Junkao Mathematics - independent shared foundations study guide
Junkao Mathematics - independent shared foundations · Work through your exam, one topic at a time.
This independent study page provides practice for Junkao Mathematics - independent shared foundations. Its editorial learning areas include Functions and differential calculus; Trigonometry; Sequences and series; Vectors and solid geometry; Analytic geometry and conics; Algebra, sets and inequalities; Probability and statistics. The Junkao Mathematics - independent shared foundations study guide has 7 sections and about 3,021 words.
01Algebra and functions
Algebra and functions tests manipulation of polynomials and rational expressions, and the behaviour of functions as objects: domain, range, inverse, composition and graph transformations. Expect factor and remainder theorem questions, partial fractions, modulus equations and inequalities, and sketching transformed curves.
452 words, about 2 min02Sequences and series
Sequences and series examines arithmetic and geometric progressions, sigma notation, sums to infinity and the binomial expansion. You should be able to derive and apply the standard formulae, decide when an infinite sum converges, and extract a specified coefficient from a binomial expansion without expanding everything.
400 words, about 2 min03Trigonometry
Trigonometry tests radian measure, the reciprocal and Pythagorean identities, solving trigonometric equations over a stated interval, and combining sine and cosine into a single harmonic term. You should be fluent in both degrees and radians and know the exact values for the standard angles.
463 words, about 2 min04Differentiation and applications
Differentiation and applications tests the technique of differentiating standard, composite, product, quotient, implicit and parametric functions, and the use of derivatives to analyse curves: gradients, tangents and normals, stationary points, rates of change and optimisation. Standard results include d/dx(xⁿ) = nx^(n−1), d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x, d/dx(sin x) = cos x and d/dx(cos x) = −sin x, with angles in radians.
368 words, about 2 min05Vectors and three-dimensional geometry
Vectors and three-dimensional geometry tests vector arithmetic in column and i, j, k notation, magnitude and unit vectors, the scalar product, angles between vectors, and the vector equation of a line in three dimensions, including intersections and the classification of line pairs. The magnitude of a = (x, y, z) is a = √(x² + y² + z²), and for a nonzero vector the unit vector in its direction is a/ a .
388 words, about 2 min06Analytic Geometry
The Analytic Geometry domain connects algebra and shape: lines, distance and midpoint, circles, parabolas, ellipses, and hyperbolas described by equations. Questions typically supply a general second-degree equation and ask for center, radius, vertex, foci, axes, or asymptotes - or reverse the process and build an equation from described features.
491 words, about 2 min07Probabilidad y estadística: combinatoria, distribuciones e inferencia
Esta revisión editorial reúne combinatoria, probabilidad condicionada, modelos binomial y normal e inferencia elemental. Los contextos y distribuciones son ejercicios de fundamentos compartidos, no una afirmación del contenido o peso de una convocatoria regional.
459 words, about 2 min