Math Rocket: The Best 2024/2025 Digital SAT Math Prep Course

Master scientific notation by expressing large or small numbers as a coefficient between 1 and 10 times ten to an integer exponent, using base ten with positive or negative exponents.

Learn to add and subtract numbers in scientific notation by aligning exponents and adding or subtracting coefficients, then verify the result is in proper scientific notation.

Master numerical expressions by applying the order of operations—parentheses, exponents, multiplication and division, and addition and subtraction—using the pemdas mnemonic.

Discover the heart of algebra by defining algebra, distinguishing algebraic from numerical expressions, and identifying terms, variables, constants, coefficients, and like terms.

Explore the commutative and associative properties of addition and multiplication, with examples. Learn the identity properties for addition (zero) and multiplication (one), and apply the distributive property to simplify expressions.

Learn to simplify algebraic expressions by applying distributive property, combining like terms, and evaluating expressions with integers and absolute values for digital SAT prep.

Explore the coordinate system by extending a number line into a coordinate plane, using ordered pairs (x, y) to plot points, identify quadrants, and interpret x- and y-intercepts.

Explore how transformations manipulate shape position, size, and orientation, distinguishing rigid translations from non rigid dilations, and illustrate translating points and triangles using ordered pairs.

Explore how reflections flip figures across lines of symmetry in the coordinate plane, keeping one coordinate fixed while negating the other, with x-axis and y-axis examples.

Explore how rotation moves a shape about a fixed point, including 90, 180, and 270 degree counterclockwise turns, with coordinate rules like (-y, x) and (-x, -y).

Explore dilation, a transformation that scales a figure by a scale factor k by multiplying coordinates; k>1 enlarges, 0<k<1 reduces, illustrated by scaling a triangle.

Learn the properties of equality, including addition, subtraction, multiplication, and division, to manipulate both sides of an equation, along with reflexive, symmetric, transitive, and substitution properties for solving problems.

Explore inverse operations to undo equations and isolate x, and identify coefficients as numbers in front of variables while recognizing and combining like terms.

Learn how to identify the domain and range of a relation and determine whether a set of ordered pairs defines a function. Explore function notation f(x) and evaluating functions.

Explore perimeters and areas by applying formulas to rectangles and triangles, using perimeter as the boundary distance and area as the enclosed surface in square units.

Learn to solve equations by isolating the variable, moving terms across sides, applying the distributive property, and combining like terms to recognize one, infinite, or no solutions.

Explore solving inequalities by isolating the variable, moving terms across the inequality, and flipping the sign when multiplying or dividing by negatives, then graph the solution on the number line.

Graph linear inequalities by treating them as lines, then decide the boundary style (solid if equals, dashed otherwise) and shade the correct region using a test point.

Concept 030 teaches setting up percent equations by translating verbal statements into equations using is (equals), of (times), and percent; solve for x and convert decimals to percent.

Explore how price markup uses percentages to calculate the final sales price from cost, and express the markup as dollars or as a percent of cost.

Learn how discounts reduce an item's original price to the sale price, using either the discount amount or the percent of the original price.

Apply the simple interest formula i = p r t to calculate interest from principal, rate, and time, with examples and methods to derive the rate from total payments.

Explore how rate of change measures how one quantity changes with another, including positive, negative, and zero rates, and identify constant versus non-constant rates in linear relationships.

Explore slope as the constant rate of change for a line, defined by rise over run and computed from two points using (y2−y1)/(x2−x1), including vertical undefined and horizontal zero cases.

Explore the slope-intercept form y = mx + b to identify slope and y-intercept, convert other equations to this form, and graph lines from examples.

use the point-slope form to find a line through two points, and learn parallel and perpendicular slope relationships and how to handle intercepts.

Learn to manipulate inequalities with the addition and subtraction properties, and apply multiplication and division rules, including flipping the inequality when multiplying or dividing by negatives, for efficient solving.

Practice solving inequalities by applying the distributive property, combining like terms, and isolating x, including flipping the inequality when dividing by a negative number.

Learn to solve compound inequalities using and or, graph the solutions on number lines, and express results in set notation by finding intersections and unions of partial inequalities.

Learn to solve absolute value inequalities by splitting into two cases, use intersection for less-than scenarios and union for greater-than ones, and graph results on the number line.

Learn to solve systems of equations by graphing, identify intersections as solutions, and distinguish one, no, or infinite solutions using parallel or coincident lines and x- and y-intercepts.

Master the substitution method for solving systems of equations by solving for one variable and substituting into the other, with examples illustrating solutions and no solution cases.

Master solving systems of equations using the elimination method by adding equations to cancel a variable, then substituting back to find both variables.

Graph systems of inequalities by plotting lines, identifying intercepts, and shading the feasible region. Determine the intersection of the regions to find the solution set, noting solid and dotted lines.

Apply the zero product property to solve real-number equations by setting each factor to zero, e.g., (x-2)(x-3)=0 gives x=2 or 3, x^2=5x gives x=0 or x=5.

learn to factor algebraic expressions by identifying the greatest common factor, applying the distributive property, and using factoring by grouping for four-term polynomials.

