Digital SAT Formula Master
Your complete guide to acing the Digital SAT Math Section with proven strategies and formulas
Created by Prof. Suraj Makwana
SAT Math Expert with 8+ years experience
1500+ Students achieved 800/800 in SAT Math
Key Math Formulas You'll Master:
Algebra
→Geometry
→Trigonometry
→Statistics & Probability
→Functions
→Questions? Contact: +91 8141082193
Scroll to explore
About
Learn about the expertise and methodology behind Digital SAT Formula Master and how we help students achieve perfect scores.
Meet Prof. Suraj Makwana
With over 8 years of specialized experience in SAT Mathematics instruction, Prof. Makwana has helped more than 1,500 students achieve a perfect 800/800 score in the SAT Math section.
Experienced Educator
8+ years specialized in SAT Math instruction
Proven Track Record
1500+ students achieved perfect 800/800 scores
Digital SAT Specialist
Expert in the new Digital SAT format
"My teaching methodology focuses on mastering key formulas and developing strategic problem-solving skills specific to the Digital SAT format."
- Prof. Suraj Makwana
Ready to master the Digital SAT Math section?
Contact: +91 8141082193
Topics
Comprehensive coverage of all Digital SAT Math topics with proven formulas and strategies.
Algebra
Master essential algebra concepts and formulas for solving equations, inequalities, and word problems.
- Linear Equations
- Quadratic Equations
- Systems of Equations
Geometry
Learn key formulas for areas, volumes, angles, and coordinate geometry to solve SAT problems.
- Area & Volume Formulas
- Coordinate Geometry
- Special Right Triangles
Trigonometry
Understand trigonometric ratios, the unit circle, and solving problems involving triangles.
- Sine, Cosine, Tangent
- Law of Sines & Cosines
- Unit Circle
Statistics & Probability
Learn to analyze data, calculate probabilities, and interpret statistical measures accurately.
- Mean, Median, Mode
- Standard Deviation
- Probability & Counting
Functions
Master different function types, transformations, and solving function-based problems.
- Domain & Range
- Transformations
- Composition of Functions
Algebra Formulas
Quick reference to essential algebraic formulas for solving Digital SAT questions faster.
- Quadratic Formula
- Linear Equations and Slope
- Exponents and Logarithms
Contact Prof. Makwana for personalized guidance: +91 8141082193
Algebra
Master key algebraic concepts and formulas essential for acing the Digital SAT Math section.
Why Algebra Matters
Algebra questions make up approximately 35% of the Digital SAT Math section, making it the most heavily tested topic.
Quick recognition of algebraic patterns can save you valuable time during the test.
Mastering formula shortcuts helps solve complex problems in fewer steps.
Understanding algebraic fundamentals helps in all other math sections.
Algebra Success Rate
95%
of our students improve their algebra scores
42%
of Digital SAT questions involve algebraic concepts
Key Algebra Formulas
Tap to expandx = (-b ± √(b² - 4ac)) / 2a
For any quadratic equation in the form:
ax² + bx + c = 0
SAT Application Tips:
- Use when you need exact solutions to quadratic equations
- Discriminant (b² - 4ac) helps determine the number of solutions
- For a = 1, try factoring first to save time
Example Problem:
Solve for x: 2x² - 5x - 3 = 0
Hint: Use a = 2, b = -5, c = -3
y = mx + b
Slope-intercept form, where:
- m = slope
- b = y-intercept
m = (y₂ - y₁) / (x₂ - x₁)
SAT Application Tips:
- Quickly identify parallel lines (same slope)
- Perpendicular lines have slopes that are negative reciprocals
- Convert between point-slope and slope-intercept forms
Example Problem:
Find the equation of a line passing through (2, 5) with a slope of 3.
Hint: Use y = mx + b and substitute the known values.
Exponent Rules:
- xa · xb = xa+b
- xa ÷ xb = xa-b
- (xa)b = xab
- x-a = 1/xa
Logarithm Rules:
- logb(xy) = logbx + logby
- logb(x/y) = logbx - logby
- logb(xn) = n · logbx
- blogbx = x
SAT Application Tips:
Digital SAT logarithm questions typically involve changing forms and solving equations.
