Subtest II: Math & Science

Perimeter

Distance around a 2D shape (add the sides)

Area

Space inside a 2D shape (l * w)

Volume

3D Space contained (l * w * h)

Mean

Average (Sum divided by total)

Median

Middle number when ordered least to greatest (if even, average of the two middle)

Mode

Number that appears most frequently

Range

Difference between greatest and least

Prime

Whole number >1 with only two factors: 1 and itself (2 is the only even prime number)

Composite

Whole number with more than 2 factors (0 and 1 are neither prime or composite)

Order of Operations

PEMDAS

Circumference

C=2pi*r or C=pi*d

Area of a circle

A = pi*r²

Area of a Triangle

A = (b x h) /2

Area of a Trapezoid

A = average of two bases(a+b)/2 multiplied by h

Area of a Parallelogram

A = b*h

Volume of a Rectangular Prism

V = l * w * h

Volume of a cylinder

area of base x height = pi * r² * h

Pythagorean Theorem (Right Triangles)

a² * b² = c² (c = hypotenuse)

Sum of Angles in a Triangle

180 degrees

Sum of Angles in a Quadrilateral

360 degrees

Sum of Angles in a Polygon

(n - 2) * 180

Volume of a pyramid

v = 1/3 x b x h

Adding/Subtracting Fractions

Find the common denominator

Multiplying fractions

Straight across (numerator x numerator, denominator x denominator)

Dividing fractions

Keep the first fraction, change the division to multiplication, flip the 2nd fraction

Converting Mixed Numbers to Improper Fractions

2 ¾ = (4 × 2) + 3 over 4 = 11/4

Percent Formula

Part = percent (as a decimal) x whole

Percent Change

(|new value - old value| / old value) x 100

Distance formula

D = speed x time

Slope of a Line (m)

m = y2 - y1 / x2 -x1

Slope Intercept

y = mx + b

• m = slope

• b = y-intercept (where the line crosses the vertical axis)

Probability of Single Event

event = # of favorable outcomes/ total # of possible outcomes

Probability of Independent Events (both happening)

P(A and B) = P(A) x P(B)

Fundamental Counting Principle

m x n ways

3 shirts 4 pants = 3 × 4 = 12 outfits

Newton’s 1st Law

Object stays at rest or in motion unless acted upon by an outside force

Newton’s 2nd Law

F = ma force = mass x acceleration

Newton’s 3rd Law

Equal/Opposite Reaction

Physical change

reversible change in state or appearance no new substance formed (ice melting)

Chemical change

irreversible reaction forming a new substance with different property (baking a cake, rusting iron, burning wood)

Photosynthesis

Sunlight + Water + CO2 → Glucose + Oxygen

Cellular Respiration

Glucose + Oxygen → Energy (ATP) + Water + CO2

Plant cell

• cell wall

• chloroplasts

• large central vacuole

animal cell

• membrane only (no cell wall)

• smaller vacuoles

Convergent Tectonic Plates

plates collide → Mountains volcanoes, trenches

Divergent Tectonic Plates

plates pull apart → mid-ocean ridges, rift valleys

Transform Tectonic Plates

Plates slide past each other → earthquakes

Water cycle

• Evaporation

• Transpiration

• Condensation

• Precipitation

DNA vs RNA

DNA: double-strand helix holds genetic blueprint

RNA: single-strand; carries instructions from DNA to build proteins

Mitosis

Cell division for growth and repair: produces 2 daughter cells with a full set of chromosomes

Meiosis

• sexual reproduction

• Produces 4 genetically unique mating cells w/ half the chromosomes

Genotype

The genetic allele combination

Phenotype

Physical observable trait (brown hairs/blond hair)

Punnett Square

Used to calculate the probability of offspring inheriting specific traits

Mutualism

Both benefit (+/+)

Commensalism

1 benefits, 1 unaffected

Parasitism

1 benefits, 1 is harmed

Lunar Eclipse

Sun → Earth → Moon (Earth blocks light from hitting the moon)

Solar Eclipse

Sun → Moon → Earth (Moon blocks Sun from Earth view)

Moon Phases

New → Waxing Crescent → 1st ¼ → Waxing Gibbous → Full → Waning Gibbous → Last Quarter → Waning Crescent → New

Igneous Rock

Cooled magma (obsidian, basalt, granite)

Sedimentary Rocks

Compressed layers (sandstone, limestone) where fossils are found

Metamorphic

existing rock → Heat + pressure (marble, slate)

Weathering

breaking down of rocks into smaller pieces in place

Erosion

movement/transport of rock particles by wind, water, or ice

Protons

• Positive charge

• in nucleus

• determines atomic number

Neutrons

• Neutral charge

• Located in nucleus

Electrons

• Negative charge

• Orbit surrounding cloud

States of Matter

• Liquid

• Solid

• Gas

• Plasma

Phase Changes

• melting (solid → liquid)

• freezing (liquid → solid)

• evaporation (liquid → gas)

• condensation (gas → liquid)

• sublimation (solid →gas)

Potential Energy

stored energy based on position or condition (boulder at top of a hill)

Kinetic Energy

Energy of motion

Conduction

Heat transfer by direct contact (solids)

Convection

Heat through fluid movement (air or liquid)

Radiation

Heat through electromagnetic waves (sunlight, warmth of a campfire)

Scientific Method

Queen Rachel Hopes Every Coward Gains Courage

1. Question

2. Research

3. Hypothesis

4. Experiment

5. Collect data

6. Graph/Analyze data

7. Conclusion

pH Scale: Acids

1-6 (lemon juice, vinegar)

pH Scale: Bases

8-14 (lye, bleach, baking soda)

pH Scale: Neutral

7 (pure water)

Monocots (plant biology)

1 seed leaf (corn, wheat, grass)

Dicot

2 seed leaves (beans, peanuts, oak trees)

Homozygous

Two identical alleles AA or aa. Offspring inherit that specific trait with 100% certainty

Heterozygous

Two different alleles (Aa)

Box Plot

• Minimum: lowest data value

• Lower Quartile(Q1): Median of the lower half (25th percentile)

• Median(Q2): Middle value of the data set (50th percentile)

• Upper Quartile(Q3): Median of the upper half (75th percentile)

• Maximum: Highest data value

Interquartile range (IQR)

IQR = Q3 - Q1

Independent Variable

What the experiment changes/manipulates (x-axis)

Exercise to lose weight?

Exercise

Dependent Variable

What is measured/observed as a result (y-axis)

Exercise to lose weight?

Weight

Control Group

the baseline group kept under normal conditions (no treatment) for comparison

Constant/Controlled Variables

Factors kept identical across all groups to ensure a fair test

Exercise to lose weight

Diet

Energy Pyramid

• Producers (Autotrophs) Plants that make their own food via photosynthesis

• Consumers (Heterotrophs) Primary (herbivores) Secondary/Tertiary (carnivores/omnivores)

• Decomposers: break down dead organic matter to recycle nutrients back to the soil

10% Rule

Only 10% of energy transfers up to the next trophic level; 90% is lost as heat/metabolism

Troposphere

1st lowest layer; where weather occurs

Stratosphere

2nd layer contains the ozone layer (absorbs harmful UV radiation)

Mesosphere

3rd layer, where meteors burn up

Thermosphere

4th layer; high heat layer; location of auroras and orbiting space station