six tests in English this semester and has an 87 average. What score must she get on her
seventh test to have exactly a 90 average for the semester?
A) 90
B) 95
C) 108
D) 110
E) NOTA
7. Find the solutions(s) to the equation 2x 2 + 6x - 3 = 0 on the domain (0,∞).
A)
−3 ± √15
2
B)
−3+ √3
2
C)
−3 + √15
2
D)
−3 ± √3
2
E) NOTA
8. There is a 100 mL solution that is 35% NaOH (sodium hydroxide) and the rest pure water. How much pure
water must be added to the solution to reduce the percentage of NaOH to 20%?
A) 50
B) 75
C) 85
D) 175
E) NOTA
9. Let 𝑗 ∀ ℎ = 𝑗ℎ2 + ℎ𝑗 2 . Solve for 6 ∀ (3 ∀ 2).
A) 360
B) 624
C) 2240
D) 6480
E) NOTA
February Regional
Algebra I Individual Test
For questions 10 – 12, match the law to its example.
A. Distributive Law
B. Associate Law for Addition
C. Commutative Law for Multiplication
D. Identity Law for Addition
E. NOTA
10. 3(10 + 𝑥) = 3 ∗ 10 + 3𝑥
11. 5𝑥𝑦 = 𝑦5𝑥
For questions 10 – 12, match the law to its example.
12. (𝑚 + 𝑐) + 𝑗 = 𝑚 + (𝑐 + 𝑗)
13. June wants to go to Wiggie’s Wonderful World of Ice Cream. She leaves home and walks due north for
three blocks on Vanilla Street. Then she walks due east for 5 blocks on Pistachio Almond Avenue (which
happens to be June’s favorite ice cream flavor). Finally, June walks one block north and ends at Wiggie’s
Wonderful World of Ice Cream. What is the slope of the straight line drawn from June’s home to Wiggie’s
Wonderful World of Ice Cream?
A) -
5
4
B) -
4
5
C)
4
5
5
4
D)
E) NOTA
14. From her home to Wiggie’s Wonderful World of Ice Cream, June walked at a constant rate without
stopping. What was that rate in blocks per minute if the trip took her 21 minutes?
A)
1
7
B)
8
21
C)
7
3
D)
21
8
E) NOTA
15. Steve has a collection of chocolate truffles but refuses to say how many he has. If the number of Steve’s
chocolate truffles is twenty times the greatest common factor between 242 and 132, how many truffles does
he have?
A) 180
B) 220
C) 440
D) 880
E) NOTA
16. Simplify: (
𝑥 −3 𝑦 2 𝑧
−2
) .
𝑧 −6 𝑥 5 𝑦 3
A)
𝑥2
B)
𝑦𝑧 5
𝑦 2 𝑧 10
C)
𝑥4
𝑥 16 𝑦 2
D)
𝑧 14
𝑧7
𝑥8𝑦
17. Find the roots of 5𝑥 2 − 7𝑥 − 6 = 0.
A) -3, -
2
5
2
5
B) - , 3
3
5
C) - , 2
3
5
D) , 2
E) NOTA
18. Find the sum of the reciprocals of the roots of the equation 12𝑥 2 − 25𝑥 − 7 = 0.
A) -
31
7
B) -
25
7
C) -
25
12
D) -
5
3
E) NOTA
E) NOTA
February Regional
Algebra I Individual Test
19. Jeremy steals Emily’s coloring book and says that he’ll only return it if Emily answers his math question
correctly: What is the equation of the line perpendicular to the line 𝑦 =
5
A) 𝑦 = − 2 𝑥 +
15
2
5
B) 𝑦 = − 2 𝑥 −
45
2
C) 𝑦 =
5
𝑥
2
+
45
2
2
𝑥
5
+ 12 at the point (-5,10)?
5
D) 𝑦 = − 2 𝑥 −
5
2
E) NOTA
20. In retaliation, Emily takes Jeremy’s golf clubs and will only give them back if he answers her question:
Solve for 𝑥 in the equation
A)
9 ± √97
2
B)
27
+
12
𝑥
𝑥2
9 ± √65
2
= 3.
C)
−9 ± √97
2
D)
−9 ± √65
2
E) NOTA
21. In March, Bryan sees three turtles at Silver Springs. In April, he sees four turtles at Silver Springs. In
May, he sees six turtles at Silver Springs. In June, he sees ten turtles at Silver Springs. If the number of turtles
Bryan sees per month at Silver Springs follows a pattern involving two simple arithmetic operations, how
many turtles does Bryan see at Silver Springs in July of the same year?
A) 18
B) 22
C) 34
D) 40
E) NOTA
22. Triple Justin’s age is two years less than twice Jeremy’s age. Fourteen years ago, Jeremy was two years
older than Justin. How old was Jeremy when Justin was born?
A) 2
B) 3
C) 6
D) This scenario is impossible E) NOTA
23. A well-known mathematical sequence of numbers is the Fibonacci sequence in which 𝑎𝑛+2 = 𝑎𝑛 +
𝑎𝑛+1 . For example, the first five terms are 1, 1, 2, 3, 5. What is the ninth term?
A) 13
B) 21
C) 34
D) 55
E) NOTA
24. Solve: 32 < −4𝑥 + 6 < 46
A)
−13
2
< 𝑥 < −10 B) −10 < 𝑥 <
−13
2
C)
−19
2
< 𝑥 < −13
D) −20 < 𝑥 < −13
E) NOTA
25. Kathy goes shopping and buys a pair of shoes for $15.00. These shoes were on sale at half off of 70% of
the original price. How much would Kathy have paid if the shoes were not on sale?
A) $32.14
B) $42.86
C) $75.00
D) $100.00
E) NOTA
26. Find the distance between the points (7,11) and (1,17).
A) 5√3
B) 4√17
C) 4√53
D) 6√2
E) NOTA
27. The square root of the speed of Alex’s tennis serve is directly proportional to the cube of the amount of
Gatorade he drinks and inversely proportional to the number of hours he sleeps the night before. If Alex’s
tennis serve is 64 mph when he drinks three bottles of Gatorade and sleeps for nine hours the night before,
what is the speed of his serve in mph when he drinks 2 bottles of Gatorade and sleeps for 6 hours?
A)
16
9
B)
32
9
C)
256
81
D)
1024
81
E) NOTA
February Regional
Algebra I Individual Test
28. Peter wants to kayak from San Francisco to Honolulu. On a coordinate plane, let (23,1) and (2,-9)
represent San Francisco and Honolulu respectively. Exactly halfway through his trip, Peter must stop to
replenish his supplies. At what point will Peter stop?
21
2
A) ( , 10)
25
, −4)
2
B) (
C) (−4,
25
)
2
D) (10,
21
)
2
E) NOTA
29. Colleen and June are sisters. Five years ago, June was twice Colleen’s age. Last year, June was 11 more
than half Colleen’s age. How old will June be 4 years from now?
A) 13
B) 17
C) 21
D) 25
E) NOTA
5
30. The number 3 is:
I. Rational
II. Whole
III. Real
IV. Natural
A) I and III only
B) I, III, IV only
C) I, II, IV only
D) I only
E) NOTA