Maths Autumn Term Revision

• If we have the equation $3 +$$x =$$7$, what is the value of $x$?


  $4$
• In the expression $3x +$$5$, what is $3$ considered?


  A constant
• How would you express "five times a number minus two" in algebraic form?

  $5x - 2$
• In the expression $2y - 7 +$$4x$, which part is a variable?


  $y$
• What is the term for a fixed value in algebra?

  Constant
• What does the term "terms" refer to in an algebraic expression?


  Individual values or products of variables and constants
• If you have the expression $3y +$$5 - 2x$, what are the constant terms?


  $5$
• How would you express "the sum of four times a number and three" in algebraic form?

  $4x +$$3$
• What is the algebraic expression for "the quotient of a number divided by three plus five"?


  $\frac{x}{3} +$$5$
• What is the purpose of using letters in algebra?

  To represent unknown numbers
• How do you derive the expression for "the quotient of a number divided by three plus five"?

  Divide the number by three and add five
• What is the first step to solve the equation 2x + 3 = 7?

  Subtract 3 from both sides
• What must you remember when solving inequalities involving negative numbers?


  You must flip the inequality sign
• What is the first step to graph an equation in the form $y =$$mx +$$b$?


  Rewrite the equation in $y =$$mx +$$b$ form
• What type of line do you use for graphing the inequality $y < -3x +$$2$?


  Dashed line
• What is the correct shading for the inequality $y < -3x +$$2$?


  Shade below the dashed line
• What is the correct step when graphing an equation in the form $y =$$mx +$$b$?


  Plot the y-intercept on the y-axis
• What are the steps to graph an inequality?

  1. Convert to $y =$$mx +$$b$ form
  2. Graph the related equation (dashed for < or >, solid for ≤ or ≥)
  3. Shade the appropriate region (above or below the line)
• What are the steps to graph an equation?

  1. Rewrite in $y =$$mx +$$b$ form
  2. Plot the y-intercept on the y-axis
  3. Use the slope to find additional points
  4. Draw a straight line through the points
• Directed Number Line


  A number line that includes both positive and negative numbers, used to represent directed movements.
• Fact Family


  A set of four arithmetic operations that are related by the commutative and associative properties, used to demonstrate equivalent expressions: addition and subtraction, multiplication and division.
• Arithmetic Sequence


  A sequence of numbers in which each term is obtained by adding a fixed constant to the previous term.
• Arithmetic Sequence Formula
• Term to Term Difference

  The difference between two consecutive terms in a sequence.
• Sequence: +3


  1, 4, 7, 10, ...
• Term-to-Term Difference: +2


  A simple arithmetic sequence where each term increases by 2
• Directed Number: -5


  A number that is 5 units to the left of zero on the number line
• Fact Family: 2 × 3 = 6

  2 + 3 = 5</br>2 - 3 = -1</br>6 ÷ 2 = 3</br>3 × 2 = 6
• Arithmetic Sequence Formula


  Tn = a + (n - 1)d</br>(Tn: term, a: starting value, n: term number, d: common difference)
• Directed Number Addition


  +2 + (-4) = ?</br>-2 + (+3) = ?</br>-5 + (+2) = ?
• Directed Number Subtraction


  +5 - (-2) = ?</br>-3 - (+2) = ?</br>+1 - (-4) = ?
• Describe Sequence: −1, 1, 3, 5, ...

  A sequence that increases by 2 each time, starting from -1
• Continue Sequence: 2, −4, 6, 8, ...

  10, ...
• Predict Next Term: 1, −3, 5, 7, ...

  9</br>Why: The sequence is increasing by 4 each time
• Check Next Term: 3, −1, 5, 9, ...

  13</br>Why: The sequence is increasing by 4 each time
• Describe Sequence: 3, 9, 15, 21, ...

  A sequence that increases by 6 each time, starting from 3
• Continue Sequence: 1, −5, 9, 13, ...

  17, ...
• Predict Next Term: 2, −1, 4, 7, ...

  10</br>Why: The sequence is increasing by 3 each time
• Check Next Term: −2, 3, 8, 13, ...

  18</br>Why: The sequence is increasing by 5 each time
• What type of sequence is the one below?


  1, 2, 3, 4, ...