Algebra STAAR Review

A 1953 convertible Hudson Hornet was sold at a car auction. The seller had bought the car in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. If the auction took place in 2004, what was the approximate value of the car at the time of the auction?

$41,778

4. What is the vertex of the graph of the quadratic function f(x) = x2 + 6x + 10?

(-3, 1)

Solve the following system of equations: y= 3x + 15 2x - 3y = -17

(-4, 3)

Which expression is equivalent to -12x2 + 13x + 4?

(4x + 1)(-3x + 4)

What is the range of the function y = 2x +3 for the domain 3 < x < 9?

9 ≤ y ≤ 21

Which statement about the quadratic equation -3.5x2 + 31.5 = 0 is false?

There is 1 real solution

Dejan was asked to solve the following system of linear equations on an algebra exam. 3x + 8y = 39 6x + 16y = 68 He had a difficult time finding a solution, so he incorrectly guessed (0, 0) before turning in his exam. What is the correct answer to the exam question?

There is no solution

Which of the following point is a solution to the inequality 2x - y > 6?

(2, -4)

A grocer purchased orange juice for 3 dollars a bottle and cranberry juice for 6 dollars a bottle. The inequality 3x + 6y < 24 can be used to determine the number of bottles of orange juice, x, and the number of bottles of cranberry juice, y, the grocer purchased for less than 24 dollars, not including tax. Which of the following represents a reasonable combination of bottles of orange juice and cranberry juice that the grocer could purchase?

(3, 2)

At which points does the graph of f(x) = 3x2 -11x - 4 intersect the x-axis?

(4, 0) and (-1/3, 0)

What is the value of x in the equation: 2(2x +3) - 2x +1 = -3(x +1)

-2

Look at the arithmetic sequence shown below. { 2, -1, -4, -7, ...} Which equation best describes the nth of the arithmetic sequence and the value of the 47th term?

-3n + 5 and 47th term equals-136

Examine the sequence 5, 2, -1, -4,... Which equation best describes the nth term of the sequence?

-3n + 8

What is the value of x in the equation: 0.4(2x + 8) - 0.4x = 0.2(4x -12) + 6x

.875

What is the value of the 5th term in the arithmetic sequence an = 3n + 4?

19

Solve for the value of x in : 4(2x +1) = 17 - 3(2x - 5)

2

You are looking for an apartment and you have two final choices. Apartment A has $1000 security deposit and costs $1200 each month. Apartment B has $1500 security deposit and costs $1175 each month. How many months, m, will it take for the costs to be the same?

20

Given h(x) = 3x^2 - 5x +7, find h(-8).

239

Which linear equation represents a line containing the point (7, -½) and has a

2y - x= -8

What is the slope of a line passing through the points (-3, -4) and (3, 4)?

4/3

Jamal was counting the coins in his bank. He found that he had 70 coins, which totaled $13.30. If he only had quarters and dimes, how many quarters did he have?

42

The Medina family bought trees and bushes for their backyard staying within their $700 budget. If trees are priced at $49 and bushes at $19, which inequality describes this situation if x represents the number of trees and y represents the number of bushes?

49x + 19y ≤ 700

Which expression is equivalent to (4x2 - 5x - 6) ÷ (x - 2)?

4x + 3

The distance traveled by a certain truck varies directly to the amount of fuel the truck consumes. The truck traveled 130 miles on 10 gallons of fuel. At the same rate, how far would the truck travel on 6 gallons of fuel?

78 miles

The approximate cost of a steel foundation for a skyscraper may be determined by the function C(n) = 4n + 0.75n2. In the function, C, represents the cost per square foot and n is the number of floors. If the approximate cost of a steel foundation is $5,371, how many floors are in the skyscraper?

82

The slope of the line that passes through the points (−6, w) and (−10, 4) is 1/8 . What is the value of w?

9/2

Look at the sequence below. -4, -8, -16, -32, ... Which expression represents the nth term of this sequence?

B. -4(2)^n-1

What is the solution set for the quadratic equation x2 - 64 = 0?

D. {-8, 8}

Stanley and Saul work at Ace Furniture Store where they receive a base salary per week plus a commission on their sales, s. If Stanley's salary is given by the equation r = 0.07s + 300 and Saul's salary is given by the equation r = 0.06s + 350 how does the graph of Stanley's salary differ from the graph of Saul's salary?

The graph of Stanley's salary starts lower on the y-axis and is steeper.

An electrician charges a flat fee of $900 to wire a barn and an additional $35 per outlet installed. If the flat fee would stay the same but the cost per outlet changes from $35 to $45, which characteristics of the graph of this relationship would change?

The line for the new function would be steeper than the original line.

A salesperson's weekly pay can be modeled with the function W = 400 + 0.10s where s represents the amount of sales. Which sentence describes this function's range?

