FAST Grade 7 Math flashcards
FAST Grade 7 Math · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Integer addition rule
- Same signs: add absolute values and keep the sign. Different signs: subtract the smaller absolute value from the larger and use the sign of the number with the larger absolute value.
- Subtracting integers
- Rewrite a − b as a + (−b). Change the subtraction sign to addition and replace the second number with its opposite, then apply integer addition rules.
- Zero exponent
- For any nonzero base a, a^0 = 1. Any nonzero number raised to the power zero equals one, regardless of how large or small the base is.
- Negative exponent
- For a nonzero base a and positive integer n, a^(−n) = 1/a^n. A negative exponent indicates the reciprocal of the corresponding positive power.
- Rational number
- A number that can be written as a fraction p/q where p and q are integers and q is not zero. Terminating and repeating decimals are rational.
- Absolute value
- The distance from a number to zero on the number line. It is never negative, and opposites have equal absolute values: |−7| = |7| = 7.
- Unit rate
- A rate with a denominator of 1, found by dividing the first quantity by the second. For example, 150 miles in 3 hours is 50 miles per hour.
- Proportional relationship
- A relationship that can be written as y = kx with constant k not equal to zero. Its graph is a straight line passing through the origin.
- Constant of proportionality
- The value k in y = kx, equal to y divided by x for any corresponding pair. It equals the unit rate of the relationship.
- Cross multiplication
- A method for solving proportions: from a/b = c/d, multiply to get a·d = b·c. Then solve the resulting equation for the unknown value.
- Percent change
- The change divided by the original amount, multiplied by 100%. A positive result is an increase; a negative result is a decrease.
- Percent proportion
- part/whole = percent/100. Use it to find a missing part, a missing whole, or an unknown percent when the other two values are known.
- Like terms
- Terms with identical variable parts, including the same exponents. Only their coefficients are added: 3x + 5x = 8x, while 3x + 5x² cannot be combined.
- Distributive property
- a(b + c) = ab + ac. Multiply the factor outside the parentheses by each term inside, and track negative signs carefully.
- Two-step equation
- An equation needing two inverse operations to isolate the variable. Undo addition or subtraction first, then undo multiplication or division, keeping both sides balanced.
- Inequality reversal rule
- Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol. For example, −2x > 6 becomes x < −3.
- Inequality graph circles
- An open circle marks a strict inequality, less than or greater than, meaning the endpoint is excluded. A closed circle marks less than or equal to, or greater than or equal to.
- Circumference of a circle
- The distance around a circle, given by C = 2πr or C = πd. Radius and diameter relate by d = 2r, so either formula works.
- Area of a circle
- A = πr², where r is the radius. Square the radius first, then multiply by π, using about 3.14 unless told otherwise.
- Triangle area formula
- A = ½bh, where b is the base and h is the perpendicular height measured at a right angle to that base, not the slanted side length.
- Scale drawing
- A drawing in which every length is a fixed multiple of the actual length. The scale, such as 1 cm : 5 m, sets up a proportion to find unknown lengths.
- Surface area of a prism
- The total area of all faces. For a rectangular prism, SA = 2lw + 2lh + 2wh; for a cube with edge s, SA = 6s².
- Volume of a prism
- V = (area of the base) × height of the prism. For a rectangular prism this becomes V = lwh, where the base area is length times width.
- Vertical angles
- The two nonadjacent angles formed by intersecting lines. Vertical angles are congruent, meaning they have equal measures, and each pair shares a vertex.
- Transversal angle pairs
- When parallel lines are cut by a transversal, alternate interior angles and corresponding angles are congruent, while same-side interior angles are supplementary and sum to 180°.
- Random sample
- A sample in which every member of the population has an equal chance of being chosen, which supports valid inferences about the entire population.
- Mean absolute deviation
- The average distance of data values from the mean. Find each value's distance from the mean, add those distances, and divide by the number of values.
- Mean versus median
- The mean is the sum divided by the count and is pulled by outliers. The median is the middle ordered value and resists outliers.
- Theoretical probability
- The ratio of favorable outcomes to all equally likely outcomes, calculated from analysis rather than trials, and expressed as a number from 0 to 1.
- Complement rule
- P(not A) = 1 − P(A). The probability that an event does not occur equals one minus the probability that it does occur.
- Uniform probability model
- A model in which every outcome in the sample space has the same probability, such as 1/6 for each face of a fair number cube.
- Experimental probability
- The ratio of times an event occurs to the total number of trials performed. It can differ from theoretical probability, especially with few trials.