Cale Algebra Proficiency

The table shows the total cost of purchasing x same-priced items and a catalog. What is the initial value and what does it represent?

$6 the cost of the catalog

The simple interest formula is I= Prt where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal. What is the amount of money, P, that will generate $40 in interest at 10% interest rate over 5 years?

$80

Using only the values given in the table for the function, f(x)= x3 -3x -2, , what is the interval of x-values over which the function is decreasing?

(-1, 1)

A rectangle with an area of x2-4x-12 square units is represented by the model. What side lengths should be used to model the rectangle?

(x+2) and (x-6)

What is the factored form of x2-6x-16?

(x-8)(x+2)

Which equation is equivalent to -k + 0.03 + 1.01k = -2.45 - 1.81k?

-100k + 3 + 101k = -245 - 181k

Simplify the expression -3(x + 3)2 - 3 + 3x. What is the simplified expression in standard form?

-3x2 - 15x - 30

Ren recorded an outside temperature of -2 at 8 am. When she checked the temperature again it was 4 at 12:00 pm. If x represents the time and y represents the temperature in degrees F, what is the slop of the line through these two data points?

1.5

Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each. Dance World: y = 15xToe Tappers: y = 25 + 12.5x How many classes would Gina need to take for the total cost to be the same at both dance studios? 10 15 100 150

10

What is the missing coefficient of the x-term of the product (-x-5)2 after it has been simplified?

10

What is the product? 3a(8a-6b)

24a2-18ab

Which statement is true about the end behavior of the graphed function?

As the x- values go to the negative infinity, the functions values go to the positive infinity.

Which statement is true about the graphed function f(x)?

F(x)>0 over the intervals (-∞, -2.5) and -0.75, 0.75)

Formula for circumference of a circle is C=πd, where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference?

It is an irrational number.

Which is the graph of y-3 = -2/3 (x+6)?

It's choice A

Becky created a graph to represent her distance away from home one afternoon. She left home and ran to the park, met some friends and stayed in the park, and then walked back home using the same route. Which graph could Becky have created?

See graph.

Which is the graph of linear inequality 6x + 2y > -10?

See pic.

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. The area of the enlarged photo is 256 square inches. In the equation (x + 10)2= 256, x represents the side measure of the original square photo.

What were the dimensions of the original photo? 6 inches by 6 inches

Which expression is equivalent to 7a2b + 10a2b2 + 14a2b3?

a2b (7 + 10b + 14b2)

What is the domain of the function on the graph

all real numbers

What is the solution to the linear equation? -12 + 3b - 1 = -5 - b

b=2

This table represents a function. What is the value of f(-1)?

f(-1)=0

Which linear function represents the line given by the point-slope equation y-2 = 4(x-3)?

f(x)= 4x-10

Which function has real zeros at x= -8 and x = 5?

g(x)=x2+3x-40 (see pic)

The table shows how an elevator 500 feet above the ground is descending at a steady rate. Which equation represents the height h(t) of the elevator in feet? The number of seconds during which it has been descending?

h(t) = -5t + 500

The potential energy, P, in a spring is represented using the formula P= 1/2 kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework.

see pic

Which graph shows the solution to the system of linear equalities?

see pic

Which system of linear inequalities has the point (2, 1) in its solution set?

see pic

which graph represents the function y = 2x - 4?

see pic

Which is the graph of linear inequality x - 2y > -12?

see pic. two graphs look the same but one has dotted line and one has solid line. It is the solid line one.

Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

(-12, 2)

Which ordered pair needs to be removed in order for the mapping to represent a function?

(-2,-1)

Shannon graphed the system of equations. 7x - 4y= -8 y = x - 3 What is the closest approximate solution to the system of equations?

(-5, -6.8)

What is the solution (a , c) to this system of linear equations? 2a- 3c = -6 a + 2c = 11

(3, 4)

The diagram represents the polynomial 4x2 + 23x - 72 What is the factored form of 4x2 + 23x - 72?

(4x - 9) (x + 8)

The weight of Jacob's backpack is made up of the weight of the contents of the backpack as well as the weight of the backpack itself. Seventy percent of the total weight is textbooks. His notebooks weigh a total of 4 pounds, and the backpack itself weighs 2 pounds. If the backpack contains only textbooks and notebooks, which equation can be used to determine t, the weight of the textbooks?