The range values are all greater than or equal to 400

A cable company charges an installation fee of $40. They charge $32 a month for a package including most major cable channels. This month, the cable company is offering free installation for any new subscriber. Based on this information, which statement describes the change in this situation?

The total cost for a new subscriber will be $40 less.

A 1000-gram rock falls from the top of a cliff that is 500 meters high. Denote by h the height (in meters) of the rock above the ground when it attains a speed of v meters per second. The equation below relates h and v. h= 500 - 0.05v^2 What is the domain of this relationship?

[0, 100]

A car approaches a stoplight at a speed of 24 meters per second. When the light turns red, the car begins decelerating uniformly at 1.5 meters per second squared. Let v(t) denote the speed of the car (in meters per second) t seconds after it begins decelerating. The equation below relates v(t) and t. v(t) = 24 - 1.5t What is the domain of this relationship?

[0, ∞)

Solve the following equation for a: 7a + 4(5 - x) = 24a - 3(a-4)

a = 4/9

Solve the following equation for a: -0.3a - 0.5(a+16) = 0.8(a +15)

a= -100

What expression is equivalent to 5( 1/5 c - 5) - 6(c - 1) + 6(c + 3)?

c - 1

What is the solution to the inequality 23 - t ≤ 2(t -9) - 3(t + 2)

no solution

A club has 239 members. There are 114 more females than males. Let x represent the number of females and let y represent the number of males. Which system of equations represents this situation?

x + y = 239 x = y + 114

What is the equation in standard form of the line that passes through the point (4, −8) and has a slope of 1/4 ?

x - 4y = 36

Which of the following describes all the solutions to the inequality 7y - 5x ≥ 22 when y = −4?

x ≤ -10

17. The cheerleaders made spirit buttons and sold them for homecoming. The table shows the amount of profit they made for different numbers of buttons sold. # Sold (x): 50, 100, 150, 200 Profit (y): $0, $45, $90, $135 Which equation represents this relationship?

y = 0.9x - 45

What is the equation of the line parallel to y = 5x + 3 that passes through the point (-1, 2)?

y = 5x + 7

11. The set of ordered pairs below represents some points on the graph of function f. {(-2,11), (-1,5), (0,3), (2,11)} What is the parent function?

y = x^2

Which inequality is equivalent to -6x + 3y < 6y + 24?

y > -2x - 8

Solve: - 4(2y + 3) < 20 - 4y

y ≤ -8

What is the equation of the line that is perpendicular to 2x - y = 3 and passes through the point (2, 5)?

y= -.5x+6

A line is parallel to the x-axis and passes through (2, 3). Which answer choice shows the line's equation and correct slope?

y=3; m=0

What is the solution set of the equation below? x(2x + 5) = 3

{-3, 1/2}

In the Mojave Desert in California, temperatures can drop quickly from day to night. Suppose the temperature drops from 100°F at 2 PM to 70°F at 5 AM. What is the approximate rate of change between the hours of 2 PM and 5 AM?

-2°F per hour

A college professor purchased 20 fancy pens for $70. He purchased blue fancy pens for $2 each and red fancy pens for $5 each. Which system of equations can be used to determine b, the number of blue fancy pens, and r, the number of red fancy pens, that the college professor purchased?

2b + 5r = 70 b + r = 20

10. What are the solutions to the equation 3x^2 - 11x + 6 = 0?

3, 2/3

A candy store sells 8-pound bags of mixed hazelnuts and cashews. If c pounds of cashews are in a bag, the price, p, of the bag can be found using the formula: p= 2.59c + 1.72(8-c). If one bag is priced at $18.11, how man pounds of cashews does it contain?

5

What is the value of x in the solution to the system of equations below? 6x + 3y = 13 3x - y = 4

5/3

The table below shows pairs of values that satisfy a linear function: x: -3, -2, -1, 0, 1, 2 y: 18, 16, 14, 12, 10, 8 What is the x-intercept of the graph of this function?

6

11. The intensity of light near a certain bulb is given by the equation 3(15 - d)^2 = 192, where d is the distance from the bulb in meter. How far away is the light bulb for this intensity?

7 meters

If f(x)= 2/3x^2+ 8x what is the value of f(6)?

72

Which equation below is perpendicular to the line 2x - y = -2 and passes thru the point (2, -8)?

B. y = -1/2x - 7

A train travels at a constant speed of 30 miles per hour for 6 hours from Houston to Dallas. What are the domain and range of this situation if h is the time in hours and d is the distance in miles?

Domain: 0 ≤ h ≤ 6 Range: 0 ≤ d ≤ 180

A system of equations is shown below. 4x - 5y = -10 2x - 7y = 4 Which operations on the system of equations will isolate the y quantity?

Multiply the second equation by -2 and add the result to the first equation.

The first six numbers in a pattern are shown below. 1/3, 4/3, 3, 16/3 , 25/3 , 12,... If the pattern continues, which expression can be used to find the nth number in the pattern?

n^2/3