Math Knowledge

2.24. Reduce: (2)^30 + (2)^30 + (2)^30 + (2)^30 . A. (2)^32 B. (2)^30 C. (8)^120 D. (8)^32 E. (10)^32

A. (2)^32

3.8. Solve for 𝑥: (x+2)/(x+1) = 5 A. -(3/4) B. (3/4) C. −3 D. 1 E. 3

A. -(3/4)

2.11. Which has the least value? A. .0009 B. .0108 C. .0059 D. .2000 E. .0010

A. .0009

2.8. (1/8)^3 = A. 1/512 B. 1/24 C. 3/24 D. 3/512 E. 9/512

A. 1/512

3.14. How many sets of supplementary angles are represented? (see figure) A. 24 B. 12 C. 8 D. 6 E. 4

A. 24

2.19. John sent Douglas y text messages every hour for 5 hours, and Peter sent Douglas z text messages every hour for 3 hours. Which is the correct way to represent the total number of messages that Douglas received? A. 5y + 3z B. 8yz C. 15yz D. 15y + z E. 8 + yz

A. 5y + 3z

3.23. The expression (2𝑥 + 5)^3 is equivalent to ________________ . A. 8x^3 + 60x^2 + 150x + 125 B. 8x^3 + 20x^2 + 50x + 125 C. x^3 + 20x^2 + 50x + 125 D. 4x^3 + 20x^2 + 25 E. 8x^3 + 1252

A. 8x^3 + 60x^2 + 150x + 125

2.16. Calculate the surface area of the object. (see figure) A. 90 square feet B. 108 square feet C. 54 square feet D. 12 square feet E. 18 square feet

A. 90 square feet

3.15. If (a+b)/(a-b) = 9/7 then _________ must also be true. A. a/b = 8 B. a/b = -8 C. (a+2b)/(a-b) = 10/7 D. b -a = -7 E. b -a = 7

A. a/b = 8

3.2. Given a line that is represented by the equation y = 4x + 3, which of the following lines is parallel to it? A. −4x + y = 12 B. 4x + 2y = 8 C. 2x + y = 6 D. −2x + 2y = 6 E. −2x + 2y = 3

A. −4x + y = 12

3.22. How many real solutions are there for the equation: 𝑥^2 - 8𝑥 + 16 = 0? A. 0 B. 1 C. 2 D. 3 E. 4

B. 1

2.3. Calculate the area of the rectangle: (see figure) A. 4 square inches B. 12 square inches C. 14 square inches D. 16 square inches E. 60 square inches

B. 12 square inches

3.19. If (t-3)/(t-5) = 7, what is the value of 𝑡? A. 8/3 B. 16/3 C. 18/5 D. 21/5 E. 35/5

B. 16/3

3.6. Solve for 𝑥: (5/6)x - (1/6)x = (2/3) + (1/2) + (5/6) A. 2 B. 3 C. 5 D. 6 E. 7

B. 3

3.18. Solve for 𝑥: (5/8)x - (3/8)x = (3/4) + (1/2) A. 1/4 B. 5 C. 8 D. 15 E. 24

B. 5

2.22. Out of 75 students, 40 are taking French, 20 are taking German, and an additional 9 are taking both. How many students are not enrolled in either French or German? A. 4 B. 6 C. 24 D. 75 E. 0

B. 6

2.7. Round 657,258 to the nearest ten thousand and express in scientific notation. A. 6.6 x 10^4 B. 6.6 x 10^5 C. 6.57 x 10^4 D. 6.57 x 10^5 E. 7.0 x 10^4

B. 6.6 x 10^5

3.13. What is the value of ∠b, if ∠a measures 65 degrees? (see figure) A. 25° B. 65° C. 115° D. 135° E. 180°

B. 65°

3.10. An oil storage container is a right circular cylinder with a diameter of 20 meters and a height of 8 meters. What is the volume of the container in cubic meters? A. 640π B. 800π C. 1,280π D. 3,200π E. 3,400π

B. 800π

2.15. ½(b x h) is the formula for _________. A. the area of a circle B. the area of a triangle C. the area of a parallelogram D. the volume of a cube E. the volume of a rectangle

B. the area of a triangle

2.20. Anne's hotel room costs $99.99 per night, plus 7% tax, and a flat fee of $10.00 per stay. If Anne stays for 6 nights, how much will she owe? A. $52.00 B. $641.94 C. $651.94 D. $652.00 E. $1029.99

