BCS-012: Basic Mathematics – IGNOU
Welcome to the BCS-012 course offered by IGNOU, designed specifically for students pursuing the Bachelor of Computer Applications (BCA) degree. This course, titled “Basic Mathematics for Computing,” serves as a fundamental building block for understanding various mathematical concepts essential in the field of computer science and information technology.
Throughout this course, you will gain proficiency in mathematical reasoning, problem-solving, and analytical skills, which are crucial for a successful career in computing. Whether you’re developing software, working on data analysis, or engaging in any technology-driven project, the mathematical principles learned in BCS-012 will be invaluable.
Introduction Of BCS-12
BCS-012 covers a range of topics that provide a strong mathematical foundation required for advanced studies and applications in computing. The syllabus includes subjects such as algebra, calculus, probability, and discrete mathematics, all of which are integral to solving computational problems and developing algorithms.
Understanding the Importance of BCS-12 Short Notes:
1. Overview : Brief notes reduce an extensive amount of material into essential ideas and points. They offer a rapid and effective means of studying the key subjects in advance of the examination.
2. Focus on the Essentials: You may focus on each topic’s key elements by summarizing the available information. This guarantees that you cover the most relevant subjects and helps in setting priorities for your study materials.
3. Improved Retention: Taking quick notes requires you to take an active role with the information. Compared to passive reading, active learning promotes improved understanding and retention of knowledge.
4. Quick Reference: Brief notes are a quick reference that come in helpful when making last-minute changes. To fast brush up on specific concepts or formulas, you can swiftly scan them.
5. Time management: You may cover a lot of ground in less time by taking brief notes. This is very helpful if you don’t have much time to study before the test.
Most Repeated BCS-12 Important Questions for IGNOU BCA Exams Semester Wise :
Topic – Determinants
Q1. Determinants of order
| b+c c+a a+b |
| b+c c+a a+b |
| b+c c+a a+b |
Q2. find the area of the triangle whose vertices are :
(-3, 5 ) , (3, -6 ), (7, 2)
A (1, 3 ) , B (2, 2 ), (0, 1)
Q4.Cramer Rule
x + 2y – z = 1 , 3x + 8y + 2z = 28, 4x + 9y + z = 14
x + y + z = 5 , y + z = 2 , x + z = 3
Q4.The exponent of a square
matrix :
Let A =| 2 3| and f (x) = x ^ 2 – 4x + 7. Show that f (a) = O upon 2*2. Hence find A ^ 50
|-1 2|
Q5.Inverse Matrixs :
3x + 4y + 7z = 14 , 2x – y + 3z + 4 , x + 2y – 3z = 0
3x + 4y + 7z = -2 , 2x – y + 3z = 6, 2x + 2y – 3z = 0
Q6. If a= |½ underroot -3/2| , find A ^ 3
|underroot -3/2 ½|
If A=|1 -1 2|
|0 4 7|
|3 2 1 | show that A is a row equivalent to I upon 3 .
Topic – Matrix
Q1. Determine the rank of matrix
|0 1 2 1|
A=|5 3 14 4|
|1 -1 2 0|
Q2. Show that 8 divides 3 ^ 2n – 1 ∀ εN (for all, epsilon.)
Q3. Use the principle to show that number for every natural number n
2 + 2 ^ 2 + ……….. + 2 ^ n = 2 ^ n + 1 – 2
1 ^ 3 = 2 ^ 3+ ……… + n ^ 3 = 1 / 4n ^ 2 ( n + 1 ) 2
Q4. Find the sum of all integers between 100 and 1000 which are divisible by 9
Q5. Find the sum of first all integer between 100 and 1000 which are divisible by 7
Topic – Arithmetic Progression (A.P.)
Q1. 0.4 + 0.44 + 0.444 + ….. Find the n terms.
Q2. If the 7th time of an AP is equal to 11th times the 11th term of the A.P., find the 18th term.
32x ^ 3 – 48 ^ 2 + 22x – 3 = 0, give the roots are in A.P.
Topic – Geometric Progression (G.P.)
Q1.The common ratio of a G.P. is -4 / 5 and the sum of infinity is 80 / 9. Find the term of the G.P.
Q2. How many terms of the GP under root 3, 3, 3 under root 3, .….Add upto 39 + 13 under root 3.
