Heart of Algebra
If a/b = 2, what is the value of 4b/a?
2
(x2 + bx − 2) (x + 3) = x3 + 6x2 + 7x − 6
In the equation above, b is a constant. If the equation is true for all values of x, what is the value of b?
3
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
If (x− 1)/3=k and k = 3, what is the value of x ?
10
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
If (ax + 2)(bx + 7) = 15x2 + 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
Every month Jamal adds two new books to his library. Which of the following types of functions best models the number of books in Jamal’s library as a function of time?
A. Increasing linear B. Decreasing linear C. Increasing exponential D. Decreasing exponential
A. Increasing linear
In a right triangle, one angle measures x°, where sin x° =4/5. What is cos(90° − x°) ?
4/5
On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Write an expression to represent the total number of messages sent by Armand and Tyrone on Saturday afternoon.
5m+4p
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
A circle has a radius of 1. A sector of the circle has an arc length of Pi/3 . How many degrees is the central angle of the sector?
60
Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 − 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?
Kathy will start each week with 108 phones to fix
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?
4 to 6
If an object of mass m is moving at speed v, the object’s kinetic energy (KE) is given by the equation KE = (1/2)mv2 . If the mass of the object is halved and its speed is doubled, how does the kinetic energy change?
The kinetic energy is...
A. Halved B. Unchanged C. Doubled D. Quadrupled
C. Doubled
A local television station sells time slots for programs in 30-minute intervals. If the station operates 24 hours per day, every day of the week, what is the total number of 30-minute time slots the station can sell for Tuesday and Wednesday?
96
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 72Pi cubic yards, what is the diameter of the base of the cylinder, in yards?
6
h = 3a + 28.6
A pediatrician uses the equation 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 equation, what is the estimated increase, in inches, of a boy’s height each year?
3
In 2014, County X had 783 miles of paved roads. Starting in 2015, the county has been building 8 miles of new paved roads each year. At this rate, in which year will County X first have at least 1,000 miles of paved roads? (Assume that no paved roads go out of service.)
2042
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
A furniture store buys its furniture from a wholesaler. For a particular style of table, the store usually sells a table for 75% more than the cost of the table from the wholesaler. During a sale, the store sells the table for 15% more than the cost from the wholesaler. If the sale price of the table is $299, what is the usual price for the table?
$455
A circle is defined by the equation (x - 1)2 + (y - 2)2 = 36. The center of the circle has coordinates (j, k). What is the value of j?
1
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