Commerce Exam > Commerce Notes > Mathematics (Maths) Class 11 > Past Year Paper, Maths(Set - 5), 2016, Class 11, Mathematics
Past Year Paper, Maths(Set - 5), 2016, Class 11, Mathematics | Mathematics (Maths) Class 11 - Commerce PDF Download
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FAQs on Past Year Paper, Maths(Set - 5), 2016, Class 11, Mathematics - Mathematics (Maths) Class 11 - Commerce
| 1. How do I solve quadratic equations by factoring? |  |
Ans. To solve quadratic equations by factoring, follow these steps:
1. Write the equation in the form ax^2 + bx + c = 0.
2. Factor the quadratic expression on the left side of the equation.
3. Set each factor equal to zero and solve for x.
4. Check the solutions by substituting them back into the original equation.
Example: Solve the equation x^2 + 5x + 6 = 0.
Step 1: Write the equation in the form (x + )(x + ) = 0.
Step 2: Factor the quadratic expression: (x + 2)(x + 3) = 0.
Step 3: Set each factor equal to zero: x + 2 = 0 and x + 3 = 0.
Step 4: Solve for x: x = -2 and x = -3.
Step 5: Check the solutions: Substitute -2 and -3 back into the original equation to ensure they satisfy it.
| 2. How can I find the vertex of a parabola? | |
Ans. To find the vertex of a parabola, follow these steps:
1. Write the equation of the parabola in the form y = ax^2 + bx + c.
2. Use the formula x = -b/2a to find the x-coordinate of the vertex.
3. Substitute the x-coordinate of the vertex into the equation to find the y-coordinate.
Example: Find the vertex of the parabola y = 2x^2 + 4x - 3.
Step 1: The equation is already in the required form.
Step 2: Calculate x = -b/2a = -4/(2*2) = -1.
Step 3: Substitute x = -1 into the equation: y = 2(-1)^2 + 4(-1) - 3 = -1.
Therefore, the vertex is (-1, -1).
| 3. How do I solve a system of linear equations using substitution method? | |
Ans. To solve a system of linear equations using the substitution method, follow these steps:
1. Solve one equation for one variable in terms of the other variable.
2. Substitute this expression into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value of the remaining variable back into the expression obtained in step 1 to find the value of the first variable.
5. Check the solution by substituting the values into both original equations.
Example: Solve the system of equations:
2x + y = 5
x - y = 1
Step 1: Solve the second equation for x: x = 1 + y.
Step 2: Substitute x = 1 + y into the first equation: 2(1 + y) + y = 5.
Step 3: Simplify and solve for y: 2 + 2y + y = 5, 3y = 3, y = 1.
Step 4: Substitute y = 1 into x = 1 + y: x = 1 + 1 = 2.
Step 5: Check the solution: Substitute x = 2 and y = 1 into both original equations to ensure they satisfy them.
| 4. How do I find the domain and range of a function? | |
Ans. To find the domain and range of a function, follow these steps:
1. Determine the set of all possible x-values (inputs) for the function. This set is called the domain.
2. Determine the set of all possible y-values (outputs) for the function. This set is called the range.
Example: Find the domain and range of the function f(x) = 2x + 3.
Step 1: The function is a linear function, and there are no restrictions on the x-values. Therefore, the domain is all real numbers.
Step 2: The function is a linear function, and it can take any real number as an input. Therefore, the range is also all real numbers.
| 5. How do I find the equation of a line given two points? | |
Ans. To find the equation of a line given two points, follow these steps:
1. Calculate the slope of the line using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
2. Use the slope-intercept form of a line, y = mx + b, and substitute the slope and one of the points into the equation to find the y-intercept (b).
3. Write the final equation of the line using the slope (m) and the y-intercept (b).
Example: Find the equation of the line passing through the points (1, 3) and (4, 7).
Step 1: Calculate the slope: m = (7 - 3)/(4 - 1) = 4/3.
Step 2: Substitute the slope and one point (1, 3) into the slope-intercept form: 3 = (4/3)(1) + b.
Step 3: Solve for b: b = 3 - 4/3 = 5/3.
Therefore, the equation of the line is y = (4/3)x + 5/3.
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Dec 22, 2024 Last updated |
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