ISEE Math Achievement flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of Operations

Evaluate grouping symbols first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. So 3 + 4 × 2 equals 11, not 14.

Absolute Value

The distance of a number from zero on the number line, always nonnegative. Both 7 and −7 have absolute value 7, and |x| = 5 gives x = 5 or x = −5.

Prime Number

A whole number greater than 1 whose only positive factors are 1 and itself. Examples include 2, 3, 5, 7, 11, and 13; 1 is not prime and 9 is composite.

Greatest Common Factor

The largest number dividing two or more given numbers evenly. For 36 and 48, factor to 2²·3² and 2⁴·3, so the GCF is 2²·3 = 12.

Least Common Multiple

The smallest positive number divisible by each of two or more numbers. For 6 and 8, multiples are 6, 12, 18, 24 and 8, 16, 24, so the LCM is 24.

Equivalent Fractions

Fractions naming the same value, made by multiplying or dividing numerator and denominator by the same nonzero number. Since 3/4 = 9/12, cross-multiplication gives 36 = 36.

Dividing by a Fraction

Multiply by the reciprocal of the divisor. To compute 3/5 ÷ 2/7, rewrite as 3/5 × 7/2 = 21/10, which equals 2.1 as a decimal.

Decimal to Fraction

Write the decimal over its place value and reduce. The decimal 0.375 becomes 375/1000, which reduces to 3/8 after dividing both parts by 125.

Repeating Decimal to Fraction

For a repeating decimal, set it equal to x, multiply by a power of ten to shift the repeat, and subtract. If x = 0.333…, then 10x − x = 3, so x = 1/3.

Percent Change Formula

Percent change equals (new value − original value) divided by original value, times 100. Going from 80 to 100 is a 25% increase, but 100 to 80 is a 20% decrease.

Percent Increase Multiplier

A p percent increase multiplies by (1 + p/100). A 30% markup on $60 gives 60 × 1.30 = $78; a 30% discount gives 60 × 0.70 = $42.

Simple Interest Formula

Interest I = P × r × t, where P is principal, r is the annual rate as a decimal, and t is time in years. $500 at 4% for 3 years earns $60.

Ratio and Proportion

A ratio compares quantities; a proportion sets two ratios equal. If 3 pencils cost $1.50, then 7 pencils cost x, and 3x = 10.50 gives x = $3.50.

Unit Rate

A rate expressed per one unit of the second quantity. If 5 pounds cost $12.50, dividing gives $2.50 per pound, which allows direct comparison with other prices.

Mean, Median, Mode

Mean is sum divided by count; median is the middle value of ordered data; mode is the most frequent value. For 2, 3, 3, 8 the mean is 4, median 3, mode 3.

Range of a Data Set

The difference between the largest and smallest values. For the set 4, 9, 12, 15, 20, the range is 20 − 4 = 16, a measure of spread, not center.

Probability of an Event

Favorable outcomes divided by total equally likely outcomes. Drawing a red marble from a bag with 3 red and 5 blue marbles gives probability 3/8.

Counting Principle

If one choice can be made in m ways and another in n ways, together they can be made in m × n ways. Three shirts and four pants give 12 outfits.

Rectangle Area and Perimeter

Area equals length times width; perimeter equals 2(l + w). A 7 by 4 rectangle has area 28 square units and perimeter 22 units, so the two measures differ in units.

Triangle Area Formula

Area equals one-half times base times height, where height is perpendicular to the base. A triangle with base 10 and height 6 has area ½ × 10 × 6 = 30.

Triangle Angle Sum

The three interior angles of any triangle total 180 degrees. If two angles measure 55 and 65 degrees, the third measures 180 − 120 = 60 degrees.

Pythagorean Theorem

In a right triangle, a² + b² = c², where c is the hypotenuse. Legs 6 and 8 give 36 + 64 = 100, so the hypotenuse is 10.

Circle Circumference and Area

Circumference equals 2πr and area equals πr². A circle of radius 5 has circumference 10π and area 25π; diameter is twice the radius.

Rectangular Solid Volume

Volume equals length times width times height, reported in cubic units. A box 3 by 4 by 5 has volume 60 cubic units and surface area 2(12 + 15 + 20) = 94.

Coordinate Plane Quadrants

The plane is divided into four quadrants by the axes. Point (3, −4) lies in quadrant IV because x is positive and y is negative; axes points belong to no quadrant.

Slope of a Line

Slope equals rise over run, or (y₂ − y₁) ÷ (x₂ − x₁). Through (1, 2) and (4, 11), slope is 9 ÷ 3 = 3; a horizontal line has slope 0.

Slope-Intercept Form

The equation y = mx + b has slope m and y-intercept b. For y = −2x + 5, the line falls 2 units per 1 unit right and crosses the y-axis at (0, 5).

Solving Linear Equations

Undo operations in reverse order, applying each step to both sides. For 3x + 7 = 22, subtract 7 to get 3x = 15, then divide by 3 for x = 5.

Inequality Sign Flip

Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign. From −2x > 8, dividing by −2 gives x < −4.

Exponent Product Rule

When multiplying powers with the same base, add the exponents: xᵃ · xᵇ = xᵃ⁺ᵇ. So 2³ × 2⁴ = 2⁷ = 128, and x⁵ · x⁻² = x³.

Square Root Simplification

Factor out perfect squares: √72 = √(36 × 2) = 6√2. A square root of a positive number has two values, one positive and one negative.

Scientific Notation

A number written as a × 10ⁿ with 1 ≤ a < 10. The value 0.00042 becomes 4.2 × 10⁻⁴, and 53,000 becomes 5.3 × 10⁴.