0.7 (t + 4 + 2) = t

Which equation has an a-value of 1, b-value of -3, and c-value of -5?

0= -3x - 5 + x2

The equation x2-1x-90=0 has solutions {a, b}. What is a + b?

1

A recipe calls for 1/4 cup of broth. The largest volume-measuring tool that Tabitha has is a teaspoon. She knows that there are 16 teaspoons in 1 cup and 3 teaspoons in 1 tablespoon. How many teaspoons of broth should she use?

12 teaspoons

The soccer team is conducting a fundraiser selling long-sleeved T-shirts for $14 and short-sleeved T-shirts for $10. So far the team has sold less than $200 worth of the two types of T-shirts. Which inequality BEST represents x, the number of long-sleeved T-shirts they have sold and y, the number of short-sleeved T-shirts they have sold?

14x + 10y < 200

This map shows a functional relationship. When f(x)=4, what is the value of x?

2

Which expression is a difference of squares with a factor of 5x-8?

25x2-64

At a carnival, food tickets cost $2 each and ride tickets cost $3 each. A total of $1,240 was collected at the carnival. The number of food tickets sold was 10 less than twice the number of ride tickets sold. The system of equations represents x, the number of food tickets sold, and y, the number of ride tickets sold. 2x + 3y = 1240 x = 2y - 10 How many of each type of ticket were sold? 180 food tickets and 293 ride tickets 180 food tickets and 350 ride tickets 293 food tickets and 180 ride tickets 350 food tickets and 180 ride tickets

350 food tickets and 180 ride tickets

Using a stopwatch, Tyrone determines it takes him 58.2 minutes to travel 30 miles to work. The stopwatch measures to hundredths of a minute. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of feet per second Tyrone traveled on his way to work?

45.3 feet per second

Which term can be added to the list so that the greatest common factor of the three terms is 12h3? 36h3, 12h6, ________________

48h5

Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation 0.10d+0.05n=5.25, where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have?

63

The monomial 36x4 is a perfect square. What is the square root of 36x4?

6x2

The formula for density is given by p= M/V, where p is density, M is mass and V is volume. If a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density of the substance in g/ml?

7.7

Line JK passes through points J(-3, 11) and K(1, -3). What is the equation of line JK in standard form?

7x + 2y = 1

Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 21 + 2w = 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?

9 feet

Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below. 3x + 2y = 36.502x + 5y = 50.00 At which job does Percy earn the greater hourly wage? How much does Percy earn each hour at this job?

Percy earns a greater hourly wage of 7.50 at the library.

What are the factors of 2x2 + 3x - 54?

Select the two options. 2x - 9 x + 6

Marlena created a table of values representing the height in feet, h(t), of a coconut falling to the hard ground with a height of 0 feet, collected over t seconds. Assume the coconut does not bounce. Which statement is true?

The values of h(t) when t=4 and 5 should be 0.

How many intersections are there of the graphs of the equations below? 1/2x + 5y = 6 3x + 30 y = 36

infinitely many

When a number is added to 1/5 of itself, the result is 24. The equation that models this problem is n + 1/5n = 24. What is the value n?

n = 20

Half of the product of two consecutive numbers is 105. Which equation can be used to solve for n, the smaller of the two numbers?

n2 + n -210 = 0

A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed. Which word describes the slope of the line representing the data in the table?

negative

Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book. What are the slope and y-intercept of the line represented by the points shown in the table? slope: 2, y-intercept: -20 slope: 2, y-intercept: 10 slope: 5, y-intercept: -20 slope: 5, y-intercept: 10

see chart

Ray was in charge of filling the soccer team's water jug for practice. At the beginning of practice he filled the jug. Halfway through practice the team took a water break. After the break Ray refilled the jug so the players could have water after practice. At the end of practice Ray drained the jug. Which graph could represent the level of the water in the jug during and after practice?

see graph.

A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units. Which equation can be used to solve for x, the side length of the original square?

x2-2x-120 = 0

The variables A, B, and C represent polynomials where A = x +1 , B = x2 + 2x -1, and C = 2x. What is AB + C in simplest form?

x3 + 3x2 + 3x - 1

Which is a zero of the quadratic function f(x)= 4x2 + 24x +11 =

x= -5,5

Solve x2 + 12x = -11 by completing the square. Which is the solution set of the equation?

{ -11, -1 }