Prepare Mathematics for Important US Competitive Exams

Q: How to Improve SAT/ACT Math Scores?

To improve your SAT/ACT math scores, practice regularly with full-length mock tests, focus on weak areas, and master key formulas. Use resources like Testbook’s SAT Practice Tests to simulate real exam conditions, track progress, and develop test-taking strategies.

Q: Should I Take the ACT or SAT for Math?

It depends on your strengths. The SAT focuses more on algebra and data analysis, while the ACT includes advanced topics like matrices, logarithms, and more geometry. If you’re comfortable with a faster-paced test, ACT might be better. If you prefer multi-step problem-solving, SAT could be a good fit.

Q: What Are the Best Resources for SAT and ACT Math?

The best resources include official CollegeBoard and ACT practice tests, Testbook’s SAT Practice Tests, and math prep books from trusted publishers. A mix of full-length tests, topic-specific drills, and problem-solving strategies is ideal for preparation.

Q: Is the SAT Math Section Harder Than the ACT Math Section?

It depends on your math strengths. The ACT Math section is longer and faster-paced, covering a broader range of topics. The SAT Math section has more multi-step word problems but provides formulas upfront. If you struggle with time pressure, SAT Math might feel easier.

Q: Do I Need to Study Calculus for the SAT or ACT?

No, calculus is not tested on the SAT or ACT. These exams focus on algebra, geometry, trigonometry, and data analysis. However, if you're preparing for AP Calculus, GRE, or GMAT, then calculus is important.

Q: How Is Math Tested in the GRE vs. the GMAT?

The GRE Math section tests a broad range of algebra, arithmetic, geometry, and data analysis. The GMAT Quantitative section is more focused on problem-solving and data sufficiency, requiring logical reasoning rather than straightforward calculations. Which US Exams Allow a Calculator, and Which Don’t? SAT: Yes, but only in the calculator-allowed section. ACT: Yes, for the entire Math section. GRE: Yes, an on-screen calculator is provided. GMAT: No, calculators are not allowed in the Quant section. AP Calculus: Yes, but only in certain sections.

Q: How Can I Improve My Problem-Solving Speed for Math Exams?

Practice solving problems under timed conditions, master mental math techniques, and familiarize yourself with calculator shortcuts. Taking adaptive digital tests, like those offered by Testbook, can help improve speed and accuracy. What Are Some Common Mistakes Students Make in Standardized Test Math? Misreading questions and skipping key details. Not managing time well and spending too long on difficult problems. Making careless errors in calculations or bubbling answers incorrectly. Ignoring word problems and data analysis topics, which appear frequently. Not practicing with official digital test formats before the exam.

Q: What Math Score Do I Need to Get Into Top US Universities?

For top-tier universities like Harvard, MIT, Stanford, and Ivy League schools, aim for: SAT Math: 750+ ACT Math: 33+ For competitive state universities, scores around 650+ SAT Math or 28+ ACT Math are usually sufficient.

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Topics Covered in SAT, ACT, PSAT/NMSQT, GED, GRE, GMAT, AP, Exams, PERT, Accuplacer, MCAT

If you're gearing up for college or career-focused exams, math is going to be a big deal! Whether you're tackling the SAT, ACT, PSAT/NMSQT, GED, GRE, GMAT, AP exams, PERT, Accuplacer, or even the MCAT, strong math skills are a must. From algebra and geometry to probability and calculus, SAT Math Prep and beyond will help you master these topics and boost your test scores!

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Arithmetic

Arithmetic is the foundation of all math skills! Whether you're working with fractions, percentages, or ratios, mastering these basics is crucial for success in standardized tests like the SAT, ACT, PSAT/NMSQT, GED, GRE, GMAT, PERT, and Accuplacer. You'll see arithmetic concepts in word problems, data analysis, and algebra-based questions—so getting comfortable with them will definitely boost your confidence on test day!

Subject	Subtopics	Description	Examples
Arithmetic	Whole numbers, fractions and decimals, percentages	Basic number operations, conversions between forms, and working with percentages.	Convert 0.75 to a fraction → 3/4. Find 25% of 200 → 50.
	Ratios and proportions	Solving problems involving proportional relationships and direct/inverse variation.	If a map scale is 1 inch = 5 miles, how many miles is 3 inches? → 15 miles.
	Order of operations (PEMDAS)	Following the correct sequence of mathematical operations.	Solve 5 + 3 × (8 ÷ 4) - 2 → 5 + 3 × 2 - 2 = 9.
	Number properties (even/odd, prime numbers, divisibility rules)	Understanding number classifications and divisibility shortcuts.	Is 47 a prime number? → Yes. Is 144 divisible by 9? → Yes (Sum of digits = 9, divisible by 9 rule).