C. $651.94

2.5. The sum of the internal angles of an isosceles triangle is ______. A. 45º B. 90º C. 180º D. 270º E. 360º

C. 180º

2.25. Which of the following numbers is a prime number? A. 6 B. 4 C. 2 D. 0 E. -1

C. 2

2.10. Which number has the greater value? A. 1/10 B. 2/10 C. 2/2 D. 5/10 E. 5/100

C. 2/2

3.25. If 12 + 3𝑥 is 10 more than 17, what is the value of 4𝑥? A. 3 B. 5 C. 20 D. 40 E. 47

C. 20

3.11. If 𝑦 = 5𝑥 + 𝑏 represents a line on the xy-plane with y-intercept b, and the line passes through the point (-1,-2), what is the value of b? A. -9 B. -7 C. 3 D. 7 E. 9

C. 3

2.18. π = A. 3.15 B. 3.411593... C. 3.141592... D. 4.151592... E. 5.141592...

C. 3.141592...

3.5. What is the measure of ÐPRQ shown below? (see figure) A. 60° B. 50° C. 45° D. 30° E. 5°

C. 45°

2.14. What is the total surface area of an eleven foot tall cylinder with a base radius of 8 feet, rounded to the nearest whole number? A. 176π square feet B. 304 square feet C. 955 square feet D. 955π square feet E. 1007 square feet

C. 955 square feet

3.24. An elementary school is holding a bake sale to fund student activities. Cookies cost $2 each and brownies cost $3 each. The school hopes to earn a minimum of $500, and students have provided a total of 400 items to sell. Which of the following systems of equations yields the number of cookies (c) and brownies (b) that the school needs to sell to meet its goal? A. b + c < 400 3c + 2b > 500 B. b + c ≤ 400 3c + 2b ≤ 500 C. b + c ≤ 400 2c + 3b ≥ 500 D. b + c < 400 2c + 3b < 500 E. b + c ≥ 400 2c + 3b ≥ 500

C. b + c ≤ 400 2c + 3b ≥ 500

3.17. A swimming pool is 3 meters deep. Its length is 4 meters longer than twice its width. If the pool can hold 60 cubic meters of water, which of the following equations can be used to find the width (w) of the pool? A. 𝑤^2 + 2𝑤 + 10 = 0 B. 𝑤^2 + 4𝑤 + 20 = 0 C. 𝑤^2 + 2𝑤 - 10 = 0 D. 𝑤^2 + 2𝑤 − 20 = 0 E. 𝑤^2 + 2𝑤 − 60 = 0

C. 𝑤^2 + 2𝑤 - 10 = 0

2.23. The mean age of male elephants at a local zoo is 20 years old, while the mean age of the female elephants is 16 years old. Which of the following must be true about the mean age (m) of all elephants at the zoo? A. m = 18 B. m > 18 C. m < 18 D. 16 < m < 20 E. m = 18.5

D. 16 < m < 20

3.16. Sarah has a budget of $1,000 for a home improvement project. She can buy cans of paint for $50 each and bundles of lumber for $100 each. If she buys at least one can and one bundle, what is the maximum amount of paint that she can afford? A. 4 cans B. 8 cans C. 10 cans D. 18 cans E. 20 cans

D. 18 cans

2.9. Convert 6/18 to a percent. A. 90% B. 62% C. 60% D. 33% E. 30%

D. 33%

3.20. Which is closest to the volume of the cone in the figure below if the diameter of the base is 12cm? (see figure) A. 65.3 cm^3 B. 130.6 cm^3 C. 195.9 cm^3 D. 391.8 cm^3 E. 430.6 cm^3

D. 391.8 cm^3

3.7. What is the least possible value for 𝑐𝑐 if 5𝑐𝑐 - 12 ≥ 8? A. 1 B. 2 C. 3 D. 4 E. 5

D. 4

2.1. 7/8 - 2/3 + 1/5 = A. 6/5 B. 3/5 C. 5/8 D. 49/120 E. 1/120

D. 49/120

2.17. Calculate the volume of the object. (see figure) A. 18 cubic feet B. 90 cubic feet C. 108 cubic feet D. 54 cubic feet E. 180 cubic feet

