Algebra MP1 Benchmark PDF

## Math Questions **Question 1.** What is the value of *x* in the equation -(1 - *x*) = -2(3*x* - 1)? * A. 1/7 * B. 1/5 * C. 3/5 * D. 3/7 **Question 2.** If -5*x* + 7 = 2*x* - 3, then what is *x*? * A. 4/3 * B. 4/7 * C. 10/7 * D. 10/3 **Question 3.** What is the so...

## Math Questions **Question 1.** What is the value of *x* in the equation -(1 - *x*) = -2(3*x* - 1)? * A. 1/7 * B. 1/5 * C. 3/5 * D. 3/7 **Question 2.** If -5*x* + 7 = 2*x* - 3, then what is *x*? * A. 4/3 * B. 4/7 * C. 10/7 * D. 10/3 **Question 3.** What is the solution for *n* in the inequality? -17 + 3*n* ≤ 7(*n* - 2) * A. *n* ≥ 15/4 * B. *n* ≤ 15/4 * C. *n* ≥ 3/4 * D. *n* ≤ -3/4 **Question 4.** Which point is on the graph of 2*x* -16*y* = 8? * A. (-4, 0) * B. (0, 2) * C. (0, 4) * D. (1/2, 0) **Question 5.** The formula A = 1/2 (b₁ + b₂)h can be used to determine the area of a trapezoid. Solving this equation for b₁ will result in which equation? * A. b₁ = 2A/h - b₂ * B. b₁ = 2Ah - b₂ * C. b₁ = 2h/A - b₂ * D. b₁ = A - b₂h **Question 6.** The profit (*P*) that a company earns selling T-shirts depends on the number (*n*) that they sell, according to the equation shown below: P = 2*n* - 800 The equation can be rearranged so that *n* is a function of *P*. Complete the equation with the correct terms. *n* = 1/2 ______ **Question 7.** Counting the number of cricket chirps can provide an estimate of the temperature. The formula gives the temperature in degrees Celsius based on the number of cricket chirps (*n*) in 15 seconds: C = (5*n* + 40)/9 This formula can be rearranged to solve for the number of chirps as a function of the temperature in degrees Celsius. Which formula has been rearranged correctly? * A. *n* = (C - 8) / 9 * 5 * B. *n* = 9/5 C - 40 * C. *n* = (C - 8) / 5 * 9 * D. *n* = 9/5 (C - 40) **Question 8.** Grace wants to buy some new clothes, but she cannot afford more than $75 before the sales tax is added. The blouses she wants are priced \$17 each and the pants she wants are priced \$25 each. Which inequality could be used to determine *b*, the number of blouses, and *p*, the number of pants Grace can afford? * A. 17*b* + 25*p* ≥ 75 * B. 17*b* + 25*p* ≤ 75 * C. 25*b* + 17*p* ≥ 75 * D. 25*b* + 17*p* ≤ 75 **Question 9.** The measures of the acute angles of the right triangle below are represented by *x* and *y*. In this triangle, *y* is 15 less than twice *x*. [Image: This is a right triangle with one acute angle labeled *x* and the other one *y*] Which system of equations could be used to solve for *x* and *y*? *NOTE: A right angle measures 90° and the angles in a triangle sum to 180°.* * A. *x* + *y* = 90 2*x* - *y* = 15 * B. *x* + *y* = 90 *x* - 2*y* = 15 * C. *x* + *y* = 180 2*x* - *y* = 15 * D. *x* + *y* = 180 *x* - 2*y* = 15 **Question 10.** Harry needs to buy hamburgers and hot dogs for a picnic. He has only $41.00 to spend and must buy at least 98 hamburgers or hot dogs. A store charges $0.50 per hamburger and $0.25 per hot dog. Which of the following is a possible way Harry might buy the hamburgers and hot dogs? * A. 78 hamburgers and 20 hot dogs * B. 69 hamburgers and 28 hot dogs * C. 66 hamburgers and 33 hot dogs * D. 64 hamburgers and 35 hot dogs **Question 11.** Which set of ordered pairs represents a function? * A. {(3, 2), (4, 4), (6, 3), (4, 5)} * B. {(4, -3), (4, 1), (4, 3), (4, 6)} * C. {(-4, 4), (-2, 4), (1, 4), (5, 4)} * D. {(-3, -3), (-2, -4), (-2, -1), (-1, -5)} **Question 12.** The graph shows the temperature of water as a function of time as it is heated to its boiling point (212°F). [Image: A graph of water heating, Y axis is Temperature(°F) and X is Time(Minutes)] What is the range of this function? * A. All real numbers less than or equal to 212. * B. All real numbers greater than or equal to 50. * C. All real numbers between and including 0 and 8. * D. All real numbers between and including 50 and 212. **Question 13.