Algebra

Algebra is where math starts getting interesting! Whether you're solving for x, graphing functions, or factoring quadratics, algebra forms the backbone of many advanced math concepts. You’ll encounter algebra questions on standardized tests like the SAT, ACT, PSAT/NMSQT, GED, GRE, GMAT, PERT, and Accuplacer, so mastering these topics is a must. Brush up on your algebra skills to tackle equations, functions, and inequalities with confidence!

Subject	Subtopics	Description	Examples
Algebra	Linear equations and inequalities	Solving for variables in single-variable and multi-step equations.	Solve 2x + 5 = 15 → x = 5. Solve 3x - 4 < 11 → x < 5.
	Quadratic equations and factoring	Solving quadratic equations using factoring, completing the square, and the quadratic formula.	Solve x² - 5x + 6 = 0 by factoring → (x - 2)(x - 3) = 0, so x = 2 or x = 3.
	Linear Function Quadratic Function Exponential Function Linear Function Graph Quadratic Function Graph Exponential Function Graph	Understanding how functions behave and interpreting their graphical representations.	For f(x) = x² - 4, the graph is a parabola opening upwards with roots at x = -2, 2.
	Systems of equations	Solving multiple equations with multiple variables using substitution, elimination, and graphing.	Solve x + y = 7 and 2x - y = 3 using substitution → x = 4, y = 3.
	Polynomials and rational expressions	Simplifying expressions, performing operations, and solving polynomial equations.	Simplify (x² + 2x - 3) ÷ (x - 1) → x + 3.

Geometry

Geometry is all about shapes, angles, and spatial reasoning—basically, the math that helps you understand the world around you! Whether you're calculating the area of a triangle, finding the slope of a line, or working with circles, geometry plays a big role in standardized tests like the SAT, ACT, PSAT/NMSQT, GED, GRE, GMAT, PERT, and Accuplacer. Mastering these topics will boost your problem-solving skills and help you score higher!

Subject	Subtopics	Description	Examples
Geometry	Lines, angles, and triangles	Understanding geometric relationships, including parallel lines, angle properties, and triangle classifications.	If two parallel lines are cut by a transversal, corresponding angles are equal. If a triangle has angles 30°, 60°, and 90°, the sides are in a ratio of 1:√3:2.
	Circles (chords, tangents, sectors)	Solving problems involving arc lengths, sector areas, and circle properties.	The circumference of a circle with radius r is 2πr. The area of a sector with angle θ in a circle of radius r is (θ/360) × πr².
	Coordinate geometry (midpoint, slope, distance)	Using formulas to find slopes, distances, and midpoints on the coordinate plane.	Find the midpoint of (2, 4) and (6, 8) using the formula ((x₁ + x₂)/2, (y₁ + y₂)/2) → (4,6). The slope between (1, 2) and (4, 8) is (8 - 2) / (4 - 1) = 2.
	Area, perimeter, and volume of geometric shapes	Calculating measurements for two-dimensional and three-dimensional shapes.	The area of a triangle with base b and height h is (1/2) × b × h. The volume of a cylinder with radius r and height h is πr²h.
	Transformations (reflection, rotation, dilation)	Understanding how shapes change under transformations and symmetry.	A point (3, 5) reflected across the x-axis becomes (3, -5). A shape dilated by a scale factor of 2 doubles in size.

Trigonometry

Trigonometry might sound fancy, but it’s really just about understanding angles, triangles, and how they relate to each other! Whether you're working with sine, cosine, and tangent or diving into special right triangles, these concepts are super useful for solving tricky math problems. You'll see trigonometry pop up in SAT, ACT, PSAT/NMSQT, GRE, GMAT, AP Calculus, and some college placement tests like PERT and Accuplacer, so mastering these topics will definitely give you an edge!

