Accuplacer Advanced Algebra Formulas

Questions and Answers

What is the point slope form of a linear equation?

y = ax² + bx + c

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

y = mx² + b

y = mx + b

What does sin equal in a right triangle?

opposite/hypotenuse

What is the formula for the difference of cubes?

a³-b³=(a-b)(a²+ab+b²)

What is the Point Distance Formula?

√(x2-x1)² + (y2-y1)² Signup and view all the answers

What is the area formula for a square?

A=s² Signup and view all the answers

What is the formula for the area of a rectangle?

A=lw Signup and view all the answers

What is the formula for the area of a parallelogram?

A=bh Signup and view all the answers

What is the area formula for a triangle?

A=1/2bh or A=bh/2 Signup and view all the answers

What is the formula for the circumference of a circle?

C=2πr Signup and view all the answers

How is distance calculated in relation to rate and time?

rate x time Signup and view all the answers

What is the formula for the volume of a cube?

s³ Signup and view all the answers

What is the volume formula for a rectangular prism?

V=lwh Signup and view all the answers

What is the volume formula for a cone?

1/3πr²h Signup and view all the answers

What is the formula for the volume of a sphere?

4/3πr³ Signup and view all the answers

What is the tangent in trigonometry?

opposite/adjacent Signup and view all the answers

What is the Exponential Decay Formula?

y=a(1-r)^t Signup and view all the answers

What is the Exponential Growth Formula?

y=a(1+r)^t Signup and view all the answers

What is the surface area formula for a rectangle?

2lw + 2lh + 2wh Signup and view all the answers

What is the midpoint formula?

(x₁+x₂)/2, (y₁+y₂)/2 Signup and view all the answers

Perpendicular lines are ___ (ex. 5, -1/5).

opposite reciprocal Signup and view all the answers

What does cosine equal in a right triangle?

adjacent/hypotenuse Signup and view all the answers

What is the surface area formula for a cube?

6s² Signup and view all the answers

What is the area formula for a circle?

A=πr² Signup and view all the answers

What is csc in trigonometry?

hypotenuse/opposite Signup and view all the answers

What is sec in trigonometry?

hypotenuse/adjacent Signup and view all the answers

What is cot in trigonometry?

cos/sin Signup and view all the answers

What is the Arc Length Formula?

L = 2πr (m⁰/360⁰) or S = rθ Signup and view all the answers

Parallel lines have ___ slopes.

equal Signup and view all the answers

What is the formula for work in terms of job rate?

work rate x work time Signup and view all the answers

What is the Mixture Formula?

(percentage of solution) * (volume of solution) = amount of liquid Signup and view all the answers

What are the x and y values of the unit circle?

(cos, sin) Signup and view all the answers

What is the area formula for an equilateral triangle?

s² × root 3/4 Signup and view all the answers

What are the Triangle Congruence Theorems?

SSS, SAS, ASA, AAS, HL Signup and view all the answers

What transformation occurs for 90 degrees clockwise rotation?

(x,y) -> (y,-x) Signup and view all the answers

What transformation occurs for 90 degrees counterclockwise rotation?

(-y,x) Signup and view all the answers

What transformation occurs for 180 degrees rotation?

(-x,-y) Signup and view all the answers

What is the formula for sin(A+B)?

sinAcosB+cosAsinB Signup and view all the answers

What transformation occurs for 270 degrees clockwise rotation?

(-y,x) Signup and view all the answers

What transformation occurs for 270 degrees counterclockwise rotation?

(y,-x) Signup and view all the answers

What is the Law of Sines?

a/sinA = b/sinB = c/sinC Signup and view all the answers

What is the formula for the volume of a cylinder?

πr²h Signup and view all the answers

What is the volume formula for a pyramid?

1/3lwh or (lwh/3) Signup and view all the answers

What is the formula for cos(A+B)?

cosAcosB-sinAsinB Signup and view all the answers

What is the Law of Cosines formula?

a²=b²+c²-2bcCosA Signup and view all the answers

What is the formula for sin(2x)?

2sinxcosx Signup and view all the answers

What is the formula for cos(2x)?

cos²x-sin²x Signup and view all the answers

What is the formula for tan(2x)?

2tanx/1-tan²x Signup and view all the answers

What is the formula for sin(A-B)?

sinAcosB-cosAsinB Signup and view all the answers

What is the formula for cos(A-B)?

cosAcosB+sinAsinB Signup and view all the answers

What is the formula for the area of a trapezoid?

