PRAXIS 4-8 Math and Science (5155)

Prime Number

A number with exactly two factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

Composite Number

A number with more than two factors. (e.g., 12 has factors 1, 2, 3, 4, 6, 12)

Factor

A number that divides evenly into another number. (e.g., Factors of 18: 1, 2, 3, 6, 9, 18)

Multiple

The result of multiplying a number by whole numbers. (e.g., Multiples of 5: 5, 10, 15, 20...)

Greatest Common Factor (GCF)

Largest factor shared by two numbers. (e.g. factor of 18 and 24 is 6)

Least Common Multiple (LCM)

Smallest multiple shared by two numbers. (e.g., factor of 4 and 6 is 12)

Absolute Value

Distance from zero

Equivalent Fractions

Fractions with the same value. (e.g., 1/2 = 2/4 = 3/6)

Reciprocal

Flip the numerator and denominator. (e.g., 3/5 becomes 5/3)

Improper Fraction

Numerator is larger than the denominator. (e.g., 9/4 converts to 2¼)

Ratio

Compares two quantities. (e.g., 3 boys : 5 girls = 3:5)

Rate

Ratio comparing different units. (e.g., 60 miles per hour)

Unit Rate

Rate with a denominator of 1. (e.g., $12 for 3 notebooks = $4 per notebook)

Proportion

Two equal ratios. (e.g., 3/2 = 12/x, so cross-multiplying gives x = 8)

Percent

Per hundred. (e.g., 35% = 35/100 = 0.35)

Variable

Letter representing an unknown. (e.g., x in x + 5 = 12)

Expression

Numbers and variables without an equals sign. (e.g., 4x + 7)

Equation

Two expressions joined by an equals sign. (e.g., 4x + 7 = 31)

Coefficient

Number multiplying the variable. (e.g., 7 in 7x)

Constant

Number without a variable. (e.g., 12 in 5x + 12)

Slope

Rise over run: m = (y₂ - y₁) / (x₂ - x₁). (e.g., points (2,3) and (6,11) have __________ = 2)

Y-Intercept

Where the graph crosses the y-axis. (e.g., 5 in y = 3x + 5)

Perimeter

Distance around a figure: P = 2L + 2W. (e.g., L=8, W=5 gives P=26)

Area of a Rectangle

A = length × width. (e.g., 8 × 5 = 40)

Area of a Triangle

A = ½bh. (e.g., base=10, height=6 gives A=30)

Volume of a Rectangular Prism

V = lwh. (e.g., 4 × 3 × 2 = 24 cubic units)

Surface Area

Add the area of every face. (e.g., Cube with side 3 has SA = 6(3²) = 54)

Diameter

Distance across a circle: d = 2r. (e.g., radius = 7 means diameter = 14)

Circumference

Distance around a circle: C = 2πr or πd. (e.g., d=10 means C = 10π)

Mean

Average: add all numbers, then divide by the count. (e.g., 6, 8, 10, 12 average is 9)

Median

Middle number in a sorted list. (e.g., 4, 7, 8, 12, 20 has median 8)

Mode

Most common number. (e.g., in 3, 3, 5, 8, the mode is 3)

Range

Largest minus smallest value. (e.g., 18, 21, 25, 30 has range 30 - 18 = 12)

Probability

Favorable outcomes ÷ total outcomes. (e.g., 3 red out of 10 total = 3/10)

Hypothesis

A testable prediction.

Independent Variable

What the scientist changes in an experiment.

Dependent Variable

What is measured or observed in an experiment.

Constant (Scientific)

Factor kept the same throughout an experiment.

Control Group

Group that does not receive the experimental treatment.

Qualitative Data

Descriptive observations using senses.

Quantitative Data

Numerical measurements and counts.

Cell Membrane

Controls what enters and leaves the cell.

Cell Wall

Provides rigid support and protection in plant cells.

Nucleus

Controls cell activities and holds DNA.

Mitochondria

Produces energy (ATP) for the cell.

Chloroplast

Site of photosynthesis in plant cells.

Photosynthesis

Process where plants use sunlight to make glucose.

Cellular Respiration

Process where cells break down glucose for energy.

Producer

Organism that makes its own food.

Consumer

Organism that eats other organisms for energy.

Decomposer

Organism that breaks down dead organic matter.

Food Chain

Single pathway showing energy flow.

Food Web

Multiple interconnected food chains in an ecosystem.

Ecosystem

Living (biotic) and nonliving (abiotic) things interacting.

Habitat

The physical place where an organism lives.

Niche

An organism's specific role in its ecosystem.

Weathering

Breaking rock down into smaller pieces.

Erosion

Movement of weathered material by wind, water, or ice.

Deposition

Dropping or settling of sediments in a new location.

Igneous Rock

Forms from cooled magma or lava.

Sedimentary Rock

Forms from compacted and cemented sediments.

Metamorphic Rock

Forms from existing rock changed by heat and pressure.

Mantle

Thick layer of hot, solid-flowing rock beneath Earth's crust.

Outer Core

Liquid layer of iron and nickel.

Inner Core

Solid sphere of iron and nickel.

Plate Tectonics

Theory explaining the movement of Earth's lithospheric plates.

Force

A push or a pull.

Gravity

Attraction force between masses.

Friction

Force that opposes motion between touching surfaces.

Inertia

Resistance to changes in motion.

Mass

Amount of matter in an object.

Weight

Force of gravity acting on an object.

Velocity

Speed of an object in a specific direction.

Acceleration

Rate of change in velocity.

Potential Energy

Stored energy based on position or state.

Kinetic Energy

Energy of motion.

Conduction

Heat transfer by direct physical contact.

Convection

Heat transfer through fluids (liquids or gases) by density currents.

Radiation

Heat transfer through electromagnetic waves.

Mechanical Wave

Wave that requires a physical medium to travel (e.g., sound).

Electromagnetic Wave

Wave that does not require a medium to travel (e.g., light).

Frequency

Number of waves passing a point per second.

Wavelength

Distance between two consecutive wave crests.

Rotation

Spinning of an object on its axis.

Revolution

Orbiting of one object around another.

Waxing

The illuminated phase of the Moon appears to grow.

Waning

The illuminated phase of the Moon appears to shrink.

New Moon

Phase when the Moon is directly between the Earth and Sun.

Full Moon

Phase when the Earth is directly between the Moon and Sun.

Integers

Whole numbers, their opposites, and zero. Example: -3, -2, -1, 0, 1, 2

Rational Number

A number that can be written as a fraction. Examples: 3, 0.5, -7/8

Irrational Number

Cannot be written as a fraction. Examples: π or √2

Order of Operations (PEMDAS)

Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right)

Percent Increase

New Value = Original × (1 + Percent as a Decimal) Example: $50 increased by 20% = $60

Percent Decrease

New Value = Original × (1 − Percent as a Decimal) Example: $80 decreased by 25% = $60

Pythagorean Theorem

a² + b² = c². Used with right triangles.

Distance Formula

= Rate × Time (d = rt)

Speed Formula

= Distance ÷ Time

Force Formula

= Mass × Acceleration (F = ma)

Atom

Smallest unit of an element that retains its properties.