SAT Math Reference Sheet: Your Ultimate Guide to Ace the Math Section

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SAT Math Reference Sheet: Your Ultimate Guide to Ace the Math Section

Introduction

The SAT Math section can be daunting, but with the right knowledge and tools, you can conquer it. This comprehensive SAT Math reference sheet provides you with everything you need to master the SAT Math syllabus, from foundational concepts to advanced techniques.

Algebra & Functions

Linear Equations & Inequalities: Solve equations and inequalities involving one or two variables.
Quadratic Equations: Solve quadratic equations using factoring, completing the square, or the quadratic formula.
Systems of Equations: Solve systems of linear equations involving two or three variables by substitution, elimination, or graphing.
Functions: Identify and graph different types of functions, including linear, quadratic, absolute value, and polynomial functions.
Logarithms: Understand the logarithmic function and solve logarithmic equations.

Geometry & Measurement

sat math reference sheet

Triangles: Calculate angles, side lengths, and areas of triangles.
Quadrilaterals: Identify and classify quadrilaterals, find areas and perimeters.
Circles: Find areas, circumferences, and equations of circles.
Volume & Surface Area: Calculate volumes and surface areas of spheres, cones, cylinders, and prisms.
Coordinate Geometry: Use the coordinate plane to locate points and graph functions.

Additional Math Topics

Probability: Calculate probabilities of events.
Combinatorics: Determine the number of possible arrangements or combinations of objects.
Trigonometry: Solve right triangles using sine, cosine, and tangent.
Matrices: Perform operations on matrices, find determinants, and solve matrix equations.
Complex Numbers: Understand and perform operations on complex numbers.

Useful Tables

Table 1: Trigonometric Ratios

Angle	Sine	Cosine	Tangent
0°	0	1	0
30°	1/2	√3/2	√3/3
45°	√2/2	√2/2	1
60°	√3/2	1/2	√3
90°	1	0	Undefined

Table 2: Common Function Transformations

SAT Math Reference Sheet: Your Ultimate Guide to Ace the Math Section

Function	Translation Up	Translation Down	Horizontal Stretch	Horizontal Shrink	Vertical Stretch	Vertical Shrink
y = f(x)	y = f(x) + k	y = f(x) - k	y = f(mx)	y = f(x/m)	y = af(x)	y = f(x)/a

Table 3: Area and Volume Formulas

Shape	Area	Volume
Rectangle	A = lw	V = lwh
Triangle	A = 1/2bh
Circle	A = πr²	V = 4/3πr³
Cylinder	A = 2πr(r + h)	V = πr²h
Cone	A = πr(r + l)	V = 1/3πr²h
Sphere	A = 4πr²	V = 4/3πr³

Table 4: Matrix Operations

Operation	Definition
Matrix Addition	A + B = a + b, where a and b are corresponding elements in matrices A and B
Matrix Subtraction	A - B = a - b, where a and b are corresponding elements in matrices A and B
Scalar Multiplication	kA = ka, where k is a scalar and a is an element in matrix A
Matrix Multiplication	AB = C, where C is an m x n matrix and its ijkth element is the sum of the products of the elements in the ith row of A and the jth column of B

Tips for Success

Understand the Concepts: Master the foundational concepts before tackling advanced topics.
Practice Regularly: Solve practice problems consistently to reinforce your understanding.
Identify Your Weaknesses: Take diagnostic tests to pinpoint areas for improvement.
Manage Your Time: Allocate time wisely during the actual SAT.
Guess Strategically: Make educated guesses when uncertain, focusing on the questions you're most confident about first.
Don't Panic: Stay calm and focused, even if you encounter challenging questions.

Conclusion

By utilizing this comprehensive SAT Math reference sheet, you'll gain a thorough understanding of the concepts and techniques tested on the SAT Math section. With consistent practice and a positive mindset, you can ace the SAT Math section and achieve your desired score.

Introduction