Factor a quadratic trinomial by rewriting it as a product of two binomials, choosing factors through trial and error to match the middle term.

master factoring the difference of squares using a plus b or a minus b. apply gcd and grouping to polynomials like x^2−49 and 2x^4−32.

Factor perfect square trinomials by recognizing a^2 and b^2 with a middle term of ±2ab, forming (a ± b)^2, as shown in (6y-4)^2 and (2x+5)^2.

Covers the quadratic function f(x)=ax^2+bx+c (a != 0) and its parabola. Explains axis of symmetry x = -b/2a, the vertex, and the y- and x-intercepts.

Learn to solve quadratic equations by factoring, identify the roots (zeros) as the x-intercepts, and apply the zero product property through step-by-step examples.

Learn to complete the square to convert quadratic expressions into a perfect square, ensure the x^2 term has coefficient 1, compute C as (B/2)^2, and solve by taking square roots.

Solve quadratic equations using the quadratic formula, a standard form ax^2+bx+c=0 with a not equal to zero; compute x = (-b ± sqrt(b^2 - 4ac)) / (2a).

Explore how the discriminant, B^2 minus 4AC, determines the roots in a quadratic equation. Identify the four conditions for real rational, real irrational, and complex roots with examples.

Learn how quadratic functions use vertex form y = a(x-h)^2 + k to reveal the vertex (h,k), the axis of symmetry x=h, and how a shapes opening and width.

Explore horizontal and vertical translations of quadratic functions in vertex form, shifting right or left by h and up or down by k, while a controls opening and width.

Learn how to graph quadratic inequalities by treating the boundary as a parabola, choosing solid or dashed lines, testing a point inside or outside, and shading the solution region.

Explore the laws of exponents, including product and quotient rules, negative exponents, power of a power, and power of a product, with practical examples.

Explores monomials, their simplified form, and rules for exponents, including negative exponents and radicals. It covers finding greatest common factors and combining monomials through multiplication, division, and power rules.

Learn to multiply binomials using the foil method (first, outer, inner, last) and extend to binomial and trinomial multiplication with the distributive property, including combining like terms.

Explore special products for factoring polynomials using the square of a sum, square of a difference, and the product of a sum and a difference, illustrated by 2x+5 and 2x-5.

Explore polynomials as sums of monomials, identify terms and like terms, determine degree and leading coefficient, and recognize the constant term in polynomial functions.

Learn to divide polynomials by monomials and polynomials using exponent rules, long division, and the division algorithm, with examples showing cancellation and zero remainder.

Discover synthetic division for dividing polynomials by a binomial, obtain quotients and remainders, and apply the remainder theorem; practice synthetic substitution to evaluate functions.

Graph polynomial functions by building value tables, plotting points, and analyzing behavior as x approaches infinity, considering even/odd degree, zeros, sign changes, and turning points.

Master polynomial equation solving by transforming into quadratic form, factoring, and applying the zero-product property. Practice covers difference of squares, square roots, and extracting all roots from multiple exercises.

Apply the factor theorem to determine if x minus a is a factor by evaluating f(a) and using synthetic substitution, with examples like x minus 1 and x plus 5.

Explore the fundamental theorem of algebra, showing every nonzero polynomial has a complex root, with examples of real, imaginary, and multiple roots across degrees.

Explore exponential functions, y = a b^x, covering domain all real numbers, positive or negative range, 1-1 and continuous, x-axis asymptote, and y-intercept a, with graphing examples.

Learn how exponential functions transform via y = a b^(x−h) + k, including horizontal shifts, vertical translations, and reflections. Explore how a's magnitude controls stretch or compression with real examples.

Explore exponential growth with y = a b^x and y = c(1 + r)^t, where c is initial amount and r the growth rate, for population and virus spread.

Explore exponential decay and depreciation, using the formula y = C(1 − r)^t to model how initial amounts shrink over time with units and rates.

Learn how compound interest extends exponential growth by using the compounding term n to show how often interest is calculated, via the formula A = P(1+R/N)^(N T).

Rationalize denominators by multiplying by radicals or conjugates, using the difference of squares method. Simplify expressions to eliminate radicals in the denominator and present the simplest form.

Apply the product property of radicals to separate and simplify expressions under radicals, for even and odd roots, with examples illustrating how to break multi-term radicals into separate radicals.

Explore the quotient property of radicals to simplify fractions under a square root by separating numerator and denominator. See the square root of nine over four equals three halves.

Explore properties of radicals, multiply and simplify radicals using FOIL, rationalize denominators with conjugates, and combine like terms in addition and subtraction of radical expressions.

Explore the square root property by solving x^2=n with plus or minus roots, illustrated through examples like 36, 25, and 9, and connect to difference of squares and perfect squares.

Solve radical equations by raising both sides to the root's index, using square and cube roots, and verify solutions to avoid extraneous results.

Apply radical inequality solving by ensuring the radical is defined (even roots require nonnegative radicands), then intersect domain conditions with the inequality solution and verify.

