ACT Math Practice Flashcards

Gas Cost Calculation

• To determine gas costs, divide total miles by miles per gallon: 2,727 miles ÷ 27 mpg = 101 gallons.
• Multiply gallons by gas price: 101 × $4.04 = $408.04, indicating total gas cost for travel.

Expression Evaluation

• Given values x = 3 and y = 5, calculate expressions:
  • 3x² - 2y → 3(3)² - 2(5) = 27 - 10 = 17
  • 2x² - 3y → 2(3)² - 3(5) = 18 - 15 = 3
• The difference: 17 - 3 = 14 indicates how much one expression exceeds the other.

Simple Equation Solving

• Solve for x in the equation:
  • Start with 2x + 3 = 3x - 4
  • Rearrange to x - 4 = 3, leading to x = 7.

Greatest Common Factor

• Factor 42, 126, and 210:
  • 42 = 2 × 3 × 7
  • 126 = 2 × 3² × 7
  • 210 = 2 × 3 × 5 × 7
• The greatest common factor is 2 × 3 × 7 = 42.

Sales Growth Calculation

• Define sales: first year = x, second year = x + 3, third year = 2(x + 3).
• Given the third-year sales as 38 million: 2(x + 3) = 38 leads to first-year sales of x = 16 million after solving.

Pump Capacity for Mines

• Pumping requirement based on mine depth (D feet):
  • Given D = 150: the pump must pump (+ 4D - 250) gallons per minute.
  • Substituting gives: + 4(150) - 250 = 350 gallons per minute.

Irrational Numbers

• Between any two real numbers, such as 1 and 6, there are infinitely many irrational numbers.

Sugar Consumption Reduction

• A typical high school student consumes 67.5 pounds of sugar yearly.
• Track team members aim to reduce consumption by 20%, i.e., they will consume 80% of 67.5, yielding 54 pounds as a maximum for each member.

Screw Turns Calculation

• Each turn of the screw advances 1/8 inch; the screw is 2 ½ inches long.
• To find turns to embed the screw, use: (Total length of screw ÷ Lead per turn), resulting in 20 complete turns.

Problem Solving with Quadratic Equations

• Given xy = 144 and x + y = 30 with the condition x > y.
• Substitute to convert into a quadratic equation: (x² - 30x + 144 = 0).
• Solutions yield x = 24 and y = 6 leading to x - y = 18.