math

• How many practice questions are included in the review video for the grade 10 math course?

  22 practice questions
• What is the total time the ministry of education suggests it should take to learn the entire grade 10 math course?

  110 hours
• What are the three methods to solve a linear system mentioned in the video?

  Graphing, substitution, and elimination
• What does solving a linear system involve?

  Finding the values of the variables that make both equations true
• What is the process to graph a linear equation in the form of \(y = mx + b\)?

  • Rearrange the equation to isolate \(y\)
  • Identify the slope \(m\) and y-intercept \(b\)
  • Plot the y-intercept on the graph
  • Use the slope to find another point
  • Connect the points with a straight line
• What is the slope and y-intercept of the equation \(x - y = 5\) after rearranging it?

  Slope is 1, y-intercept is -5
• How do you interpret the slope in the context of graphing a line?

  Slope represents the rise over run between points on the line
• What is the slope and y-intercept of the equation \(3x + y = 3\) after rearranging it?

  Slope is -3, y-intercept is 3
• What is the solution to the system of equations given in the video?

  The solution is \(x = 2\) and \(y = -3\)
• How do you solve a linear system using elimination?

  By making the coefficients of one variable have the same absolute value and then adding or subtracting the equations
• What is the first step in using substitution to solve a linear system?

  Isolate one of the variables in either of the equations
• What is the final solution for the second example of the linear system?

  The solution is \(x = 1\) and \(y = 3\)
• How do you set up equations for a word problem involving sales of two types of shoes?

  1. Define variables (e.g., \(x\) for Adidas, \(y\) for Air Jensen)
  2. Create an equation for total pairs sold (e.g., \(x + y = 75\))
  3. Create an equation for total sales (e.g., \(82x + 95y = 6241\))
• What is the formula for calculating the midpoint between two points?

  Midpoint is \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\)
• How do you calculate the distance between two points using the distance formula?

  Distance is \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
• What is the distance between the two points calculated in the video?

  10 units
• What is the process to find the equation of a median in a triangle?

  1. Identify the vertex and the midpoint of the opposite side.
  2. Calculate the slope using the two points.
  3. Use the slope-intercept form \(y = mx + b\) to find the equation.
• What is the definition of a median in a triangle?

  A median is the line segment that joins a vertex to the midpoint of the opposite side
• What is the first step to draw a triangle given its vertices?

  Plot the vertices on a graph
• How do you find the equation of a line given two points?

  Calculate the slope and use one point to find the y-intercept
• How does the elimination method differ from substitution in solving linear systems?

  Elimination combines equations to eliminate a variable, while substitution replaces a variable with an expression
• What is the significance of the coefficients in the elimination method?

  They must have the same absolute value to eliminate a variable
• What is the purpose of rearranging equations into \(y = mx + b\) form?

  To easily identify the slope and y-intercept for graphing
• What is the total sales amount mentioned in the shoe sales problem?

  6241 dollars
• What does the term "combined pairs of shoes" refer to in the context of the problem?

  The total number of Adidas and Air Jensen shoes sold
• What is the cost of a pair of Adidas shoes as mentioned in the video?

  82 dollars
• What is the cost of a pair of Air Jensen shoes as mentioned in the video?

  95 dollars
• What is the relationship between the two equations formed in the shoe sales problem?

  They represent the total pairs sold and the total sales amount
• How do you determine which variable to isolate when using substitution?

  Choose the variable that is easiest to isolate based on the equation's coefficients
• What is the final step after finding the value of one variable in substitution?

  Substitute that value back into one of the original equations to find the other variable
• What is the significance of the point of intersection in graphing linear equations?

  It represents the solution to the system of equations
• What is the formula for the distance between two points derived from the Pythagorean theorem?

  Distance is \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
• What does the term "variables" refer to in the context of solving equations?

  Symbols that represent unknown values in equations
• How can you verify the solution of a linear system?

  By substituting the values back into the original equations
• What is the first step in solving a linear system by graphing?

  Rearranging the equations into \(y = mx + b\) form
• Why is it important to line up equations when using elimination?

  To easily combine like terms and eliminate a variable
• What is the relationship between the coefficients of the variables in elimination?

  They must be manipulated to have the same absolute value for elimination to occur
• What is the total number of pairs of shoes sold in the example problem?

  75 pairs
• What is a median in a triangle?

  A median is the line segment that joins a vertex to the midpoint of the opposite side.
• How do you find the midpoint of a line segment?

  By averaging the x-coordinates and the y-coordinates of the endpoints.