GENMATH FINALS U6-U8

SURFACE AREA OF A SOLID FIGURE

total area of all their flat or curved surfaces calculated using specific formulas

SURFACE AREA OF A SOLID FIGURE

measured in square units

SURFACE AREA

all sides including the base

LATERAL AREA

all sides or walls only

PRISM

a solid figure with two parallel, congruent polygonal bases connected by rectangular lateral faces

PRISM

the lateral faces join the corresponding sides of the two bases

PYRAMID

a solid figure with a polygonal base and triangular faces that meet at a single point called the vertex

CYLINDER

a solid figure with two parallel, congruent circular bases connected by a curved surface

CONE

a solid figure with a circular base and a curved surface that tapers smoothly to a single point called the vertex

SPHERE

a perfectly round solid figure where every point on the surface is equidistant from a fixed point called the center

NETS

help visualize and calculate surface area by showing all faces of a solid in one flat layout

VOLUME OF SOLID FIGURES

the amount of space a three-dimensional object occupies

VOLUME OF SOLID FIGURES

indicates how much substance, such as liquid, gas, or solid material, can fit inside a given shape

VOLUME OF SOLID FIGURES

measured in cubic units

CUBE

a special type of prism where all faces are squares, and all sides are equal in length

PRISM

has two identical and parallel bases connected by rectangular faces

PYRAMID

has a polygonal base and triangular faces that meet at a single point called the vertex

CYLINDER

has two circular bases that are parallel and congruent, connected by a curved surface

CONE

has a circular base and a curved surface that narrows to a single point called the vertex

SPHERE

a perfectly round solid where every point on the surface is the same distance from the center

ARCHITECTURE AND CONSTRUCTION

surface area is used to plan materials like paint or tiles

ARCHITECTURE AND CONSTRUCTION

volume is used to calculate how much concrete is needed

ENGINEERING AND MANUFACTURING

surface area is used to estimate materials for coatings

ENGINEERING AND MANUFACTURING

volume is used to design tanks or parts that hold liquids

PACKING AND LOGISTICS

surface area is used to determine wrapping materials

PACKING AND LOGISTICS

volume ensures products fit into containers efficiently

ENVIRONMENTAL SCIENCE

surface area is used in studying evaporation and heat absorption

ENVIRONMENTAL SCIENCE

volume is used in managing water storage

HEALTH AND MEDICINE

surface area is used to calculate drug dosages

HEALTH AND MEDICINE

volume is essential in designing accurate medical tools

AGRICULTURE

surface area helps design efficient greenhouses

AGRICULTURE

volume is used to measure water, fertilizers, and crop storage

FOOD INDUSTRY

surface area affects cooking and coating coverage

FOOD INDUSTRY

volume is used for ingredient measurement and packaging

SCALE

shows the relationship between a measurement on a drawing and the actual measurement it represents

SCALE FACTOR

number used to multiply or divide measurements in a drawing or model to get the actual size or vice versa

CURRENCY EXCHANGE

allows you to convert one currency into another using exchange rates

EXCHANGE RATE

tells us how much one unit of a currency is worth in another

COUNTRY SYMBOL MEANING

United States USD US Dollars / Japan JPY Japanese Yen / United Kingdom GBP Great British Pound / Hongkong HKD Hongkong Dollars / Canada CAD Canadian Dollars / Singapore SGD Singaporean Dollars / Australia AUD Australian Dollars / South Korea KRW Korean Won / Thailand THB Thai Baht / Indonesia IDR Indonesian Rupiah

