NB Grade 7 Math cheat sheet

Integers include positive numbers, negative numbers, and zero; opposites are the same distance from zero on opposite sides.

Absolute value is the distance of a number from zero on a number line, so it is always zero or positive.

To add integers with the same sign, add their absolute values and keep the sign; with different signs, subtract the smaller absolute value from the larger and use the sign of the larger absolute value.

Subtracting an integer is the same as adding its opposite: a - b = a + (-b).

For multiplication and division of two integers, the result is positive when the signs are the same and negative when the signs are different.

Order of operations: evaluate brackets first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

On a horizontal number line, values increase to the right, so any negative number is less than zero and less than every positive number.

Divisibility tests: by 2 when the last digit is even, by 3 when the digit sum is divisible by 3, by 5 when the last digit is 0 or 5.

Equivalent fractions are formed by multiplying or dividing both numerator and denominator by the same nonzero number.

To add or subtract fractions, rewrite them with a common denominator, combine the numerators, and keep the denominator.

To multiply fractions, multiply numerators and multiply denominators; to divide fractions, multiply by the reciprocal of the divisor.

To convert a decimal to a percent, multiply by 100; to convert a percent to a decimal, divide by 100.

Percent of a number: part = (percent ÷ 100) × whole; percent = (part ÷ whole) × 100.

A ratio compares two quantities with the same units; a rate compares quantities with different units; a unit rate has denominator 1.

A proportion states that two ratios are equal; if a/b = c/d and b and d are nonzero, then ad = bc.

A fraction in lowest terms produces a terminating decimal only when its denominator has no prime factors other than 2 and 5.

To compare fractions, rewrite them with a common denominator or cross-multiply: a/b > c/d when ad > bc for positive denominators.

A pattern rule describes how each term is generated; in an arithmetic sequence, consecutive terms differ by a constant common difference.

A linear relation has a constant rate of change, and its graph is a straight line.

The equation y = mx + b represents a linear relation, where m is the rate of change or slope and b is the y-intercept.

The y-intercept is the output when x = 0, so it is the point where the graph crosses the y-axis.

To solve an equation, apply the same inverse operation to both sides until the variable is isolated.

Substitute a proposed value into the original equation to check whether it makes the two sides equal.

An expression contains numbers, variables, and operations but no equals sign; an equation states that two expressions are equal.

Like terms have exactly the same variable part and can be combined by adding or subtracting their coefficients.

The distributive property states that a(b + c) = ab + ac, and it can be used to expand or factor expressions.

Circumference of a circle: C = πd or C = 2πr, using π approximately equal to 3.14 unless another value is given.

Area of a circle: A = πr², where r is the radius and the result is in square units.

Area formulas: rectangle A = lw, triangle A = ½bh, parallelogram A = bh.

Volume of a rectangular prism: V = lwh; volume of a cube: V = s³.

Volume of a cylinder: V = πr²h, where r is the base radius and h is the height.

Surface area is the sum of the areas of all faces or surfaces of a 3-D object and is measured in square units.

The diameter of a circle passes through the center and is twice the radius; the radius is half the diameter.

Volume is measured in cubic units, and 1 cm³ = 1 mL, 1000 cm³ = 1 L, and 1 m³ = 1 000 000 cm³.

A net shows all faces of a 3-D object laid out flat, so its total area equals the surface area of the object.

A translation slides every point of a figure the same distance and direction, leaving shape, size, and orientation unchanged.

A reflection flips a figure over a line, producing a mirror image; corresponding points are the same distance from the line.

A rotation turns a figure around a fixed center by a given angle, leaving shape and size unchanged.

On a coordinate plane, the x-axis is horizontal and the y-axis is vertical; a point is named by the ordered pair (x, y).

Quadrant signs: I (+, +), II (-, +), III (-, -), IV (+, -), with the origin at (0, 0).

Reflection over the x-axis changes (x, y) to (x, -y); reflection over the y-axis changes (x, y) to (-x, y).

A 90° clockwise rotation about the origin maps (x, y) to (y, -x); a 180° rotation maps (x, y) to (-x, -y).

A 90° counterclockwise rotation about the origin maps (x, y) to (-y, x).

Congruent figures have exactly the same shape and size; translations, reflections, and rotations preserve congruence.

Mean = sum of all data values ÷ number of data values.

Median = middle value when data are ordered; with an even number of values, it is the mean of the two middle values.

Mode = value that occurs most often; a data set may have no mode or more than one mode.

Range = maximum value - minimum value, a measure of how spread out the data are.

Probability of an event = number of favorable outcomes ÷ total number of equally likely outcomes.

Probability values range from 0 to 1; 0 means impossible, 1 means certain, and P(not A) = 1 - P(A).

A bar graph compares categories, a line graph shows change over time, and a circle graph shows parts of a whole.

A random sample is more likely to represent the population than a sample chosen because it is easy to reach.

An outlier is a value far from the rest of the data; it can strongly affect the mean but usually affects the median less.