Learn to simplify complex fractions by treating division as multiplication, flipping the second fraction, and canceling terms in the numerator and denominator, using common-denominator techniques.

Explore rational exponents, convert between radical form and exponent form for any real number and positive integer n, and apply exponent laws to simplify roots.

Solve exponential equations by equalizing bases and equating exponents; rewrite numbers to a common base, then apply exponent rules to find solutions.

Master simplifying rational expressions by factoring polynomials, canceling common factors, and recognizing domain exclusions where the denominator is zero.

Learn to solve rational equations by eliminating fractions, cross-multiplying with the LCD, and isolating x through distributing and combining like terms with examples.

Explore the six basic trigonometric functions—sine, cosine, tangent—and their reciprocals cosecant, secant, cotangent—using right-triangle definitions of opposite, adjacent, and hypotenuse to solve example problems.

Explore cofunctions: sine and cosine of complementary angles, with key identities such as sin x = cos(90 degrees minus x) and related sums. Apply to right-triangle and complementary-angle problems.

Study special right triangles, 30-60-90 and 45-45-90, with their simple side ratios and trig values. Use sine, cosine, tangent, and complementary angles to solve for unknowns.

Learn how angles of elevation and depression describe line-of-sight in right triangles, with practical examples like boats and lighthouses, jet descent, and distance calculations using tangent.

Learn radians as an angle measure where the intercepted arc equals the radius, connect to circumference 2πr, and apply conversion formulas with examples like 130° to 13π/18.

Explore imaginary numbers and the imaginary unit i, including powers of i, how to simplify expressions with complex numbers, conjugates, and the rules for radicals and combining like terms.

Explore adding and subtracting functions and computing their product and quotient, with attention to combining full terms, domain restrictions to avoid division by zero, and example calculations.

Learn how to compose functions when the range of g lies in the domain of f by plugging g(x) into f(x), noting that order matters and it is not multiplication.

Explore inverse functions and inverse relations by swapping domain and range. Learn to find the inverse by solving for y and verify inverses via f(g(x)) and g(f(x)) equal the identity.

Explore sequences and arithmetic sequences, identify the first term and common difference, and use a_n = a1 + (n-1) d to find any term, including a10, with positive integer order.

Define geometric sequences through the common ratio, apply the formula a_n = a_1 r^{n-1}, and practice finding terms from examples.

Define points, lines, and planes as undefined terms; describe points as locations with no size, lines as thicknessless and infinite, straight, and planes as infinite surfaces extending in all directions.

Explore the types of lines, including line segments with end points, rays with one end point extending to infinity, opposite rays, and how lines intersect when they are not parallel.

Explore essential postulates and axioms that form the foundation of mathematical reasoning, and apply them to solve digital SAT math problems.

Explore how to determine the coordinates of a point on the coordinate plane using x and y values, and apply these concepts to SAT math problems.

Delve into midpoints and segment bisectors, learning how to locate a midpoint and apply bisector concepts to geometric problems, with SAT math prep strategies.

Identify the vertex and sides of an angle, distinguish interior from exterior, classify acute, right, obtuse, and straight angles, and apply angle addition to find measures in degrees.

Explore congruent, adjacent, vertical, linear pair, complementary, and supplementary angles, learn to denote congruence with arcs, and solve problems using angle relationships.

Learn how angle bisectors split a vertex angle into two congruent parts, with examples, and how perpendicular bisectors find midpoints and equal segments, including solving for x from 3x+6.

Learn to find midpoints on a number line and coordinate plane using averages, and to calculate distances between points with the distance formula derived from the Pythagorean theorem.

Explore concept 107 polygons in the Math Rocket digital SAT math prep course to strengthen your ability to solve polygon-related questions.

Explore the properties of congruence in geometry, including reflexive, symmetric, and transitive. Learn to construct two-column and paragraph proofs with angle and segment examples and definitions such as supplementary angles.

Explores the concept of congruency of angles, showing vertical angles are congruent and how supplementary and complementary relationships lead to congruent angles; includes examples solving for x.

Explore lines and angles by comparing parallel lines and transversals, identify interior and exterior angle pairs, and apply congruent or supplementary relationships to solve for x.

Explore how parallel and perpendicular lines relate: lines parallel to the same line are parallel, and a line perpendicular to one of two parallel lines is perpendicular to the other.

Learn that the sum of interior angles in a triangle equals 180 degrees, solve for missing angles, and apply the exterior angle equals the sum of the remote interior angles.

Learn how congruent figures and polygons share the same size and shape, with corresponding parts congruent and vertices named in the same order, plus the third angles congruency principle.

Identify the four primary methods to prove congruent triangles: side-side-side, side-angle-side, angle-side-angle, and angle-angle-side, noting that angle-angle-angle cannot prove congruence.

Learn isosceles triangles, their legs and base angles, and how congruent sides arise; explore angle bisectors and SAS-based triangle congruence.

Explore right triangle congruency by using a shared hypotenuse and a pair of corresponding legs to prove right triangles are congruent, then determine angle measures from examples.