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Essential
SkillsSystems
Functions &
Inequalities
Quadratics
Potpourri
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Essential
SkillsSystems
Functions &
Inequalities
Quadratics
Potpourri
Essential Skills - $100There is the same number of boys and girls on a school bus when it departs from school. At the first stop, 4 boys get off the bus and nobody gets on. After the first stop, there are twice as many girls as boys on the bus. How many girls are on the bus?
Essential Skills - $100 Answer
8
Essential Skills - $200In the figure below, three line segments meetat a point to form three angles. What is the value of x? (Not drawn to scale.)
2
x
4
x 3
x
Essential Skills - $200 Answer
3
Essential Skills - $300
If p is an integer and 3 is the remainder when
2p + 7 is divided by 5, then p could be
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Essential Skills - $300 Answer
(B) 3
Essential Skills - $400
1If , what is the
21 1
value of ?1
x
x x
Essential Skills - $400 Answer
0
Essential Skills - $500
How old was a person exactly 1 year ago if exactly x years ago the personwas y years old?
Essential Skills - $500 Answer
1 y x
Systems - $100
If 2 5 and 5 6 ,
what does equal in terms of ?
r s s t
r t
Systems - $100 Answer
3t
Systems - $200
For how many ordered pairs of positive integers (x, y) is
2 3 6?x y
Systems - $200 Answer
one
Systems - $300
What is the value of k thatsatisfies both equations below?
10 3
5 8
k
k
Systems - $300 Answer
13
Systems - $400
Edna and Nancy leave the house of a common friend at the same time and walk for 4 hours. Edna walks dueeast at the average rate of 4 kilometers per hour and Nancy walks due north at the average rate of 3 kilometersper hour. What is the straight-line distance betweenthem, in kilometers, at the end of the 4 hours?
Systems - $400 Answer
20
Systems - $500
In the xy-plane, line l passes through the origin and is perpendicular to the line 4x + y = k, where k is a constant. If the two lines intersect at the point (t, t + 1), what is the value of t?
Systems - $500 Answer
4
3
Functions & Inequalities - $100
The figure below shows the graph of the function h.Which of the following is closest to h(5)?
(A) 1(B) 2(C) 3(D) 4(E) 5
Functions & Inequalities - $100 Answer
(B) 2
Functions & Inequalities - $200
In the xy-coordinate plane, line l is perpendicular to the y-axis and passes through the point (5, −3).What is an equation of line l?
Functions & Inequalities - $200 Answer
y = –3
Functions & Inequalities - $300
The total daily profit p, in dollars, from producing and selling x units of a certain product is given by the function p(x) as defined below, where b is a constant.If 300 units were produced and sold yesterday for atotal profit of $1,900, what is the value of b?
17 10 p x x x b
Functions & Inequalities - $300 Answer
200
Functions & Inequalities - $400
A regulation for riding a certain amusement parkride requires that a child be between 30 inchesand 50 inches tall. Write an absolute valueinequality that can be used to determine whether0r not a child’s height h satisfies the regulationfor this ride.
Functions & Inequalities - $400 Answer
40 10 h
Functions & Inequalities - $500If 0 8 and 1 3,
which of the following gives
the set of all possible values of ?
x y
xy
A 4
(B) 0 24
(C) 1 11
(D) 1 24
(E) 8 24
xy
xy
xy
xy
xy
Functions & Inequalities - $500 Answer
(E) −8 ≤ xy ≤ 24
Quadratics - $100
For what value of x is the statement above FALSE?
(A) −3(B) 0(C) 1/3(D) 1(E) For no value of x
223 3x x
Quadratics - $100 Answer
(B) 0
Quadratics - $200
The figure above shows the graph of a quadraticfunction f that has a minimum at the point (1, 1).If f(b) = f(3), what is the value of b?
Quadratics - $200 Answer
1
Quadratics - $300
In the figure above, PQRS is a rectangle, and points Q and R lie on the graph of y = ax2, where a is a constant. If the perimeter of PQRS is 10, what is the value of a?
P
Q R
S
Quadratics - $300 Answer
3
Quadratics - $400
*Daily Double!*
The table above gives values of the quadratic function f for selected values of x. Write the
quadratic function that defines f.
x 0 1 2 3
f(x) 1 2 5 10
Quadratics - $400 Answer
2 1f x x
Quadratics - $500At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h below, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t = 2.5, what was the height, in feet, of the ball at time t = 1?
24 h t c d t
Quadratics - $500 Answer
70
Potpourri - $100
According to a certain recipe, 25 pounds of flour are needed to make 300 rolls.At this rate, how many pounds of flour areneeded to make 12 rolls?
Potpourri - $100 Answer
1 pound
Potpourri - $200
The numerator of a certain fraction is
5 less than the denominator. If the
3fraction is equal to , what is the
4denominator of this fraction?
Potpourri - $200 Answer
20
Potpourri - $300
A “simple square” is any integer greater than 1 that has only three positive integer factors – itself, its square root, and 1. Which of the following is a simple square?
(A)121(B) 100(C) 81(D) 64(E) 33
Potpourri - $300 Answer
(A) 121
Potpourri - $400
The perimeter of a rectangular plot of land is250 meters. If the length of one side of the plotis 40 meter, what is the area of the plot, in square meters?
Potpourri - $400 Answer
3400
Potpourri - $500
If p, r, and s are three different prime numbers greater than 2, and n = p × r × s, how many positiveFactors, including 1 and n, does n have?
Potpourri - $500 Answer
8
Final Jeopardy Category:
Systems
Final Jeopardy Question
A school ordered $600 worth of lightbulbs.Some of the lightbulbs cost $1 each and the others cost $2 each. If twice as many $1 bulbs as $2 bulbs were ordered, how many lightbulbs were ordered altogether?
Final Jeopardy Answer
450
