Heart of Algebra
If a/b = 2, what is the value of 4b/a?
2
If 3x − y = 12, what is the value of 8x/2y?
A) 212
B)44
C) 2
D) It cannot be determined from information given.
A, 212
If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?
20
What is the sum (7 + 3i) + (−8 + 9i) ?
-1+12i
(√k+ 2) - x = 0
In the equation above, k is a constant. If x = 9, what is the value of k?
A) 1
B) 7
C) 16
D) 79
D, 79
A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
D, (14, 2)
If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c ?
A) 3 and 5
B) 6 and 35
C) 10 and 21
D) 31 and 41
D, 31 and 41
A youth activist group surveyed a random sample of 500 teenagers between the ages of 16 and 17 in the U.S. to assess their opinions about lowering the voting age to 16. The survey showed that the majority of those sampled were in favor of lowering the voting age to 16. Based on the results, the majority of which of the following populations in the U.S. are most likely in favor of lowering the voting age to 16?
A) all adults
B) all registered voters
C) all 16 and 17 year-olds
D) all students at a particular high school
C, all 16 and 17 year-olds
In a right triangle, one angle measures x°, where sin x° =4/5. What is cos(90° − x°) ?
4/5
y = x2
2y + 6 = 2 (x + 3)
If (x,y) is a solution of the system of equations above and x > 0, what is the value of xy?
A) 1
B) 2
C) 3
D) 9
A, 1
The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge’s posted weight limit?
107
h = − 4.9t2 + 25t
The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?
5.1
Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina’s observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?
120
Which of the following is an equation of a circle in the xy-plane with center (0, 4) and a radius with endpoint (4/3, 5)?
x2+(y-4)2=25/9
Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?
A) A linear function whose rate of change is not zero
B) A quadratic function with real zeros
C) A quadratic function with no real zeros
D) A cubic polynomial with at least one real zero
C, A quadratic function with no real zeros
Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?
Any number between 4-6 inclusive
For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x) ?
A) x − 5 is a factor of p(x).
B) x − 2 is a factor of p(x).
C) x + 2 is a factor of p(x).
D) The remainder when p(x) is divided by x − 3 is −2.
D, The remainder when p(x) is divided by x − 3 is −2.
Norman was 52 centimeters long when he was born. Over the next 6 months, his length grew at a rate of 2.5 centimeters a month. If f(t) is Norman's length in centimeters t months after his birth, which of the following statements best describes the function f
A) The function f is a decreasing linear function.
B) The function f is an increasing linear function.
C) The function f is a decreasing exponential function.
D) The function f is an increasing exponential function.
B, The function f is an increasing linear function.
A dairy farmer uses a storage silo that is in the shape of the right circular cylinder with height 8. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?
6
h = 3a + 28.6
A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what value represents the estimated increase, in inches, of a boy’s height each year?
3
y<-x+a, y>x+b
In the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?
A) b ≥ a
B) a > b
C) b > a
D) a ≤ b
B, a > b
Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)t to find the value of the account after t years. What is the value of x in the expression?
1.02
The minimum value of a data set consisting of 15 positive integers is 29. A new data set consisting of 16 positive integers is created by including 2 in the original data set. Which of the following measures must be 7 greater for the new data set than for the original data set?
A) the mean
B) the median
C) the range
D) the standard deviation
C, the range
According to the figure drawn on the board, triangle ABC is similar to triangle DEF. What is the value of sin (F)?
A) 7/24
B) 7/25
C) 24/25
D) 25/7
B, 7/25
g(x) = ax2 + 24
For the function g defined above, a is a constant and g(4) = 8. What is the value of g(−4) ?
8