D. 54 cubic feet

3.1. If (x-1)/2 = 𝑘 and 𝑘 = 4, what is 𝑥? A. 2 B. 3 C. 8 D. 9 E. 11

D. 9

2.13. B = 12A / (a + A); solve for A. A. Ba/ (a - B) B. Ba - 12 C. B / a - 12 D. Ba / (12 - B) E. B (a - 1) /12

D. Ba / (12 - B)

3.4. If 𝑦(𝑥) = √((x^2) − 6), which of the following is equivalent to 𝑦(𝑦(𝑥))? A. √((x^2) − 6) B. √((x^2) − 6) C. √((x^2) − 6) − 6 D. √((x^2) − 12) E. √(((x^2) − 6)^2) − 6

D. √((x^2) − 12)

2.2. Solve for y: 10y + 5x = 15z A. (y+x)/3z B. 3xz C. 3 D. (3z-x)/10 E. (3z-x)/2

E. (3z-x)/2

3.21. Which of the following is not divisible by 𝑥 - 8? A. 𝑥^4(𝑥 − 8) + 17(𝑥 − 8) B. 𝑥^3(𝑥 − 8) + 21(𝑥 − 8) C. 𝑥^3 − 13X^2 + 40𝑥 D. 𝑥^2𝑦 − 64𝑦 E. (X-8)(X+2) + 6

E. (X-8)(X+2) + 6

3.12. Solve for 𝑥 when 𝑦 = 6: 𝑦^2 = √𝑥 A. 6 B. 8 C. 64 D. 1,084 E. 1,296

E. 1,296

3.9. What is the sum of 7𝑥^2 − 4𝑥 + 8 and 3𝑥^2 − 𝑥 + 7? A. 10𝑥^4 − 4𝑥^2 + 15 B. 10𝑥^4 − 5𝑥^2 + 15 C. 10𝑥^4 − 5𝑥^2 - 15 D. 10𝑥^2 − 3𝑥 + 15 E. 10𝑥^2 − 5𝑥 + 15

E. 10𝑥^2 − 5𝑥 + 15

3.3. The expression (4x + 3)(5x − 10) is equivalent to _______________. A. (9𝑥 − 7) B. 20x^2 − 30 C. 20𝑥^2 − 15𝑥 − 30 D. 20𝑥^2 − 20𝑥 − 30 E. 20𝑥^2 − 25𝑥 − 30

E. 20𝑥^2 − 25𝑥 − 30

2.6. If the area of a circle is 121πft^2, what is the circumference? A. 121ft B. 11π^2 C. 22π^2 D. 11π E. 22π

E. 22π

2.21. Solve the equation for the variable: 5(6-3y) = 3y + 3 A. 1 B. 1/3 C. 2/3 D. 2 E. 3/2

E. 3/2

2.12. What is the value of the expression (15x + 3y^2 - 5) if x = 3 and y = 2? A. 0 B. 84 C. 76 D. 64 E. 52

E. 52

2.4. Solve for x: ((10^2)*x) = 7 A. 10 B. 7/10 C. 7/20 D. 10/120 E. 7/100

E. 7/100

1.12. Factor the following expression: 21𝑥^2 + 63x a) 21x(x + 3) b) 21(𝑥^2 + 3x) c) 7(3𝑥^2 + 9x) d) 7x(3x + 9x) e) 21 + 63(𝑥^2)

a) 21x(x + 3)

1.23. Multiply the terms 4x(y^2)(z^3) and 7(𝑥^2)(y^3)z a) 28(x^3)(y^5)(z^4) b) 28(x^2)(y^6)(z^3) c) 28(x^2)(y^2)(z^2) d) 11(x^3)(y^5)(z^4) e) 11(x^2)(y^6)(z^3)

a) 28(x^3)(y^5)(z^4)

1.5. What is the remainder when 267 is divided by 4? a) 3 b) 4 c) 5 d) 6 e) 7

a) 3

1.16. Which inequality is equivalent to 35 ≥ m - 7? a) 42 ≥ m b) 42 ≤ m c) 5 ≥ m d) 5 ≤ m e) -5 ≥ m

a) 42 ≥ m

1.25. Which of the following statements is true of vertical angles? a) They are always equal b) They always add up to 90 c) They always add up to 180 d) They are always even numbers e) They are always odd numbers

