Maths

• What is the first step in finding the coordinates where two lines meet?


  Identify the point where the lines cross
• How do you write the coordinates of the intersection point of lines L1 and L2?


  As (-3, 2)
• What does the equation of a horizontal line look like?


  It is written as \( y = c \), where \( c \) is a constant
• What is the equation of line L1 if all Y coordinates are equal to 2?


  Y = 2
• What is the equation of line L2 if all X coordinates are equal to -3?


  X = -3
• How do you complete the table of values for the equation \( y = 3x + 2 \)?


  Substitute values of \( x \) into the equation to find corresponding \( y \) values
• What is the value of \( y \) when \( x = 2 \) in the equation \( y = 3x + 2 \)?


  8
• What is the value of \( y \) when \( x = 1 \) in the equation \( y = 3x + 2 \)?


  5
• What is the value of \( y \) when \( x = 0 \) in the equation \( y = 3x + 2 \)?


  2
• What is the value of \( y \) when \( x = -1 \) in the equation \( y = 3x + 2 \)?


  • 1
• What is the value of \( y \) when \( x = -2 \) in the equation \( y = 3x + 2 \)?


  • 4
• How do you plot coordinates on a graph?

  • Move along the x-axis (horizontal) to the x-coordinate
  • Move up or down to the y-coordinate
  • Mark the point
• What should you do after plotting the coordinates from the table of values?


  Draw a straight line through the points
• What is the formula for calculating the gradient of a line?

  Gradient = rise/run
• How do you determine if the gradient is positive or negative?


  By observing if the line goes upwards or downwards from left to right
• If the rise is 3 and the run is 3, what is the gradient?


  1
• If the rise is 1 and the run is 3, what is the gradient?


  \(\frac{1}{3}\)
• What does the equation \( y = mx + c \) represent?


  It represents the slope-intercept form of a linear equation
• What is the gradient of the line if it is written as \( y = -2x + 7 \)?


  • 2
• What are the coordinates of the y-intercept in the equation \( y = -2x + 7 \)?


  (0, 7)
• How do you find the equation of a line given the gradient and y-intercept?


  Use the form \( y = mx + c \)
• If Sammy spends £1,200, how do you find out how much she saves?


  Look at the graph to find the corresponding savings amount
• What is the relationship between the number of pumps used and the time taken to empty a water tank?


  As the number of pumps increases, the time taken decreases
• What is the first step in solving the equation \( a + 24 = 39 \)?


  Subtract 24 from both sides
• What is the value of \( a \) in the equation \( a + 24 = 39 \)?


  15
• What is the opposite operation of \( -24 \) in the equation \( b - 24 = 39 \)?


  +24
• What is the value of \( b \) in the equation \( b - 24 = 39 \)?


  63
• What approach is used to solve equations in the study material?

  The arrow approach and inverse operations are used.
• If \( a + 24 = 39 \), what is the value of \( a \)?


  15
• What operation is performed to isolate \( a \) in the equation \( a + 24 = 39 \)?


  Subtracting 24 from both sides.
• What is the result of \( 39 - 24 \)?


  15
• In the equation \( b - 24 = 39 \), what is the first step to isolate \( b \)?


  Add 24 to both sides.
• If \( b - 24 = 39 \), what is the value of \( b \)?


  63
• What is the first step to solve the equation \( 4C - 10 = 26 \)?


  Add 10 to both sides.
• What is the value of \( C \) in the equation \( 4C = 36 \)?


  9
• What operation is performed to isolate \( D \) in the equation \( \frac{D - 3}{4} = 11 \)?


  Multiply both sides by 4.
• If \( \frac{D - 3}{4} = 11 \), what is the value of \( D \)?


  47
• What mistake did Dora make in her equation solving process?


  She incorrectly expanded the brackets by writing \( 3 * 2 \) as \( +5 \) instead of \( +6 \).
• What is the opposite operation of multiplying by 3 in the equation \( 3x = 56 \)?


  Dividing by 3.
• What is the value of \( x \) in the equation \( 3x = 56 \)?


  \(\frac{56}{3}\)