Subject	Subtopics	Description	Examples
Trigonometry	Basic trigonometric ratios (sine, cosine, tangent)	Understanding the fundamental trig functions and their applications in right triangles.	In a right triangle with an angle of 30°, if the hypotenuse is 10, then sin 30° = 1/2, so the opposite side is 5.
	Pythagorean theorem and special triangles (30-60-90, 45-45-90)	Using common triangle properties for problem-solving.	In a 45°-45°-90° triangle, if the legs are x, then the hypotenuse is x√2. If x = 5, the hypotenuse is 5√2.
	Unit circle and radian measures	Understanding angle measures beyond degrees and applying trigonometry to circles.	π radians = 180°, so 60° = π/3 radians. sin(π/6) = 1/2, cos(π/4) = √2/2.
	Graphing trigonometric functions	Identifying key properties of sine, cosine, and tangent graphs.	The graph of y = sin(x) oscillates between -1 and 1, with a period of 2π. The graph of y = tan(x) has vertical asymptotes at x = ±π/2.
	Trigonometric identities and equations (for higher-level tests)	Applying advanced trig identities and solving complex equations.	Using the identity sin²x + cos²x = 1, if cos x = 3/5, then sin x = 4/5. Solving 2sin x = 1 gives x = π/6, 5π/6.

Statistics & Probability

Statistics & Probability might sound like a mouthful, but it’s all about making sense of numbers in the real world! From predicting outcomes to analyzing trends, these concepts help you understand data like a pro. You’ll see them on SAT, ACT, PSAT/NMSQT, GRE, GMAT, AP Statistics, GED, and college placement tests like PERT and Accuplacer, so mastering them is a must for standardized test success!

Subject	Subtopics	Description
Statistics & Probability	Mean, median, mode, and range	Calculating measures of central tendency and data spread.
	Probability rules and expected value	Understanding probability rules, expected outcomes, and chance events.
	Data interpretation (charts, tables, graphs)	Analyzing data trends, interpreting graphical information, and drawing conclusions.
	Standard deviation and normal distribution	Measuring variability in data and understanding probability distributions.
	Permutations and combinations	Using formulas to count possible outcomes and solve arrangement problems.

Data Analysis & Quantitative Reasoning

Data Analysis & Quantitative Reasoning is all about making smart decisions based on numbers! Whether you're breaking down tricky word problems or spotting trends in data, these skills are super useful in real life—and in exams. You'll see these topics on SAT, ACT, PSAT/NMSQT, GRE, GMAT, AP Statistics, GED, and college placement tests like PERT and Accuplacer, so sharpening your problem-solving skills here is a game-changer!

Subject	Subtopics	Description
Data Analysis & Quantitative Reasoning	Word problems and logical reasoning	Translating real-world scenarios into mathematical equations and logical solutions.
	Percent change and growth/decay models	Applying formulas for percentage increase/decrease and exponential growth/decay.
	Understanding and analyzing trends in data sets	Identifying patterns and making predictions from data trends.
	Correlation vs. causation	Differentiating between relationships in data sets and actual cause-effect connections.

Calculus

Calculus is where math gets next-level exciting! It’s all about change—how things grow, shrink, speed up, or slow down. Whether you're working with limits, derivatives, or integrals, mastering calculus is a must for advanced math students. You'll see these concepts in AP Calculus, GRE, GMAT, IB Math, and some college placement tests, so if you're aiming for a STEM major or business school, this is your ticket to success!

Subject	Subtopics	Description
Calculus (For Advanced Exams - AP Calculus, GRE, GMAT, IB Math)	Limits and continuity	Understanding the behavior of functions as they approach certain values.
	Differentiation (derivatives, applications of derivatives)	Calculating rates of change and slopes of curves.
	Integration (indefinite and definite integrals)	Finding accumulated quantities and areas under curves.
	Optimization and area under curves	Solving maximum/minimum problems and computing areas using calculus.

Discrete Mathematics

Discrete mathematics might sound fancy, but it’s all about solving real-world problems with logic, patterns, and structures! From set theory to matrices, this branch of math is essential for computer science, data science, and business analytics. You’ll find discrete math questions in GMAT, GRE, and some college placement tests, so mastering these concepts can give you an edge in graduate school admissions and beyond!

Subject	Subtopics	Description
Discrete Mathematics (For GMAT, GRE, Some College Placement Tests)	Set theory and logic	Understanding Venn diagrams, logical statements, and operations on sets.
	Sequences and series	Working with arithmetic and geometric sequences and summation formulas.
	Matrices and determinants	Performing matrix operations and solving linear systems using determinants.
	Graph theory and combinatorics	Studying networks, paths, and combinatorial counting techniques.

Why Choose Testbook for Preparation for Mathematics for the SAT & ACT in the US?