A=1/2(b1+b2)h Signup and view all the answers

What are the Pythagorean Identities?

sin²x + cos²x = 1, tan²x + 1 = sec²x, 1 + cot²x = csc²x Signup and view all the answers

What does the measurement of the central angle equal?

same measure of arc Signup and view all the answers

What is an inscribed angle?

1/2 arc Signup and view all the answers

What is the angle formed by a tangent and a chord?

arc/2 Signup and view all the answers

What is the angle formed by the intersection of two chords?

big arc + small arc/2 Signup and view all the answers

What is the angle outside the circle?

big arc-small arc/2 Signup and view all the answers

What is the area formula for a hexagon?

3√3/2 * a² Signup and view all the answers

Study Notes

Point Slope Form

Represents the equation of a line using a known point (x1, y1) and slope m: ( y - y_1 = m(x - x_1) )

Trigonometric Ratios

Sine (sin): Ratio of the length of the opposite side to the hypotenuse in a right triangle: ( \text{sin} = \frac{\text{opposite}}{\text{hypotenuse}} )
Cosine (cos): Ratio of the length of the adjacent side to the hypotenuse: ( \text{cos} = \frac{\text{adjacent}}{\text{hypotenuse}} )
Tangent (tan): Ratio of sine to cosine: ( \text{tan} = \frac{\text{opposite}}{\text{adjacent}} )

Difference of Cubes Formula

Can be factored as: ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) )

Distance and Midpoint Formulas

Point Distance Formula: Calculates distance between two points ((x_1, y_1)) and ((x_2, y_2)): ( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} )
Midpoint Formula: Finds the midpoint of a segment connecting two points: ( \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right) )

Area Formulas

Area of Square: ( A = s^2 )
Area of Rectangle: ( A = lw )
Area of Parallelogram: ( A = bh )
Area of Triangle: ( A = \frac{1}{2}bh ) or ( A = \frac{bh}{2} )
Area of Circle: ( A = \pi r^2 )
Area of Trapezoid: ( A = \frac{1}{2}(b_1 + b_2)h )
Area of Equilateral Triangle: ( \frac{s^2 \sqrt{3}}{4} )
Area of Hexagon: ( \frac{3\sqrt{3}}{2}a^2 )

Circumference and Volume Formulas

Circumference of Circle: ( C = 2\pi r )
Volume of Cube: ( V = s^3 )
Volume of Rectangular Prism: ( V = lwh )
Volume of Cone: ( V = \frac{1}{3} \pi r^2 h )
Volume of Sphere: ( V = \frac{4}{3} \pi r^3 )
Volume of Cylinder: ( V = \pi r^2 h )
Volume of Pyramid: ( V = \frac{1}{3} lwh )

Exponential Functions

Exponential Growth Formula: ( y = a(1 + r)^t )
Exponential Decay Formula: ( y = a(1 - r)^t )

Trigonometric Identities

Pythagorean Identities:
- ( \sin^2 x + \cos^2 x = 1 )
- ( \tan^2 x + 1 = \sec^2 x )
- ( 1 + \cot^2 x = \csc^2 x )
Double Angle Formulas:
- ( \sin(2x) = 2 \sin x \cos x )
- ( \cos(2x) = \cos^2 x - \sin^2 x )
- ( \tan(2x) = \frac{2 \tan x}{1 - \tan^2 x} )

Geometric Angle Formulas

Inscribed Angle: Measures half of the arc it intercepts.
Angle Formed by a Tangent and a Chord: Equal to half the measure of the intercepted arc.
Angle Formed by Intersection of Two Chords: Average of measures of the arcs intercepted.
Angle Outside the Circle: Difference between larger and smaller arcs, divided by 2.

Slope Relationships

Parallel lines have equal slopes.
Perpendicular lines have slopes that are opposite reciprocals, e.g., if one slope is ( 5 ), the other is ( -\frac{1}{5} ).

Job and Mixture Formulas

Work Rate Formula: ( \text{Job} = \text{Work Rate} \times \text{Time} )
Mixture Formula: ( (\text{percentage of solution}) \times (\text{volume of solution}) = \text{amount of liquid} )

Unit Circle Values

( x ) and ( y ) coordinates are represented by ( ( \cos, \sin ) ) respective to angles.

Studying That Suits You

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Description

Test your knowledge of essential algebraic formulas with this flashcard quiz. Covering topics such as point slope form, the sine function, and the area of various shapes, this quiz is perfect for those preparing for the Accuplacer exam. Enhance your understanding of advanced algebra and functions with these key concepts.