More Formulas Flashcards
Keywords: “increase,” “decrease,” “gain,” “loss,” “percent change,” “percent increase,” “percent decrease.” Scenario: Comparing an original value to a new value.
Formula: Percent Change = [(New Value - Original Value) / Original Value] * 100. Example: A price went from $10 to $12. What’s the percent increase?
Keywords: “interest,” “principal,” “rate,” “time,” “investment,” “loan.” Scenario: Calculating interest earned or paid on a sum of money.
Formula: I = PRT (Interest = Principal * Rate * Time). Example: $500 is invested at 4% interest for 3 years. How much interest is earned?
Keywords: “speed,” “rate,” “distance,” “time,” “travel,” “miles per hour,” “kilometers per hour.” Scenario: Problems involving motion or travel.
Formulas: Distance = Rate * Time; Rate = Distance / Time; Time = Distance / Rate. Example: A car travels 100 miles at 50 mph. How long did it take?
Front: Keywords: “directly proportional,” “varies directly,” “constant of variation,” “constant of proportionality.” Scenario: When one quantity increases or decreases at a constant rate with another.
Back: Formula: y = kx. Example: The cost of apples is directly proportional to the number of apples. If 3 apples cost $6, how much do 5 apples cost?
Flashcard 8: Pythagorean Theorem
Front: Keywords: “right triangle,” “legs,” “hypotenuse,” “sides.” Scenario: Finding the length of a side of a right triangle.
Formula: a² + b² = c² (where a and b are legs, c is the hypotenuse). Example: A right triangle has legs of 5 and 12. Find the hypotenuse.
Flashcard 7: Slope (Rise over Run)
Front: Keywords: “slope,” “line,” “rise,” “run,” “steepness,” “gradient,” “points on a line.” Scenario: Describing the steepness of a line on a graph.
Formula: Slope = (Change in y) / (Change in x) = (y₂ - y₁) / (x₂ - x₁).
Example: A line goes through (2, 3) and (6, 9). What’s the slope?
Flashcard 5: Circumference of a Circle
Front: Keywords: “circle,” “circumference,” “diameter,” “radius,” “around.” Scenario: Finding the distance around a circle.
Back: Formula: Circumference = π * Diameter or 2 * π * Radius. Example: A circle has a radius of 5 inches. What’s its circumference?
Word Problem: It’s 10 degrees Celsius outside. How many degrees Fahrenheit is that?
Formula: F = (9/5)C + 32
F = (9/5) * 10 + 32 = 18 + 32 = 50
Answer: 50 degrees Fahrenheit
Word Problem: It’s 68 degrees Fahrenheit outside. How many degrees Celsius is that?
Formula: C = (5/9)(F - 32)
C = (5/9)(68 - 32) = (5/9) * 36 = 20
Answer: 20 degrees Celsius
Word Problem: It’s 27 degrees Celsius. What is that in Kelvin?
Formula: K = C + 273
K = 27 + 273 = 300
Answer: 300 Kelvin
Word Problem: A triangle has a base of 4 inches and a height of 6 inches. What’s its area?
Formula: Area = (1/2) * Base * Height
Area = (1/2) * 4 * 6 = 12
Answer: 12 square inches
Word Problem: A circle has a diameter of 10 cm. What’s its circumference?
Formula: Circumference = π * Diameter Circumference = 3 * 10 = 30
Answer: 30 cm
Word Problem: A box is 5 inches long, 3 inches wide, and 2 inches tall. What’s its volume?
Formula: Volume = Length * Width * Height
Volume = 5 * 3 * 2 = 30
Answer: 30 cubic inches
Flashcard 7: Simplified “ax + by = c” (Focus on finding missing values)
Front:
Simplified Form: If 2 apples + 3 bananas = 11 dollars, and apples are $2 each, how much is one banana?
Equation: 2 * 2 + 3 * bananas = 11
4 + 3 * bananas = 11
3 * bananas = 7
bananas = 7/3 or $2.33 each approximately
Flashcard 8: Meeting Trains (Simplified)
Front:
Word Problem: Train A leaves town at 1:00 pm traveling 40 miles per hour. Train B leaves the same town at 2:00 pm traveling 60 miles per hour in the same direction. When will train B catch up to train A?
Train A has a one-hour head start, traveling 40 miles.
Train B is going 20 mph faster (60-40=20), so it closes the distance at 20 miles every hour.
It will take 40 miles / 20 mph = 2 hours to catch up.
So, Train B will catch up at 4:00 pm.
Pythagorean Theorem
Front: a² + b² = c² (for right triangles, where c is the hypotenuse); Word Problem: A right triangle has legs of 3 and 4. What’s the hypotenuse?
3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5
Distance Formula (Coordinate Plane) Two towns are marked on a map. Town A is located at coordinates (1, 2), and Town B is located at coordinates (4, 6). If each unit on the map represents one mile, what is the straight-line distance between the two towns?
Front: Distance = √((x₂ - x₁)² + (y₂ - y₁)²) ;
Distance = √((4 - 1)² + (6 - 2)²)
Distance = √(3² + 4²)
Distance = √(9 + 16)
Distance = √25
Distance = 5 miles
Slope-Intercept Form of a Line
Front: y = mx + b (m = slope, b = y-intercept); Word Problem: What’s the slope and y-intercept of y = 3x - 2?
Slope (m) = 3; y-intercept (b) = -2
slope (Rise over Run)
Front: Slope = Rise / Run = (Change in y) / (Change in x) = (y₂ - y₁) / (x₂ - x₁); Word Problem: A line goes through points (1, 2) and (4, 8). What’s the slope?
Slope = (8 - 2) / (4 - 1) = 6/3 = 2
Volume of a Sphere
Formula: V = (4/3) * π * r³
V = Volume
π (pi) ≈ 3.14 (or 22/7)
r = radius (the distance from the center of the sphere to its surface)
Word Problem: A basketball has a radius of 5 inches. What is its volume?
Solution: V = (4/3) * 3.14 * 5³ = (4/3) * 3.14 * 125 ≈ 523.33 cubic inches
Volume of a Rectangular Prism
Formula: V = Length * Width * Height
V = Volume
Length = the longest side of the rectangular base
Width = the shortest side of the rectangular base
Height = the vertical distance from the base to the top
Word Problem: A rectangular box is 8 cm long, 5 cm wide, and 3 cm high. What is its volume?
Solution: V = 8 cm * 5 cm * 3 cm = 120 cubic cm
