Month: December 2024

Warm Up #1

A line in the xy-plane has a slope of 1/9 and passes through the point (0,14). Which equation represents this line?

A. y = (-1/9)x – 14

B. y = (-1/9)x + 14

C. y = (1/9)x – 14

D. y = (1/9)x + 14

Warm Up # 2

If x/8=5, what is the value of 8/x?

Warm Up #3

Triangles ABC and DEF are congruent, where A corresponds to D, and B and E are right angles. The measure of angle A is 18°. What is the measure of angle F?

A. 18°.

B. 72°.

C. 90°.

D. 162°.

Problem 1

y = x^2 – 14x + 22

The given equation relates the variables x and y. For what value of x does the value of y reach its minimum?

Problem 2

The measure of angle R is 2π/3 radians. The measure of angle T is 5π/12 radians greater than the measure of angle R. What is the measure of angle T, in degrees?

A. 75

B. 120

C. 195

D. 390

Problem 3

What is the smallest solution to the given problem?

Problem 4

Problem 5

In the figure shown, BD=15 and AB=30. What is the length of Line AD? What is the length of Line DC?

Problem 6

For the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. If q(0)=14, which equation defines q?

Problem 7

A small business owner budgets $1,250 to purchase candles. The owner purchases 150 candles. If the owner pays $5.00 per candle to purchase small candles and $10.00 per candle to purchase large candles, how many large candles did the owner buy?

Problem 8

The function f is defined by the given equation. If g(x)=f(x+2), which of the following equations defines the function g?

Question 1

The table summarizes the distribution of color and shape for 100 tiles of equal area.

If one of these tiles is selected at random, what is the probability of selecting a red tile? What is the probability of selecting a blue tile?

Question 2

From a population of 500 people, 100 were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that 20% of people in the population support the legislation, with an associated margin of error of 1%. Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?

A. 20

B. 90

C. 98

D. 120

Question 3

What is the positive solution to the given equation?

Question 4

A rectangle has a length of x units and a width of (x – 15) units. If the rectangle has an area of 76 square units, what is the value of x?

A. 4

B. 19

C. 23

D. 76

Question 5

If the given function g is graphed in the xy-plane, where y=g(x), what is the y-intercept of the graph?

A. (0, 11)

B. (0, 132)

C. (0, 1)

D. (0, 12)

Question 6

Rosa opened a savings account at a bank. The table shows the exponential relationship between the time t, in years, since Rosa opened the account and the total amount n, in dollars, in the account. If Rosa made no additional deposits or withdrawals, which of the following equations best represents the relationship between t and n?

Question 7

A cylinder has a diameter of 4 inches and a height of 4 inches. What is the volume, in cubic inches, of the cylinder?

Question 8

The solution to the given system of equations is (x, y). What is the value of y?

A. -2

B. 7

C. 14

D. 18

Question 9

The given equation defines the function f. For what value of x does f(x) reach its minimum?

Question 10

In the xy-plane, line L passes through the point (0,0) and is parallel to the line represented by the equation  y = 8x + 2. If line L also passes through the point (3, d), what is the value of d?

Question 11

At how many points do the graphs of the equations y=x + 20 and y = 8x intersect in the xy-plane?

A. 0

B. 1

C. 2

D. Infinitely Many

Question 12

A. 4

B. 8

C. 16

D. 32

Question 13

When the quadratic function f is graphed in the xy-plane, where y=fx, its vertex is (-3, 6). One of the x-intercepts of this graph is (-7, 0). What is the other x-intercept of the graph?

A. (-1,0)

B. (1,0)

C. (5, 0)

D. (191, 0)

Question 14

A right triangle has side lengths that are 3 and 4. What is the length of the hypotenuse of the triangle?

Question 15

The circle shown has center O, circumference 144π, and diameters PR¯ and QS¯. The length of arc PS is twice the length of arc PQ. What is the length of arc QR?

A. 24π

B. 48π

C. 72π

D. 96π