Algebra: Formulas, Slope and Unit Analysis

Rearranging and applying trade formulas, slope as a rate of change on ramps, roofs and roads, and converting rates by unit analysis.

16 questions, free, marked as you go with a worked explanation on every one.

What this covers

The questions

  1. The formula for simple interest is I = Prt. A loan of $4 000 over 2 years produced $360 in interest. What was the annual interest rate, as a percent?
  2. A roof rises 4 ft for every 12 ft of horizontal run. Expressed as a percent grade, what is the slope of this roof?
  3. A highway sign warns of a 6% grade. Over a horizontal distance of 2 500 m, how many metres does the road drop?
  4. A pump moves 90 L of water every 4 minutes at a steady rate. How many litres does it move in one hour?
  5. A vehicle travels at 90 km/h. Using unit analysis, what is that speed in metres per second, rounded to one decimal place?
  6. A motor turns at 1 500 revolutions per minute. How many seconds does one full revolution take, rounded to three decimal places?
  7. The volume of a cylinder is V = πr²h. A cylindrical tank has a volume of 2.4 m³ and a height of 3 m. What is its radius, in metres, rounded to two decimal places?
  8. A wheelchair ramp must not be steeper than a 1 : 12 slope. A doorway is 0.75 m above the ground. What is the shortest horizontal run the ramp may have, in metres?
  9. A tool rental costs $6 to start plus $3 for each hour. Let x be the hours and y the cost in dollars. Graph the relation.
  10. A rectangular fish tank is 60 cm long, 30 cm wide and 40 cm tall. What is its volume, in litres? (1000 cubic centimetres equals 1 litre.)
  11. A box of cereal is shaped like a rectangular prism, 20 cm by 7 cm by 30 cm. What is its volume, in cubic centimetres?
  12. A swimming pool holds 54000 L of water. A hose fills it at 300 L per minute. About how many hours will it take to fill?
  13. A storage container is a cube with edges of 1.5 m. What is its volume, in cubic metres, rounded to two decimal places?
  14. Find the slope of the line through (3, 2) and (9, 5).
  15. A staircase rises 18 cm for every 25 cm of horizontal run. Express this as a percent grade.
  16. A road has a 6% grade. Over a horizontal distance of 500 m, how much does the road rise?

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