Example: Solve for x: log₃(x+4) - log₃(x-1) = 2
Solution Methods:
- Substitution Method: Solve for one variable and substitute
- Elimination Method: Add or subtract equations to eliminate a variable
- Matrix Method: Use determinants (rarely needed on Digital SAT)
SAT Application Tips:
- Choose the method based on the system's complexity
- For word problems, carefully define variables
- Check your solution by substituting back
Example Problem:
Solve the system of equations:
2x + 3y = 7
4x - 5y = 3
Practice Problems
Test your understanding with these sample Digital SAT algebra problems.
If 2x + 5 = 13, what is the value of x?
Solve the equation: 3(2x - 4) = 5x - 7
Ready to Master Algebra?
Join thousands of students who have achieved perfect scores with Prof. Makwana's proven methods.
What Students Say
"The algebra formulas and techniques Prof. Makwana taught me helped me solve questions in half the time. I got an 800 on my Digital SAT Math!"
- Aanya P., Perfect Score Student
Contact: +91 8141082193
Geometry
Master essential geometry concepts and formulas to solve Digital SAT problems accurately and efficiently.
Essential Geometry Formulas
Rectangle
Area: A = l × w
Perimeter: P = 2(l + w)
Diagonal: d = √(l² + w²)
Where l = length and w = width
Square
Area: A = s²
Perimeter: P = 4s
Diagonal: d = s√2
Where s = side length
Parallelogram
Area: A = b × h
Perimeter: P = 2(a + b)
Where b = base, h = height, a = side length
Trapezoid
Area: A = ½h(a + c)
Perimeter: P = a + b + c + d
Where a, c = parallel sides, h = height, b, d = non-parallel sides
Digital SAT Tip:
Area and perimeter formulas frequently appear in Digital SAT problems. Memorize them to save valuable time during the test.
Cube
Volume: V = s³
Surface Area: SA = 6s²
Diagonal: d = s√3
Where s = side length
Rectangular Prism
Volume: V = lwh
Surface Area: SA = 2(lw+lh+wh)
Diagonal: d = √(l²+w²+h²)
Where l = length, w = width, h = height
Cylinder
Volume: V = πr²h
Surface Area: SA = 2πr² + 2πrh
Where r = radius, h = height
Sphere
Volume: V = (4/3)πr³
Surface Area: SA = 4πr²
Where r = radius
Digital SAT Tip:
3D geometry problems often involve finding missing dimensions. Practice converting between different units of volume and area.
Circle Properties
Area: A = πr²
Circumference: C = 2πr
Diameter: d = 2r
Where r = radius
Sector of a Circle
Area: A = (θ/360°) × πr²
Arc Length: L = (θ/360°) × 2πr
Where θ = central angle in degrees
Important Circle Theorems
- Inscribed Angle Theorem: An angle inscribed in a circle is half the central angle that subtends the same arc.
- Power of a Point: If a point P is at distance d from the center of a circle with radius r, and a line through P intersects the circle at points A and B, then PA × PB = d² - r².
- Inscribed Quadrilateral: A quadrilateral is inscribed in a circle if and only if opposite angles are supplementary (sum to 180°).
Digital SAT Tip:
Circle problems often involve finding areas of combined shapes. Remember to use π exactly as given in the calculator or use 3.14 for quick estimations.
Triangle Properties
Area: A = ½bh
Perimeter: P = a + b + c
Angle Sum: A + B + C = 180°
Where b = base, h = height, a, b, c = sides
Special Right Triangles
45°-45°-90° Triangle:
If leg = x, then hypotenuse = x√2
30°-60°-90° Triangle:
If shorter leg = x, then longer leg = x√3, hypotenuse = 2x
Advanced Triangle Formulas
Heron's Formula for Area:
A = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines:
c² = a² + b² - 2ab·cos(C)
Median to Side a:
ma = ½√(2b² + 2c² - a²)
Digital SAT Tip:
Memorizing the properties of special right triangles (45-45-90 and 30-60-90) is essential for solving Digital SAT geometry problems quickly.
