JLAB/A ACT Math-Focused Quiz 1

If 15bx - 20 > 35, where b is a positive constant, which of the following best describes all possible values of 4 - 3bx?

• Any value less than -7

• Any value greater than -7

• Any value less than -11/3b

• Any value greater than 11/3b

T = 0.25q + 87

Manon’s statistics professor puts a bonus question on every test, which adds 0.25 points to a student’s overall grade at the end of the term. The above equation gives Manon’s overall grade, T, after taking into account q extra credit questions answered correctly. What does the 87 mean in this equation?

• Manon must get an 87 or above to pass.

• Manon's average is an 87 before adding extra credit.

• AFter adding in her extra credit, Manon's average is an 87.

• Manon's professor gave 87 opportunities for extra credit this term.

The property taxes in a town decrease as the distance from the local elementary school increases. The greatest property taxes are 4.5% and for every 10 miles from the school, property taxes decrease by 0.5 percentage points. If a house’s property taxes are 3%, what is the distance of that house from the school?

• 10 miles

• 20 miles

• 30 miles

• 40 miles

A barber charges $12 for a haircut. His operating expenses are, on average, $37 per day. He calculates his profit by subtracting his operating costs from the money he earns from the haircuts he gives. In a given day, the barber expects to make a profit of at least $86. If the barber gives h haircuts in a day, which inequality best models the situation?

• 12h - 37 ≥ 86

• 12(h - 37) ≥ 86

• 12h + 37 ≥ 86

• 12(h + 37) ≥ 86

The equation y = 3/2(x - 8) is graphed in the xy-plane. Which of the following equations will have a graph that is parallel to the graph of the above equation and have an x-intercept on the negative x-axis?

• 7 = 3/2x - 8

• y = 3/2(x + 8)

• y = -2/3(x + 8)

• y = -2/3x - 8

A 300-room hotel collects $75 per occupied room and does not collect any money for vacant rooms. Which of the following functions best represents how many dollars, d, the hotel generates if there are v vacant rooms in the hotel?

• d = 300(75 + v)

• d = 300(75 - v)

• d = 75(300 + v)

• d = 75(300 - v)

Anouk is an engineer planning sound and lighting for a free concert in the park. The concert was advertised with a promise to use no more than 108 kilowatts (kW) of power. It was determined that the main contributors to power usage, speakers and floodlights, use 1.8 kW and 2.2 kW, respectively. Anouk also must keep within her budget of $3,300. The rental company is charging $75 for each speaker and $42 for each floodlight. Which of the following combinations meets Anouk’s requirements?

• 40 speakers and 30 floodlights

• 12 speakers and 54 floodlights

• 26 speakers and 13 floodlights

• 38 speakers and 22 floodlights

z + w - 3 = k

6z - 10w = 8

Consider the system of equations above, where k is a constant. For which value of k are there infinitely many (w, z) solutions?

• -19/5

• 5

• 8

• None of the above.

The owner of a landscaping company is developing a proposal to maintain the grounds of a building. It is estimated that 75 gardening hours and 25 foreman horus will be required. The total budget for these hours is $1,600. The hourly wage for a foreman is 30% more than a gardener plus an additional $1.65 per hour. Which of the following systems of equations can be used to determine the hourly wages of a gardener, g, and a foreman, f, so the total wages are $1,600?

• 25g + 75f = 1,600

  f = 1.3g + 1.65

• 25f + 75g = 1,600

  f = 1.3g + 1.65

• 25g + 75f = 1,600

  g = 1.3f + 1.65

• 25f + 75g = 1,600

  1.3f + 1.65