AP Intermediate Mathematics (BIEAP) study guide
AP Intermediate Mathematics (BIEAP) · Work through your exam, one topic at a time.
The AP Intermediate Mathematics examination is the mathematics component of the Intermediate Public Examination conducted by the Board of Intermediate Education, Andhra Pradesh (BIEAP) for students in the two-year intermediate programme that bridges secondary school and university study in Andhra Pradesh. It matters most to Intermediate second-year candidates who need the subject for their Intermediate certificate and for admission into engineering, science and other degree courses, and to repeaters completing a backlog. The AP Intermediate Mathematics (BIEAP) study guide has 9 sections and about 2,925 words.
01Algebra
Algebra in the BIEAP Intermediate Public Examination (IPE) Mathematics papers covers functions, mathematical induction, matrices and rank, complex numbers, quadratic expressions, theory of equations, permutations and combinations, the binomial theorem and partial fractions. The exam rewards clean, justified steps: a 7-mark question wants the method shown, not a bare answer.
379 words, about 2 min02Trigonometry
Trigonometry in the IPE papers tests transformations (sum-to-product and product-to-sum), general solutions of trigonometric equations, inverse trigonometric functions, hyperbolic functions, and the properties of triangles with sine rule, cosine rule, projection, tangent rule, half-angle formulae and radii. sin C + sin D = 2 sin((C+D)/2) cos((C−D)/2); the companion forms for sin C − sin D and cos C ± cos D are examined together.
349 words, about 2 min03Analytical Geometry
Analytical geometry in the IPE papers means the circle, the conic sections (parabola, ellipse, hyperbola) and polar coordinates. Expect questions on centre and radius, tangents and normals in Cartesian and parametric form, chords of contact, families of circles, eccentricity, asymptotes and the conversion between polar and Cartesian coordinates.
350 words, about 2 min04Differential Calculus
Differential calculus in the IPE papers runs from limits, continuity and differentiability through the standard derivative rules, implicit and parametric differentiation, logarithmic differentiation and second derivatives, into applications: tangents and normals, rates of change and maxima–minima of a function on an interval. f is continuous at a if the left limit, right limit and f(a) agree; differentiability is stronger and implies continuity.
272 words, about 1 min05Integral Calculus
Integral calculus in the IPE papers covers indefinite integration by standard forms, substitution and integration by parts, partial fractions, trigonometric integrals and reduction formulae, plus definite integrals and their symmetry properties, ending with area under a curve. Standard forms: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1; ∫dx/x = ln x + C; ∫eˣ dx = eˣ + C.
310 words, about 2 min06Differential Equations
Differential equations in the IPE papers test order and degree, formation of a differential equation by eliminating arbitrary constants, and the three standard solution methods: variables separable, homogeneous substitution, and the first-order linear equation. Applications to growth and decay also appear.
294 words, about 1 min07Vectors
Vector algebra in the IPE papers covers addition and scalar multiplication, the scalar and vector products, the scalar triple product, coplanarity, vector equations of lines and planes, and geometric applications such as area of a triangle and volume of a parallelepiped. a·b = a b cos θ; a×b = a b sin θ n̂, with n̂ perpendicular to both and following the right-hand rule.
330 words, about 2 min08Probability and Statistics
This domain covers conditional probability and Bayes' theorem, random variables, the binomial and Poisson distributions, and the statistics of dispersion: range, mean deviation, variance, standard deviation and coefficient of variation. Conditional probability P(A B) = P(A ∩ B)/P(B); the total probability theorem builds the denominator for Bayes' theorem.
249 words, about 1 min09Coordinate Geometry in Three Dimensions
Three-dimensional coordinate geometry in the IPE papers covers direction cosines and direction ratios, the angle between lines, equations of planes in general, normal and intercept form, distance of a point from a plane, the angle between planes, and the symmetric form of a line together with line–plane intersection conditions. Direction cosines l, m, n satisfy l² + m² + n² = 1; direction ratios a, b, c are proportional to them.
392 words, about 2 min