ACET Exam Preparation for Math & Stat

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.

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.

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

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.

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.

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.

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