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COMEDK UGET Mathematics - Calculus, Coordinate Geometry and Statistics Flashcards
50 question-and-answer cards covering Mathematics - Calculus, Coordinate Geometry and Statistics as it is examined in COMEDK UGET. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics - Calculus, Coordinate Geometry and Statistics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the rule for ∫₋ₐᵃ f(x) dx for even and odd functions.
If f is even: 2∫₀ᵃ f(x) dx. If f is odd: 0.
Give the formula for the area under y = f(x) ≥ 0 between x = a and x = b.
Area = ∫ₐᵇ f(x) dx.
Give the formula for the area between two curves y = f(x) and y = g(x) with f ≥ g on [a,b].
Area = ∫ₐᵇ [f(x) − g(x)] dx.
What is the order and degree of a differential equation?
Order = highest derivative present; degree = power of the highest-order derivative after the equation is made polynomial in derivatives (rational, radical-free).
Describe the method for solving a variable-separable differential equation.
Write dy/dx = g(x)h(y), separate as dy/h(y) = g(x) dx, then integrate both sides.
State the standard form and integrating factor of a linear first-order ODE.
dy/dx + P(x)y = Q(x); integrating factor I.F. = e^∫P dx; solution: y·(I.F.) = ∫Q·(I.F.) dx + C.
What substitution solves a homogeneous differential equation dy/dx = F(y/x)?
Let y = vx, so dy/dx = v + x(dv/dx), converting it into a variable-separable equation in v and x.
Give the magnitude of vector a = a₁i + a₂j + a₃k and the unit vector along a.
|a| = √(a₁²+a₂²+a₃²); unit vector = a/|a|.
Define the dot product a·b and give its geometric formula.
a·b = a₁b₁+a₂b₂+a₃b₃ = |a||b|cos θ, where θ is the angle between them.
Define the cross product a×b: its magnitude and direction.
|a×b| = |a||b|sin θ; direction perpendicular to both a and b (right-hand rule). It equals the determinant |i j k; a₁ a₂ a₃; b₁ b₂ b₃|.
How do you test whether two vectors are perpendicular or parallel?
Perpendicular ⇔ a·b = 0. Parallel ⇔ a×b = 0 (components proportional).
Give the formula for the projection (scalar) of a onto b.
Scalar projection = (a·b)/|b|; vector projection = [(a·b)/|b|²] b.
What does the scalar triple product [a b c] represent geometrically, and when is it zero?
[a b c] = a·(b×c) = volume of the parallelepiped; it is 0 when the three vectors are coplanar.
Give the area of a triangle with two sides as vectors a and b from one vertex.
Area = (1/2)|a × b|.
Give the slope-intercept and point-slope forms of a straight line.
Slope-intercept: y = mx + c. Point-slope: y − y₁ = m(x − x₁).
Give the distance from point (x₁, y₁) to line ax + by + c = 0.
Distance = |ax₁ + by₁ + c| / √(a²+b²).
What is the condition for two lines with slopes m₁ and m₂ to be perpendicular, and the angle formula between them?
Perpendicular ⇔ m₁m₂ = −1; angle θ: tan θ = |(m₁ − m₂)/(1 + m₁m₂)|.
Give the standard equation of a circle with centre (h, k) and radius r, and the general form.
(x−h)² + (y−k)² = r². General: x²+y²+2gx+2fy+c=0 with centre (−g,−f) and r = √(g²+f²−c).
State the standard equation of a parabola opening rightward and its focus and directrix.
y² = 4ax; focus (a, 0); directrix x = −a; vertex at origin.
Give the equation of an ellipse (a>b) with its eccentricity formula.
x²/a² + y²/b² = 1; e = √(1 − b²/a²), with 0 < e < 1; foci at (±ae, 0).
Give the equation of a hyperbola and its eccentricity formula.
x²/a² − y²/b² = 1; e = √(1 + b²/a²), with e > 1; foci at (±ae, 0).
Give the direction cosines relation and the distance between points (x₁,y₁,z₁) and (x₂,y₂,z₂) in 3D.
l²+m²+n² = 1 (direction cosines); distance = √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²].
State Bayes' Theorem.
P(Eᵢ|A) = [P(Eᵢ)·P(A|Eᵢ)] / Σⱼ P(Eⱼ)·P(A|Eⱼ), for a partition {Eⱼ}.
State the conditions and objective of a Linear Programming Problem (LPP), and where the optimum occurs.
Maximize/minimize a linear objective function subject to linear inequality constraints with non-negative variables; the optimum (if it exists) occurs at a corner (vertex) of the feasible region.
What this deck covers
The Mathematics - Calculus, Coordinate Geometry and Statistics deck follows the COMEDK UGET Mathematics - Calculus, Coordinate Geometry and Statistics syllabus — 5 chapters and 16 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 75 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics - Calculus, Coordinate Geometry and Statistics flashcards FAQ
How many Mathematics - Calculus, Coordinate Geometry and Statistics flashcards are in this COMEDK UGET deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these COMEDK UGET flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Mathematics - Calculus, Coordinate Geometry and Statistics cards cover?
They follow the COMEDK UGET Mathematics - Calculus, Coordinate Geometry and Statistics syllabus — 5 chapters and 16 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.