If you're aiming for top colleges, acing the SAT & ACT Math sections is a must! These exams test your ability to solve real-world math problems, apply formulas, and think critically under pressure. Preparing well can boost your college applications, open scholarship opportunities, and set you up for success in higher education. Here's why SAT & ACT Math prep should be your priority:

Strong Math Foundations – The math tested on these exams is useful in college and beyond.
Boosts Logical & Problem-Solving Skills – Essential for success in academics and real life.
Master Digital SAT Tools – Familiarize yourself with the Desmos calculator and adaptive format.
Customized Study Plans – Structured planners keep you on track, whether you have weeks or months left.
Expert-Curated Practice Tests – SAT Practice Tests by Testbook give you 50+ full-length tests with real exam difficulty.
Personalized Performance Tracking – Get insights into strengths and weaknesses with a custom dashboard
Massive Question Bank – Access 3,000+ SAT-style questions covering every tested topic.

Want a 1400+ SAT score? Testbook’s SAT Practice Tests are tailored to CollegeBoard’s Digital SAT format to help you ace the test with confidence. Start your prep today and maximize your SAT Math score!

More Important Topics
Derivative of arctan	Derivative of arcsin
Derivative of sec x	Derivative of cot x
Derivative of log x	Derivative of sin x
Cos 2x Formula	Derivatives of Trigonometric Functions
Area of Hexagon	Derivative Rules
Value of e	First Derivative Test
Factorial	Second Derivative Test
Angle Bisector Theorem	Types of Functions
Derivative of Exponential Function	Area of Parallelogram
Elementary Statistics	Domain and Range of a Function
Area of a Circle	Derivative of Inverse Trigonometric Functions

Prepare Mathematics for Important US Competitive Exams FAQs

How to Improve SAT/ACT Math Scores?

To improve your SAT/ACT math scores, practice regularly with full-length mock tests, focus on weak areas, and master key formulas. Use resources like Testbook’s SAT Practice Tests to simulate real exam conditions, track progress, and develop test-taking strategies.

Should I Take the ACT or SAT for Math?

It depends on your strengths. The SAT focuses more on algebra and data analysis, while the ACT includes advanced topics like matrices, logarithms, and more geometry. If you’re comfortable with a faster-paced test, ACT might be better. If you prefer multi-step problem-solving, SAT could be a good fit.

What Are the Best Resources for SAT and ACT Math?

The best resources include official CollegeBoard and ACT practice tests, Testbook’s SAT Practice Tests, and math prep books from trusted publishers. A mix of full-length tests, topic-specific drills, and problem-solving strategies is ideal for preparation.

Is the SAT Math Section Harder Than the ACT Math Section?

It depends on your math strengths. The ACT Math section is longer and faster-paced, covering a broader range of topics. The SAT Math section has more multi-step word problems but provides formulas upfront. If you struggle with time pressure, SAT Math might feel easier.

Do I Need to Study Calculus for the SAT or ACT?

No, calculus is not tested on the SAT or ACT. These exams focus on algebra, geometry, trigonometry, and data analysis. However, if you're preparing for AP Calculus, GRE, or GMAT, then calculus is important.

How Is Math Tested in the GRE vs. the GMAT?

The GRE Math section tests a broad range of algebra, arithmetic, geometry, and data analysis. The GMAT Quantitative section is more focused on problem-solving and data sufficiency, requiring logical reasoning rather than straightforward calculations. Which US Exams Allow a Calculator, and Which Don’t? SAT: Yes, but only in the calculator-allowed section. ACT: Yes, for the entire Math section. GRE: Yes, an on-screen calculator is provided. GMAT: No, calculators are not allowed in the Quant section. AP Calculus: Yes, but only in certain sections.

How Can I Improve My Problem-Solving Speed for Math Exams?

Practice solving problems under timed conditions, master mental math techniques, and familiarize yourself with calculator shortcuts. Taking adaptive digital tests, like those offered by Testbook, can help improve speed and accuracy. What Are Some Common Mistakes Students Make in Standardized Test Math? Misreading questions and skipping key details. Not managing time well and spending too long on difficult problems. Making careless errors in calculations or bubbling answers incorrectly. Ignoring word problems and data analysis topics, which appear frequently. Not practicing with official digital test formats before the exam.

What Math Score Do I Need to Get Into Top US Universities?

For top-tier universities like Harvard, MIT, Stanford, and Ivy League schools, aim for: SAT Math: 750+ ACT Math: 33+ For competitive state universities, scores around 650+ SAT Math or 28+ ACT Math are usually sufficient.