Systems of Equations
Word Problems: Functions
Mystery Category
Parabolas
Polynomials
100
x + 2y = 25 2x + 2y = 35 Solve both x and y.
x = 10 y = 7.5
100
Attending a certain hagwon costs 400,000 won per month per class taken. At this rate, what is a function that would describe the cost of "n" hours?
f(n) = 400,000 n
100
Three angles form a straight line. If their measures are described by x, 3x, and 4x, what is the measure of the smallest angle in degrees?
22.5
100
Use y = x² - 6x + 8. Where would the axis of symmetry and vertex be located?
AOS: x = 3; vertex: (3, -1)
100
Find all "possible rational roots" of y = 2x³+3x²-8x+3.
±1, ±3, ±1/2, ±3/2
200
3x + y = 20 x + 3y = 4 Solve both x and y.
x = 7 y = -1
200
The cost of buying a bookshelf is 75,000 yen. The bookshelf must be stocked by books costing 15,000 yen each. What would be the cost of a bookshelf plus 25 books?
450,000 yen
200
A radar detects a cat at the exact midpoint between KICS at (3.5, 4.5) and Bucheon City Hall (3, 8.5). Where is the cat located?
(3.25, 6.5)
200
Use y = x² - 6x + 8. Find x-intercepts (solutions that make this equal to 0, aka "roots").
x = 2; x = 4
200
Test the root x = 3 in y = 2x³+3x²-8x+3 using synthetic division and tell whether it works.
x = 3 is not a root because the remainder is 60, not 0.
300
3x + 3y = 87 y = x+1 Solve both x and y.
x = 14 y = 15
300
Joining a fitness club costs $25, and you must then pay a $7 per month fee to remain with the club. How much will it cost to join this club for one year?
$109
300
A map indicates that, from Bucheon, one can travel 30 km east and 15 km south to reach Seongnam. To the nearest tenth, how far is Seongnam from Bucheon in a straight line?
33.5 km
300
Use y = x² - 6x + 8. If graphed, will this parabola open up or down? Also find the y-intercept.
Opens: up; y-intercept: (0, 8)
300
Divide 2x³+3x²-8x+3 by x-1 using synthetic division.
2x²-5x+3.
400
The width of a rectangle is 12 meters more than its length. If the area of that rectangle is 133 m^2, what are the dimensions of that rectangle?
Length: 7m; width: 19m
400
What function would describe the cost of a $400 video game console plus "x" games that cost $60 each?
C(x) = 400 + 60x (or 60x + 400)
400
What is the exact value of cos(π/6)?
Cos(π/6) = cos(30 deg) = √3/2 (about 0.866)
400
The length of a rectangle is meant to be 5 more than its width. If the area of this rectangle is to be 104 m², what need to be the length and width?
W = 8m; L = 13m
400
Divide 2x³+3x²-8x+3 by 2x-1 using synthetic division.
Quotient: (x+3)(x-1) or x²+2x-3.
500
At a local deli, Marty buys 2 sandwiches and 1 cola for $9. Sarah buys 1 sandwich and 1 cola for $5.25. What would be the cost of 1 sandwich and 2 colas?
$6.75
500
f(x) = mx + b describes a linear function. If this function contains both the points (3, -5) and (7, 8), what is the slope of the line?
m = 13/4, or m = 3.25
500
Three sisters' ages are consecutive even numbers. Sally, the youngest, is "s" years old; Christina is exactly 1.5 times as old as she is. How old is Sally?
8 years old
500
Factor completely: 2x² - 11x + 12
(2x - 3) (x - 4)
500
Solve sin(x) = -0.5 with TWO solutions in radians.
x = 5π/6 and x = 7π/6