** The graph models the price of items after a 120% markup at a small shop. [Image: A graph of price markup, Y axis is Price After Markup and X is Cost(Dollars)] Based only on the given graph, what is the function's domain? * A. Numbers between and including 0 and 30. * B. Numbers between and including 0 and 36. * C. Numbers between and including 5 and 30. * D. Numbers between and including 6 and 36. **Question 14.** The functions below represent the cost some homeowners pay for water and sewer usage. This is based on the number of 100-gallon units of water used, defined by *x*. Water usage: *W(x) = 0.129x* Sewer usage: *S(x) = 0.158*x* + 16.22 Based on this information, what is the total amount a homeowner will pay if the water and sewer usage for one month is 3800 gallons? * A. \$10.91 * B. \$21.12 * C. \$27.13 * D. \$43.35 **Question 15.** The weight, in pounds, of a baby in the first six months of life can be modeled by the function *f(x) = 1.5x + 7*, where *x* is the age of the baby in months. According to this model, what is the weight, in pounds, of a baby at age 5 months? * A. 8.5 * B. 12.0 * C. 13.5 * D. 14.5 **Question 16.** The function *f(x) = 5(x + 1) + 2x*. What is *f(3)*? **Question 17.** Based on the graph below, which of the following describes the domain? [Image: A graph of a straight line starting at (0,0) and ending at (5,5)] * A. All real numbers. * B. All whole numbers. * C. All real numbers between 0 and 6. * D. All real numbers greater than or equal to 0. **Question 18.** Place the numbers to complete the inequality. The math club is selling T-shirts to raise money. Each T-shirt sold represents a profit of $2. The club has a total of 500 T-shirts. [Image: 0, 2, 250, 500, 1000] If *P(t)* is the profit that the math club makes for selling *t* T-shirts, a reasonable domain of this function is: ______ ≤ *t* ≤ ______ **Question 19.** Select the phrase from the menu that best completes the sentence. On a small volcanic island, lava is flowing at a rate of 800 meters per day and can be modeled by the function *f(d) = 800d*, where *f(d)* represents the distance from the source of the lava flow, and *d* represents the day of the flow. The domain of *f(d)* in this context is best described as ______ * A. All real numbers. * B. All positive real numbers. * C. All non-negative integers. * D. All integers between 0 and 800. **Question 20.** The table shows the distance in miles Victoria is away from her home at given times during one day. [Image: A table with time and distance from home: 9:00a.m. - 4 miles, 10:00a.m. - 7 miles, 11:00a.m. - 7 miles, 12:00p.m. - 4 miles and 1:00p.m. - 0 miles] Victoria’s average change in distance away from home between 10:00 a.m. and 11:00 a.m. is 0. Which statement is the best interpretation of her average change in distance during this time? * A. Victoria stayed home all day. * B. Victoria went home and stayed there from 10:00 a.m. to 11:00 a.m. * C. Victoria could have stayed at the same location from 10:00 a.m. to 11:00 a.m. * D. Victoria must have left her location shortly after 10:00 a.m. and returned to the same location before 11:00 a.m. **Question 21.** What is the average rate of change for the function *f(x)* over the interval [1, 8]? [Image: A table with *x* values: 1, 6, 8, 15 and *f(x)* values: 11, 31, 39, 67] **Question 22.** Paul recorded his car’s gas mileage in the following table. [Image: A table with gallons: 8, 16, 20, 180, 380, 480 and miles: 480] Complete the expression to show the average rate of change, in miles per gallon, from 180 miles to 480 miles. 480 - ______ / ______