Q3. Solve the equation 8 ^ 3 – 14 + 7x – 1 = 0, the roots being in G.P.
Topic – DeMoivre’s theorem
Q1. i + under root of 3^ 3.
Q2. 1 + i 1 ^ 8
Topic – Cube Roots of Unity
Q1. If 1, ω, ω^2 are cube roots of units, show that :
Q2. ( 1+ω ) (1 + ω ^ 2) (1 + ω ^ 3) (1 + ω ^ 4) (1 + ω ^ 6) (1 + ω ^ 8) = 4.
Topic – Quadratic Equations
Q1. m – n / m + n , m + n / m – n.
Q2. 2 – under root 3, 2 + under root 3.
Topic – Alpha and beta
Q1. If β and α are roots of x ^ 2 – 2 k x + k ^ 2 – 1 = 0,β and α = 10, find k.
Q2. If β and α are roots of x ^ 2 – 4 a x + 4 ^ 2 – 9 = 0, β ^ 2 and α ^ 2 = 26, find a.
Q3. Find the two numbers whose sum is 54 and the product is 629.
Topic – Inequality
Q1. 15x ^2 + 4x – 4 >=0. x – 4 / 2 <= 5/ 12.
Topic – Differentiate of parametric forms
Q1. If y = lnx / x , show that d^2y / dx^2 = 2lnx – 3/x^3. Dec 16, 17 y = ae ^ mx = be ^ mx + 4x , show that d ^ 2y / dx ^ 2 = m ^ 2 ( y – 4 )
Topic – Rate of Change of Quantities
A spherical balloon is being inflated at the rate of 900 cubic centimeters per second. How fast is the radius of the balloon increasing when the radius is 15cm?
Topic – Increasing And Decreasing functions
Q1. f(x) = 16x ^ 2 + 3x + 2.
Q2. f(x)= 1 + x = x ^ 2 / 1 – x + x ^ 2, x ε R.
Topic – Local maxima and local minima
Q1. f(x) = x ^ 3 – 6x ^ 2 + 9x + 100.
Topic – Integral
Q1. I= dx / 1 + 3e + 2e ^ 2x.
Q2. X underroot of 3-2x , dx.
Q3. dx / e ^ 3 + 1.
Topic – Length of Curves
Q1. Find the length of y = 3 + x from (1 ,4 ) to ( 3,6 ).
Topic – Vector and Coplanar
Q1. a = 2i – 4j + 3k , b = λi – 2j + k , c = 2i + 3j + 3k.
Topic – Component of a vector
Q1. Prove that the three medians of a triangle meet a point called the centroid of the
triangle which divides each of the medians in the ratio of 2:1.
Q2. If the mid-points of the consecutive sides of a quadrilateral are joined, they show
by using vectors that they form a parallelogram.
Topic – Area of the parallelogram
Q1. Find the area of the triangle with vertices are :
A ( 1 , 3 ), B ( 2, 2),C ( 0 , 1)
Topic – Straight Line passing direction
Q1. ( 1 , 2 , 3 ) and ( -1 , 1 , 0)
Q2. Determine the value of x for which f ( x ) = 5x ^ 3/2 , x > 0.
Topic – Vector and Cartesian
Q1. ( 1 , -1 , -2 ) and 3i – 2j + 5k.
Topic – Shortest distance
Q1. r = (i — 7 j — 2k ) + t (i + 3 j + 2k ).
Topic – Cost Minimisation
Q1. A diet for a sick person must contain at least 1400 units of vitamins, 50 units of
minerals, and 1400 calories. Two foods A and B are available for Rs 4 and Rs 3 per
unit, respectively. If one unit A contains 200 units of vitamins, one unit of mineral
and 40 calories, and one unit of food B contains 100 units of vitamins, two units of
minerals, and 40 calories. Find what combination of food is used least cost ?
Some Playlist that may be helpful in Preparation:
Read More : ECO-01(Business Organisation) Important Short Notes| Expected Question |IGNOU BCA|
Conclusion:
With these IGNOU BCS-012 BCA short notes, you’ll be well-equipped to tackle your exams with confidence. Remember to complement your study efforts with regular practice and mock tests. Good luck!
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