ACET Exam Preparation for Math & Stat

Learn numerical methods by using calculators accurately, mastering rounding, decimal places, and significant figures for reliable final answers in exams. Explore practical techniques with scientific calculators, logs, and nested multiplication.

Explains exponential and logarithmic fundamentals, including e^x expansion, natural log properties, inverse relations, and basic graph behavior; covers absolute value, roots, and factorial concepts.

Explore algebraic expressions by mastering polynomials, exponents, and binomial expansions, solve quadratic equations and inequalities, study arithmetic and geometric progressions, and apply logarithms and their laws for simplification.

Master quadratic equations using factoring, completing the square, and the quadratic formula, with discriminants and roots explained. Learn to solve simultaneous equations by elimination and substitution for efficient exam prep.

Explore solving inequalities with interval analysis, sign charts, and factoring, and apply the arithmetic-geometric mean inequality to understand equality conditions.

Learn arithmetic and geometric progressions by identifying the first term and common difference or ratio, computing sums of first n terms, and understanding convergence and finite limits.

Master binomial expansions using the binomial theorem and Pascal's triangle, derive coefficients for negative and fractional exponents, and apply to sqrt expansions and practical approximations.

Express quantities as percentages, compute absolute and percentage changes, and analyze errors with real-world examples. Study dimensions, linear interpolation, complex numbers, and sequences to strengthen numerical methods.

Explore dimensions and units and how they affect measurements. Apply interpolation, extrapolation, and iteration using linear interpolation and Newton-Raphson to approximate values.

Explore complex numbers, mastering addition, subtraction, and multiplication, and compute modulus, argument, and conjugates using the unit circle and the e to the i theta form.

develop and solve linear difference equations with constant coefficients by using the characteristic equation; determine constants from initial values, illustrated with distinct real, complex, and repeated roots.

Explore limits, including how 1/(x-1) diverges as x approaches 1 from either side, and introduce limits at infinity with order notation such as big O and little o.

Differentiate by defining the derivative as the gradient of a curve via a limit, dy/dx. Apply the product, quotient, and chain rules, with standard functions, logs, and exponentials.

Explore higher order derivatives and the second derivative method to locate stationary points, maxima, minima, and inflection points, with practical examples and graphing guidance.

Master partial differentiation, computing first and second order derivatives with respect to x and y, and apply Lagrangian multipliers for constrained optimization, as in maximizing a rectangle’s area.

Master the integration of standard functions by applying antiderivatives, indefinite and definite integrals, and computing area under curves while handling sign changes through splitting integrals.

Explore core integration techniques—integration by inspection, substitution with variable changes, and integration by parts—plus partial fractions for decomposing complex fractions, with worked examples.

Explore convergence of improper integrals and evaluate double integrals to compute volumes under surfaces, including techniques for changing the order of integration and assessing when limits exist.

Explore numerical integration with the trapezoidal rule to approximate areas under curves when exact integration fails, compare to the true integral, and preview Taylor and Maclaurin expansions.

Explore methods for solving differential equations, including separation of variables and integrating factor, with boundary and initial conditions to obtain particular and general solutions.

Learn vector basics in two and three dimensions, covering addition, scalar multiplication, magnitude, unit vectors, dot and cross products, angles, orthogonality, and matrix operations such as transpose and determinants.

Explore matrices basics: size, transpose, addition and subtraction, symmetry, scalar and matrix multiplication, identity matrix, and determinant with minors and cofactors, noting noncommutativity.

Learn to find inverses of 2x2 matrices using the determinant and sign changes; verify with products; solve linear systems via inverses; and determine eigenvalues and eigenvectors from det(A-λI)=0 and (A-λI)v=0.

Learn to summarize data with statistical diagrams, distinguishing numerical and categorical data (discrete vs. continuous) and using bar charts and histograms for frequency analysis.

Master reading and comparing statistical diagrams such as live diagrams, dot plots, cumulative frequency plots, and box plots, using location, spread, and skewness to interpret two data groups.

Explore sample calculations for statistics, focusing on mean, median, and mode, including sample mean from lists and from grouped data using midpoints and frequency concepts.

Learn how the median resists extreme values and how to compute it from raw and grouped data, plus how a and b transform the mean.

Compute the range, lower and upper quartiles, and interquartile range from raw and grouped data, and interpret box plots for data sets.

Learn how to compute sample standard deviation and variance using n-1, explore the connection to population measures, and apply sum of squares and frequency methods to real data.

Compute the third-order central moment to assess skewness in sample data using mean, variance, and data transformations. Compare distributions with box plots to interpret symmetry and spread.

Define basic probability and the 0–1 range, including complements, two-event conditional probability, and the addition rule for mutually exclusive and non mutually exclusive events.

Explore probability basics, including independent events and the multiplication rule, plus conditional probability and dependent events with practical examples (dice, coins, buses, socks).

Explore advanced probability concepts: independent and dependent events, conditional probability, and tree diagram methods, through real-world examples and joint, marginal, and conditional calculations.

Explore permutations and combinations, learn when order matters, apply factorials and nPr/nCr to real problems like contests, lotteries, and team selections, and compute related probabilities.