Evaluate Functions
If (x-1)/3 = k and k = 3, what is the value of x?
10
On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. What equation represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
5m + 4p
Simplify.
(x2y - 3y2 + 5xy2) - (-x2y + 3xy2 - 3y2)
2x2y + 2xy2
If four distinct lines lie in a plane, and exactly two of them are parallel, what is the least possible number of points of intersection of the lines?
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) a > b
b) b > a
c) |a| > |b|
d) a = -b
a) a > b
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
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 is the estimated increase, in inches, of a boy’s height each year?
3
If (x + 1)2 = 4 and (x − 1)2 = 16, what is the value of x?
x= -3
In a right triangle, one angle measures x°, where sin(x°) = 4/5 . What is cos(90° − x°)?
0.8 or 4/5
Write an equation for a circle in the xy-plane with center (0, 4) and a radius with endpoint (4/3, 5).
x2 + (y - 4)2 = 25/9
*equation for circle is (x-h)2 + (y-k)2 = r2, with center (h, k)
*find radius using the distance formula
If a/b = 2, what is the value of (4b)/a?
2
A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck’s revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
93
Amy is two years older than Bill. The square of Amy’s age in years is 36 greater than the square of Bill’s age in years. What is the sum of Amy’s age and Bill’s age in years?
18
Daily Double!
The perimeter of a rectangle is 5x and its length is (3/2)x. If the area of the rectangle is 294, what is the value of x?
x = 14
The first term of a sequence is the number n, and each term thereafter is 5 greater than the term before. Which of the following is the average (arithmetic mean) of the first nine terms of this sequence?
a) n + 20
b) n + 180
c) 2n
d) 2n + 40
e) 9n + 180
a) n + 20
If 3x - y = 12, what is the value of of (8x)/(2y)?
212
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? (Answer must be an integer)
107
Let a and b be numbers such that a3 = b2. Which of the following is equivalent to b(a)1/2?
a) b2/3
b) b4/3
c) b2
d) b3
e) b4
b) b4/3
The perimeter of a particular equilateral triangle is numerically equal to the area of the triangle. What is the perimeter of the triangle?
a) 3
b) 4
c) 4√3
d) 12√3
e) 18√3
d) 12√3
A three-digit number, XYZ, is formed of three different non-zero digits X, Y , and Z. A new number is formed by rearranging the same three digits. What is the greatest possible difference between the two numbers? (For example, 345 could be rearranged into 435, for a difference of 435 − 345 = 90.)
792
The value of y increased by 12 is directly proportional to the value of x decreased by 6. If y = 2 when x = 8, what is the value of x when y = 16?
x = 10
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
Daily Double!
Two cars are racing at a constant speed around a circular racetrack. Car A requires 15 seconds to travel once around the racetrack, and car B requires 25 seconds to travel once around the racetrack. If car A passes car B, how many seconds will elapse before car A once again passes car B ?
75/2 = 37.5 seconds
The perimeter of square ABCD is x, and the perimeter of isosceles triangle EFG is y. If AB = EF = FG, which of the following must be true?
a] 0 < y < (x/4)
b] (x/4) < y < (x/2)
c] (x/2) < y < x
d] x < y < 2x
e] 2x < y < 4x
c] (x/2) < y < x
Daily Double!
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?
31 and 41