Distance and Midpoint
Distance Formula:
d = √[(x₂-x₁)² + (y₂-y₁)²]
Midpoint Formula:
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Slope and Line Equations
Slope: m = (y₂-y₁)/(x₂-x₁)
Slope-Intercept: y = mx + b
Point-Slope: y - y₁ = m(x - x₁)
Standard Form: Ax + By = C
Circles in the Coordinate Plane
Standard Form:
(x - h)² + (y - k)² = r²
Circle with center (h, k) and radius r
General Form:
x² + y² + Dx + Ey + F = 0
Center: (-D/2, -E/2)
Radius: r = √[(D/2)² + (E/2)² - F]
Digital SAT Tip:
Coordinate geometry questions often combine algebraic and geometric concepts. Practice recognizing shapes from their equations.
Digital SAT Geometry Strategies
-
Draw Diagrams: Even if a figure is provided, draw your own and label key information.
-
Use Similar Triangles: Identify similar triangles to find unknown lengths and angles.
-
Remember Pythagorean Triples: Know common triples like (3,4,5), (5,12,13), and (8,15,17).
-
Check for Special Cases: Identify isosceles triangles, equilateral triangles, or regular polygons.
Sample Problem
A triangle has sides of lengths 7, 24, and 25 units. What is the area of the triangle?
This is a right triangle (Pythagorean triple) since 7² + 24² = 25².
Area = (1/2) × base × height = (1/2) × 7 × 24 = 84 square units
Answer: 84 square units
Geometry Success Rate
28% of Digital SAT math questions involve geometric concepts
Over 90% of our students report significant improvement in geometry problem-solving speed after mastering these formulas.
Ready to Master Digital SAT Geometry?
Join Prof. Makwana's specialized formula training and learn proven techniques to solve even the most challenging Digital SAT geometry problems.
Contact: +91 8141082193
Trigonometry
Master essential trigonometric concepts and formulas to solve Digital SAT problems with speed and accuracy.
Core Trigonometric Concepts
The Unit Circle
The unit circle is a circle with radius 1 centered at the origin. It's the foundation for understanding trigonometric functions.
- Point (x,y) on unit circle: (cos θ, sin θ)
- Key angles: 0°, 30°, 45°, 60°, 90°, and their multiples
- Remember: sin² θ + cos² θ = 1
Primary Trigonometric Functions
Sine
sin θ = opposite / hypotenuse
On unit circle: y-coordinate
Range: [-1, 1]
Cosine
cos θ = adjacent / hypotenuse
On unit circle: x-coordinate
Range: [-1, 1]
Tangent
tan θ = opposite / adjacent
Also: sin θ / cos θ
Undefined when cos θ = 0
Digital SAT Tip:
Remember SOH-CAH-TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent
Special Angles Chart
| Angle (degrees) | Angle (radians) | sin θ | cos θ | tan θ |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 |
| 45° | π/4 | 1/√2 | 1/√2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
Memorizing these values is essential for Digital SAT success.
Advanced Trigonometric Concepts
Law of Sines
sin A / a = sin B / b = sin C / c
Use when you know:
- Two angles and one side (AAS or ASA)
- Two sides and angle opposite one of them (SSA)
Where A, B, C are angles and a, b, c are the sides opposite to them.
Law of Cosines
c² = a² + b² - 2ab·cos C
Use when you know:
- Two sides and the included angle (SAS)
- Three sides (SSS)
Generalizes the Pythagorean theorem to any triangle.
Essential Trigonometric Identities
Pythagorean Identity
sin²θ + cos²θ = 1
Angle Addition (sin)
sin(α+β) = sinα·cosβ + cosα·sinβ
Angle Addition (cos)
cos(α+β) = cosα·cosβ - sinα·sinβ
Double Angle (sin)
sin(2θ) = 2sinθ·cosθ
Double Angle (cos)
cos(2θ) = cos²θ - sin²θ
Half Angle (tan)
tan(θ/2) = (1-cosθ)/sinθ
Digital SAT Trig Strategies
-
Identify Triangle Types: Right triangles appear most frequently on the Digital SAT.