a) They are always equal

1.3. If an angle measures 75 degrees, what is its complementary angle? a) 10 b) 15 c) 25 d) 55 e) 105

b) 15

1.1. What is 1/5th of 80%? a) 15% b) 16% c) 18% d) 20% e) 25%

b) 16%

1.14. What is the value of y in the following system? 3y - 3x = 18 y - 4x = 12 a) 2 b) 4 c) 10 d) 15 e) 20

b) 4

1.24. What is 67,489 rounded to the nearest hundred? a) 67,400 b) 67,500 c) 67,480 d) 67,490 e) 67,000

b) 67,500

1.19. Which number has the greatest value? a) 16 hundreds b) 8 thousands c) 9 thousandths d) 200 tens e) 7550 ones

b) 8 thousands

1.10. Which of the following is a solution for the given equation? 2(x - 5) + 𝑥^2 - 50 = 60 a) 2 b) 5 c) 10 d) 20 e) 25

c) 10

1.11. What is the x intercept of the given equation? 15x - 5y = 30 a) - 6 b) 0 c) 2 d) 6 e) 8

c) 2

1.2. If a circle has a diameter of 16 inches, which of the following is closest to its area? a) 50 b) 185 c) 200 d) 805 e) 1000

c) 200

1.4. Simplify: √81 + √144 a) 9 b) 16 c) 21 d) 35 e) 50

c) 21

1.8. John's school is hosting a movie night. Tickets cost $6 per person and candy is sold at $3 per box. John paid a total of $21 for himself and his date. How many boxes of candy did he purchase? a) 1 b) 2 c) 3 d) 4 e) 5

c) 3

1.20. C, D, E, and F lie on a circle with center Z. If the diameter of the circle is 30, what is the sum of CZ, DZ, and EZ? a) 15 b) 30 c) 45 d) 60 e) 75

c) 45

1.6. Which of the following in equivalent to 𝑧^2(𝑧^4-6) - 3𝑧^2 - 8? a) 𝑧^6 - 3𝑧^2 - 8 b) 𝑧^4 - 3𝑧^2 - 8 c) 𝑧^6 - 9𝑧^2 - 8 d) 𝑧^4 - 9𝑧^2 - 8 e) 𝑧^6 - 6𝑧^2 - 8

c) 𝑧^6 - 9𝑧^2 - 8

1.22. In a right triangle, the measure of one leg is 16 while the measure of the other leg is 36. What is the measure of the hypotenuse? a) 16 b) 31.2 c) 36.4 d) 39.4 e) 41

d) 39.4

1.7. How long will it take a plane to fly 2500 miles from New York to Los Angeles while traveling at a constant speed of 400 mph? Use the distance formula: distance = velocity x time. a) 0.16 hours b) 2.25 hours c) 4.5 hours d) 6.25 hours e) 6.75 hours

d) 6.25 hours

1.18. Write the equation of the line which passes through the points (-4, 6) and (-6,7). a) y = (1/2)x + 4 b) y = (1/2)x + 7 c) y = -(1/2)x + 7 d) y = -(1/2)x + 4 e) y = -(1/2)x + 2

d) y = -(1/2)x + 4

1.13. Identify the pair of supplementary angles. a) 30˚ and 30˚ b) 30˚ and 60˚ c) 30˚ and 70˚ d) 30˚ and 95˚ e) 30˚ and 150˚

e) 30˚ and 150˚

1.15. What is the value of the expression 4a +3(𝑏^2) - 9, if a= -2 and b = 5? a) 208 b) 242 c) 75 d) 66 e) 58

e) 58

1.21. A fish tank at the zoo is 15 feet long, 8 feet wide, and 5 feet tall. What is the cubic volume for the tank? a) 75 cubic feet b) 120 cubic feet c) 125 cubic feet d) 300 cubic feet e) 600 cubic feet

e) 600 cubic feet

1.17. The inequality is 7a + 3b > 30 is true for which values of a and b? a) a = 1 and b = 2 b) a = 1 and b = 3 c) a = 2 and b = 2 d) a = 2 and b = 3 e) a = 2 and b = 6

e) a = 2 and b = 6

1.9. Which expression is equivalent to (x - 1)(x + 5)(x - 3)? a) 𝑥^3 + 2𝑥^2 - 8x - 15 b) 𝑥^3 - 4𝑥^2 - 8x - 15 c) 𝑥^3 - 4𝑥^2 - 2x - 15 d) 𝑥^3 - 2𝑥^2 + 2x - 15 e) 𝑥^3 + 2𝑥^2 - 17x - 15

e) 𝑥^3 + 2𝑥^2 - 17x - 15