Algebra
Algebra is a branch of mathematics where we use letters to stand for unknown numbers. These letters are called variables. In UPSC exams, algebra helps us solve problems where we do not know the exact values initially. For example, if we know the total price of apples and oranges but not their individual prices, we use 'x' and 'y' to find them. The most basic part of algebra is an equation. An equation is a statement that says two mathematical expressions are equal.
Concepts (3)
This involves comparing different variables based on a single long equation. For example, if p - 200 = q + 200, then p must be larger than q. This is because you have to subtract a value from p just to make it equal to q when something is added to q.
This involves comparing different variables based on a single long equation. For example, if p - 200 = q + 200, then p must be larger than q. This is because you have to subtract a value from p just to make it equal to q when something is added to q. UPSC often uses large years like 2024 or 2025 in these equations to distract you. Ignore the large numbers and focus on the plus and minus signs.
This concept deals with the possible values a variable can take between two limits. If X is between 1 and 3, we write 1 < X < 3. When we square these numbers, the range changes. For X squared, the range becomes 1 to 9.
This concept deals with the possible values a variable can take between two limits. If X is between 1 and 3, we write 1 < X < 3. When we square these numbers, the range changes. For X squared, the range becomes 1 to 9. Be very careful with negative numbers. If Y is between -1 and 1, then Y squared is between 0 and 1 because a square value can never be negative in basic algebra.
A linear equation represents a straight line on a graph. The standard form is y = mx + c. In this formula, 'm' is the slope and 'c' is the y-intercept.
A linear equation represents a straight line on a graph. The standard form is y = mx + c. In this formula, 'm' is the slope and 'c' is the y-intercept. If a point (x, y) lies on the line, you can plug those specific numbers into the equation to find the unknown values. For example, if a line y = mx + 2 passes through the point (2, 6), you substitute x=2 and y=6 to get 6 = 2m + 2. Solving this gives m = 2.
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Start Lesson: Relative Magnitude Comparison