-
Unit Circle Visualization: Quickly sketch the unit circle to solve angle problems.
-
SOHCAHTOA: Always start by identifying which sides of the triangle you know.
-
Radian/Degree Conversion: Know that π radians = 180° for quick conversions.
"Trig problems are predictable on the Digital SAT. Master the core concepts and you'll solve them in seconds."
- Prof. Makwana
Sample Problem
In triangle ABC, angle A = 30°, angle B = 45°, and side c = 12 units. What is the length of side a?
Step 1: Find the third angle. C = 180° - A - B = 180° - 30° - 45° = 105°
Step 2: Use the Law of Sines: a/sin(A) = c/sin(C)
Step 3: Substitute values: a/sin(30°) = 12/sin(105°)
Step 4: Solve for a: a = 12 × sin(30°)/sin(105°) = 12 × 0.5/0.9659 ≈ 6.21 units
Answer: 6.21 units
Digital SAT Trig Quick Reference
- sin(90° - θ) = cos θ
- cos(90° - θ) = sin θ
- sin(-θ) = -sin θ
- cos(-θ) = cos θ
About 18% of Digital SAT Math questions involve trigonometry concepts.
Most frequent topics: right triangles, special angles, and the unit circle.
Need Help with Trigonometry?
Get personalized guidance from Prof. Makwana to master Digital SAT trigonometry concepts.
Contact: +91 8141082193Master Trigonometry for the Digital SAT
Join Prof. Makwana's specialized trigonometry program and learn proven techniques to solve even the most challenging problems.
Over 700 students achieved perfect trigonometry scores after completing this program.
Statistics & Probability
Master essential statistical concepts and probability techniques to solve Digital SAT problems confidently and efficiently.
Core Statistical Concepts
Measures of Central Tendency
Mean (Average)
μ = (Σx) / n
Sum of all values divided by the number of values.
Median
Middle value when ordered
Less affected by outliers than the mean.
Mode
Most frequently occurring value
A dataset can have multiple modes or no mode.
Digital SAT Application:
Problems often require you to find the mean after adding, removing, or changing values in a dataset. Know how to manipulate datasets efficiently.
Measures of Spread
Range
Range = Maximum - Minimum
Simplest measure of variability, but highly affected by outliers.
Standard Deviation
σ = √[(Σ(x - μ)²) / n]
Measures how spread out values are from the mean.
Variance
σ² = (Σ(x - μ)²) / n
Square of the standard deviation. Used in more advanced statistical calculations.
Digital SAT Application:
You'll often need to compare distributions using standard deviation. Remember that larger standard deviation means more spread out data.
Data Distributions
Normal Distribution
- • Bell-shaped, symmetric curve
- • Mean = Median = Mode
- • 68-95-99.7 rule (empirical rule)
Z-Scores & Percentiles
Z = (x - μ) / σ
Where:
x = individual value
μ = mean
σ = standard deviation
Z-scores tell how many standard deviations a value is from the mean.
Digital SAT Application:
Percentiles and z-scores are common on the Digital SAT. Know how to interpret them and find proportions within normal distributions.
Probability Concepts
Basic Probability
P(A) = Number of favorable outcomes / Total number of possible outcomes
Probability always ranges from 0 (impossible) to 1 (certain).
Compound Probability
P(A and B) = P(A) × P(B|A)
P(A or B) = P(A) + P(B) - P(A and B)
For independent events: P(A and B) = P(A) × P(B)
Combinatorics
Permutations (order matters):
P(n,r) = n! / (n-r)!
Combinations (order doesn't matter):
C(n,r) = n! / (r!(n-r)!)
Used for counting the number of possible arrangements or selections.
Expected Value
E(X) = Σ[x × P(x)]
The weighted average of all possible outcomes, where each outcome is weighted by its probability.
Digital SAT Application:
Probability questions often involve multistep calculations. Draw tree diagrams for complex probability problems to visualize the outcomes.
