Worksheet: Writing and Evaluating Formulas

In this worksheet, we will practice distinguishing between formulas and expressions, writing a formula from a given description, and substituting numbers into a simple formula.

Q1:

Use the formula 𝐴=𝑏 to find the area of a parallelogram whose base, 𝑏, is 212 and height, , is 45.

  • A127
  • B123
  • C2
  • D318
  • E225

Q2:

One measure of distance is rate multiplied by time, 𝑑=𝑟𝑡. Find the distance Olivia travels if she is moving at a rate of 60 mph for 6.75 h.

Q3:

Given that the area of a trapezoid is 𝐴=12(𝑎+𝑏), find the value of 𝐴 when =4cm, 𝑎=32cm, and 𝑏=52cm.

Q4:

A company produces greetings cards with an initial cost of 2,000 LE and an extra cost of 12LE per card. The total cost is given by 𝐶=12𝑥+2,000, where 𝑥 is the number of produced cards. Find the total cost of producing 15,000 cards.

Q5:

The total surface area, 𝑇, of a rectangular prism is given by 𝑇=2(𝑥𝑦+𝑦𝑧+𝑧𝑥). Find the value of 𝑇 when 𝑥=5, 𝑦=1, and 𝑧=9.

Q6:

The speed 𝑣, in feet per second, of an ocean wave at depth 𝑑, in feet, is given by the formula 𝑣=32𝑑. Determine, to the nearest tenth, the speed of an ocean wave at a depth of 11 feet.

Q7:

A rectangle has width 𝑤 and length 𝑙. A new rectangle is formed which has the same length but double the width. Find the perimeter 𝑃 and area 𝐴 of this new rectangle.

  • A𝑃=2𝑙+𝑤, 𝐴=12𝑙𝑤
  • B𝑃=𝑙+𝑤, 𝐴=3𝑙𝑤
  • C𝑃=𝑙+2𝑤, 𝐴=4𝑙𝑤
  • D𝑃=2𝑙+2𝑤, 𝐴=𝑙𝑤
  • E𝑃=2𝑙+4𝑤, 𝐴=2𝑙𝑤

Q8:

The diameter 𝑑 of a circle with area 𝐴 is given by 𝑑=4𝐴𝜋. Determine, to the nearest tenth, the diameter of a circle with an area of 46 in2.

Q9:

Daniel drove his car for 7 hours at 50 miles per hour. Use the formula 𝑑=𝑟𝑡, where 𝑑=distance, 𝑟=rate, and 𝑡=time, to find the distance he drove.

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