Math Revision Y10

• How many practice questions are included in the review?

  22 practice questions
• What is the total time the ministry of education suggests for learning the grade 10 math course?

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

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

  Finding values of variables for two equations
• How do you rearrange an equation into y equals mx plus b form?

  Isolate y on one side of the equation
• What is the slope (m) of the equation x - y = 5?

  1
• What is the y-intercept (b) of the equation x - y = 5?

  -5
• How do you plot a point using slope?

  Rise over run from the y-intercept
• What is the goal of the elimination method?

  To eliminate a variable by adding or subtracting
• How do you eliminate a variable in the elimination method?

  Make coefficients have the same absolute value
• What happens when you add two equations with opposite coefficients?

  The variable will eliminate
• What is the first step in the substitution method?

  Isolate one variable in an equation
• What do you do after isolating a variable in substitution?

  Plug it into the other equation
• What is the value of y after using substitution?

  -3
• What is the total sales amount from the sports shop?

  6241 dollars
• What are the two variables defined for the shoe sales problem?

  x = adidas, y = air jensen
• What is the first equation derived from the shoe sales problem?

  x + y = 75
• What is the second equation derived from the shoe sales problem?

  82x + 95y = 6241
• What is the method used to solve the shoe sales problem?

  Elimination
• What is the value of y after solving the shoe sales problem?

  7
• What is the value of x after solving the shoe sales problem?

  68
• What is the formula for calculating the midpoint between two points?

  Average x and y coordinates
• How do you calculate the distance between two points?

  Use the Pythagorean theorem
• What is a median in a triangle?

  Line segment from vertex to midpoint
• How do you find the equation of a median?

  Determine slope and y-intercept
• What is needed to find the slope of a line?

  Two points on the line
• What is the formula for the distance between two points?

  \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
• What is the formula for the midpoint between two points?

  \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\)
• What are the steps to solve a linear system by graphing?

  1. Rearrange equations to y = mx + b form
  2. Identify slope (m) and y-intercept (b)
  3. Plot the y-intercept
  4. Use slope to plot additional points
  5. Draw the lines and find intersection
• What are the steps to solve a linear system by elimination?

  1. Ensure equations are in standard form
  2. Make coefficients of one variable the same
  3. Add or subtract equations to eliminate a variable
  4. Solve for the remaining variable
  5. Substitute back to find the other variable
• What are the steps to solve a linear system by substitution?

  1. Isolate one variable in one equation
  2. Substitute that variable into the other equation
  3. Solve for the remaining variable
  4. Substitute back to find the other variable
• What are the key formulas for midpoint and distance?

  • Midpoint: \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\)
  • Distance: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
• What is the process to find the equation of a median in a triangle?

  1. Identify the vertex and midpoint of the opposite side
  2. Calculate the slope using these points
  3. Use point-slope form to write the equation
• How do you find the midpoint of a line segment?

  Average the x and y coordinates
• What is the midpoint of points (-1, 3) and (1, 5)?

  (0, 4)
• What is the formula for slope between two points?

  m = (y2 - y1) / (x2 - x1)
• How do you calculate the slope of a line?

  Change in y over change in x
• If point C is (3, 1) and midpoint is (0, 4), what is the slope of the median?

  -1
• What is the y-intercept in the equation y = mx + b?

  Value of b when x is zero
• What is the equation of the median with slope -1 and y-intercept 4?

  y = -x + 4