Essential Formulas Quick Reference
Mean after Adding/Removing a Value
For adding a value y to a set with mean μ and n elements:
New mean = (nμ + y) / (n + 1)
Empirical Rule (68-95-99.7)
- • 68% of data falls within 1σ of the mean
- • 95% of data falls within 2σ of the mean
- • 99.7% of data falls within 3σ of the mean
Conditional Probability
P(A|B) = P(A and B) / P(B)
The probability of A occurring given that B has occurred.
Digital SAT Statistics Strategies
-
Organize Your Data: Always arrange values in ascending order for median and quartile calculations.
-
Check for Outliers: Identify outliers that could significantly affect the mean but not the median.
-
Use Counting Techniques: For probability problems, clearly identify all possible outcomes first.
-
Visualize the Problem: Use diagrams, tables, or tree diagrams to organize complex probability scenarios.
"Digital SAT statistics problems require careful reading. Identify exactly what the question is asking before applying formulas."
- Prof. Makwana
Sample Problem
A data set has a mean of 75 and a standard deviation of 8. If the scores are normally distributed, approximately what percentage of scores fall between 67 and 83?
Step 1: Calculate z-scores for the boundaries:
z₁ = (67 - 75) / 8 = -1
z₂ = (83 - 75) / 8 = +1
Step 2: Apply the empirical rule. Between -1σ and +1σ contains 68% of the data in a normal distribution.
Answer: Approximately 68% of scores fall between 67 and 83.
Statistics & Probability Success Rate
22% of Digital SAT Math questions involve statistics and probability concepts
Over 92% of our students report significant improvement in statistics problem-solving after mastering these concepts.
Master Statistics & Probability for the Digital SAT
Join Prof. Makwana's specialized program and learn proven techniques to solve even the most challenging statistics and probability problems.
Contact: +91 8141082193
Functions
Master essential function concepts and techniques to solve Digital SAT problems with confidence and accuracy.
Core Function Concepts
1 Function Basics
Definition of a Function
A relation that assigns exactly one output to each input in its domain.
Function Notation
f(x) represents the output of function f when the input is x.
Example: If f(x) = 2x + 3, then f(4) = 2(4) + 3 = 11
Domain and Range
Domain: Set of all possible input values (x-values)
Range: Set of all possible output values (y-values)
Vertical Line Test
A graph represents a function if and only if no vertical line intersects the graph at more than one point.
Digital SAT Tip:
Always check for domain restrictions when working with functions. Pay special attention to values that would cause division by zero or negative values under square roots.
2 Types of Functions
Linear Functions
f(x) = mx + b
- • Constant rate of change (slope m)
- • y-intercept at (0, b)
- • Graph is a straight line
Quadratic Functions
f(x) = ax² + bx + c
- • U-shaped parabola (a > 0 opens up)
- • Vertex at x = -b/(2a)
- • Axis of symmetry through vertex
Exponential Functions
f(x) = ab^x
- • Growth (b > 1) or decay (0 < b < 1)
- • y-intercept at (0, a)
- • Never touches x-axis
Logarithmic Functions
f(x) = log_b(x)
- • Inverse of exponential functions
- • Domain: x > 0
- • Vertical asymptote at x = 0
Absolute Value Functions
f(x) = |ax + b|
- • V-shaped graph
- • Vertex at x = -b/a
- • Always outputs non-negative values
Rational Functions
f(x) = P(x)/Q(x)
- • P(x), Q(x) are polynomials
- • Vertical asymptotes at Q(x) = 0
- • May have horizontal asymptotes
Digital SAT Tip:
The Digital SAT frequently asks you to identify function types from their graphs or equations. Memorize the key characteristics of each function type for quick recognition.