CONVERSION WITHIN SECONDS, MINUTES, HOURS, AND DAYS

1 day = 24 hours

CONVERSION WITHIN SECONDS, MINUTES, HOURS, AND DAYS

1 hour = 60 minutes

CONVERSION WITHIN SECONDS, MINUTES, HOURS, AND DAYS

1 minute = 60 seconds

CONVERSION WITHIN DAYS, WEEKS, MONTHS, AND YEARS

1 week = 7 days

CONVERSION WITHIN DAYS, WEEKS, MONTHS, AND YEARS

4 weeks = 1 month

CONVERSION WITHIN DAYS, WEEKS, MONTHS, AND YEARS

30 days = 1 month

CONVERSION WITHIN DAYS, WEEKS, MONTHS, AND YEARS

1 year = 12 months

CONVERSION WITHIN DAYS, WEEKS, MONTHS, AND YEARS

1 year = 52 weeks

CONVERSION WITHIN DAYS, WEEKS, MONTHS, AND YEARS

1 year = 365 days

CONVERSION WITHIN DAYS, WEEKS, MONTHS, AND YEARS

1 leap year = 366 days

EXACT NUMBERS OF DAYS IN A MONTH

January

EXACT NUMBERS OF DAYS IN A MONTH

February

EXACT NUMBERS OF DAYS IN A MONTH

March

EXACT NUMBERS OF DAYS IN A MONTH

April

EXACT NUMBERS OF DAYS IN A MONTH

May

EXACT NUMBERS OF DAYS IN A MONTH

June

EXACT NUMBERS OF DAYS IN A MONTH

July

EXACT NUMBERS OF DAYS IN A MONTH

August

EXACT NUMBERS OF DAYS IN A MONTH

September

EXACT NUMBERS OF DAYS IN A MONTH

October

EXACT NUMBERS OF DAYS IN A MONTH

November

EXACT NUMBERS OF DAYS IN A MONTH

December

LINEAR FUNCTIONS

a mathematical function that models a relationship between two variables with a constant rate of change

LINEAR FUNCTIONS

the highest power of the variable is 1

GENERAL FUNCTION

-> f(x) = mx + b

GENERAL FUNCTION

f(x) or y

GENERAL FUNCTION

x

GENERAL FUNCTION

m

GENERAL FUNCTION

b

POINT-SLOPE FORM

-> (y - y1 = m(x - x1))

POINT-SLOPE FORM

used when the slope and one point (x1, y1) on the line are known

STANDARD FORM

-> (Ax + By = C)

STANDARD FORM

especially useful in applications involving constraints or when preparing equations for systems of linear equations

DOMAIN

all valid input values (usually time, quantity, or any measurable variable)

DOMAIN

The set of all real numbers, or (-∞, ∞). This is because a linear function is defined for every real value of x.

RANGE

corresponding output values based on the domain

RANGE

The set of all real numbers, or (-∞, ∞). As x increases or decreases without bound, so does f(x).

GRAPHING LINEAR EQUATIONS

plotting its set of points and drawing the corresponding straight line

STEPS IN EVALUATING LINEAR FUNCTIONS

1. Substitute the given value of x into the function. 2. Perform the arithmetic operations. 3. Interpret the result, especially in the context of real-world problems.

QUADRATIC FUNCTION

a type of polynomial function of degree two

QUADRATIC FUNCTION

the highest power of the variable is 2

QUADRATIC FUNCTION

ensure the coefficient of x2 is nonzero (a ≠ 0)

PARABOLA

a curve that represents the graph of a quadratic function

STANDARD FORM

-> f(x) = ax² + bx + c

STANDARD FORM

It clearly shows the coefficients, but does not immediately provide the vertex or roots of the parabola.

VERTEX FORM

-> f(x) = a(x - h)² + k

VERTEX FORM

This form shows the vertex of the parabola directly as (h, k).

VERTEX FORM

It is especially useful when graphing because the vertex is the central point for plotting the curve.

INTERCEPTS FORM

-> f(x) = a(x - r1)(x - r2)

INTERCEPTS FORM

This form reveals the x-intercepts, or the zeros, of the quadratic function.

INTERCEPTS FORM

It is useful for identifying where the function crosses the x-axis and solving the related quadratic equation f(x) = 0.

DIRECTION OF OPENING

This depends on the sign of the coefficient a in any of the forms.

DIRECTION OF OPENING

if a > 0 the parabola opens upward

DIRECTION OF OPENING

if a < 0 the parabola opens downward

VERTEX

the turning point of the parabola

AXIS OF SYMMETRY

the vertical line, x = h, that passes through the vertex and divides the parabola into two symmetrical halves

Y-INTERCEPT

the point where the function crosses the y-axis

Y-INTERCEPT

it can be found by evaluating f(0)

X-INTERCEPT

the points where the graph crosses the x-axis

X-INTERCEPT

they are the solutions to f(x) = 0 / solved by factoring

MINIMUM VALUE

If a > 0, the vertex is a minimum point, and the function has a minimum value at f(x) = k.