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SkillsSystems

Functions &

Inequalities

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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


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


(B) 3


1If , what is the

21 1

value of ?1

x

x x


0


How old was a person exactly 1 year ago if exactly x years ago the personwas y years old?


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


one

Systems - $300

What is the value of k thatsatisfies both equations below?

10 3

5 8

k

k


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?


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?


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


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?


y = –3


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


200


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.


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


(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?


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


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


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


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?


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


(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?


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?


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

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