3 Function Transformations
Vertical Transformations
-
f(x) + c
Shifts graph up by c units
-
f(x) - c
Shifts graph down by c units
-
a·f(x) where a > 1
Vertical stretch by factor of a
-
-f(x)
Reflection across x-axis
Horizontal Transformations
-
f(x - c)
Shifts graph right by c units
-
f(x + c)
Shifts graph left by c units
-
f(bx) where 0 < b < 1
Horizontal stretch by factor of 1/b
-
f(-x)
Reflection across y-axis
Combined Transformations:
For a function in the form a·f(b(x - h)) + k:
- Horizontal shift by h units (right if h > 0)
- Horizontal scaling by factor 1/b
- Vertical scaling by factor a
- Vertical shift by k units (up if k > 0)
Digital SAT Tip:
Pay attention to the order of transformations. Horizontal shifts work opposite to what you might expect: f(x - 3) shifts the graph right by 3 units.
4 Function Operations
Arithmetic Operations
- (f + g)(x) = f(x) + g(x)
- (f - g)(x) = f(x) - g(x)
- (f · g)(x) = f(x) · g(x)
- (f/g)(x) = f(x)/g(x), where g(x) ≠ 0
Domain: Values of x that are in the domains of both f and g. For division, also exclude values where g(x) = 0.
Function Composition
(f ∘ g)(x) = f(g(x))
Apply function g first, then apply function f to the result.
Domain: Values of x in the domain of g where g(x) is in the domain of f.
Inverse Functions
f(f⁻¹(x)) = x
f⁻¹(f(x)) = x
The inverse function "undoes" the original function. The graph of f⁻¹ is the reflection of the graph of f across the line y = x.
Finding the Inverse:
- Replace f(x) with y
- Interchange x and y
- Solve for y
- Replace y with f⁻¹(x)
Note: A function has an inverse if and only if it is one-to-one (passes the horizontal line test).
Digital SAT Tip:
Function composition questions often involve finding specific values like (f ∘ g)(2). Work from the inside out: first find g(2), then substitute this value into f.
Digital SAT Function Strategies
-
Analyze End Behavior: Look at what happens as x approaches ±∞ to identify function types.
-
Check Key Points: For unknown functions, calculate values at x = 0, x = 1, and negative values.
-
Use Function Notation: Write intermediary steps using f(x) notation to avoid errors.
-
Break Down Compositions: For (f ∘ g)(x), solve step-by-step rather than substituting directly.
"Most function problems on the Digital SAT test your ability to interpret new information. Focus on understanding what the question is asking rather than simply applying memorized procedures."
- Prof. Makwana
Sample Problem
If f(x) = 2x - 3 and g(x) = x² + 1, find (f ∘ g)(2).
Step 1: Find g(2).
g(2) = 2² + 1 = 4 + 1 = 5
Step 2: Substitute g(2) into f(x).
(f ∘ g)(2) = f(g(2)) = f(5)
Step 3: Calculate f(5).
f(5) = 2(5) - 3 = 10 - 3 = 7
Answer: (f ∘ g)(2) = 7
Function Graphs at a Glance
Linear
Quadratic
Exponential
Logarithmic
Quick recognition of function graphs can save you valuable time on the Digital SAT.
Function Question Success Rate
25% of Digital SAT Math questions involve function concepts
Students who master function transformations and compositions see an average 40-point improvement in their Math scores.
Master Functions for the Digital SAT
Join Prof. Makwana's specialized function mastery program and learn proven techniques to solve even the most challenging problems.
Contact: +91 8141082193
Get In Touch
Have questions about the Digital SAT Math Formula Master? Contact Prof. Suraj Makwana for personalized guidance on your SAT preparation journey.
Contact Information
Phone
+91 8141082193
contact@digitalsat.edu
Experience
8+ years teaching SAT Math
1500+ Students scored 800/800
Send a Message
Frequently Asked Questions
Prof. Suraj Makwana or a team member typically responds within 24-48 hours on business days. For urgent inquiries, please contact directly via phone.
Yes, Prof. Makwana offers personalized one-on-one coaching sessions for students seeking intensive preparation. These sessions are customized to address specific areas where you need improvement.
For optimal results, we recommend starting preparation 3-6 months before your test date. This allows sufficient time to master concepts, practice extensively, and develop effective test-taking strategies.
Yes, we offer special rates for schools, educational institutions, and study groups. Please contact us with details about your group size and requirements for a customized program.