14.2.1 Applying algebraic manipulation

• Algebraic skills are only relevant for theoretical physics and not experimental data analysis.

  False
• What is the rearranged formula for \( R \) in Ohm's Law \( V = IR \)?

  R = V/I
• What is the quadratic formula used to find the roots of a quadratic equation?

  $x =$$\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}$
• Rearranging formulas involves expressing a variable in terms of others
• To solve for \( R \) in the formula \( V = IR \), you would divide both sides by I
• What is the quadratic formula?

  $x =$$\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}$
• The gradient in a linear equation \( y = mx + c \) is represented by m
• To solve for \( R \) in the formula \( V = IR \), you would divide both sides by I
• Rearranging formulas is a key algebraic technique in physics.


  True
• Steps to solve for \( x \) in \( 2x + 3 = 9 \)

  1️⃣ Subtract 3 from both sides

  2️⃣ Divide both sides by 2

  3️⃣ Simplify to find x
• To solve for R in the formula V = IR, you would divide both sides by I


  True
• In the quadratic formula, 'a' represents the coefficient of x

  False
• What is the value of R when V = 12 V and I = 2 A in the formula V = IR?

  6 Ω
• The quadratic formula is used to find the roots of the equation ax^2 + bx + c = 0


  True
• What is the value of R when V = 12 V and I = 2 A in the formula V = IR?

  6 Ω
• The quadratic formula can be used to solve all types of quadratic equations


  True
• In the equation 2x + 3x + 4 = 6x - 2, the solution is x = 6

  True
• In a linear equation, the gradient is the constant term 'c'

  False
• The quadratic formula is used to solve equations of the form ax^2 + bx + c = 0


  True
• In the quadratic formula, \( a \) is the coefficient of \( x^2 \), \( b \) is the coefficient of \( x \), and \( c \) is the constant term
• What does the gradient of a straight line indicate?

  Rate of change of y with respect to x
• To solve for \( R \) in the formula \( V = IR \), you must divide both sides by \( I \).


  True
• What are the coefficients \( a \), \( b \), and \( c \) in the quadratic formula?

  Coefficients of quadratic equation
• What is the quadratic formula used to solve quadratic equations?

  $x =$$\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}$
• Algebra is essential for understanding physics equations, allowing for manipulation and simplification of formulas
• A variable is a symbol representing an unknown value
• The general form of a quadratic equation is \( ax^2 + bx + c = 0 \), and it can be solved using the quadratic formula
• Algebraic manipulation allows you to solve equations, rearrange formulas, and work with linear and quadratic equations in physics.


  True
• The y-intercept in a linear equation \( y = mx + c \) is represented by \( c \).


  True
• The quadratic equation \( ax^2 + bx + c = 0 \) can be solved using the quadratic formula
• Steps to solve the equation \( 3x + 5 = 14 \)

  1️⃣ Subtract 5 from both sides

  2️⃣ Divide both sides by 3

  3️⃣ Simplify to find x
• Algebraic manipulation helps express a variable in terms of others.

  True
• To solve \( 3x + 5 = 14 \), the first step is to subtract 5
• Simplifying and solving equations involves finding the value of an unknown variable
• How do you solve an equation to find the unknown variable?

  Isolate the variable
• What is the quadratic formula used to solve?

  ax^2 + bx + c = 0
• Steps to solve the equation 3x + 5 = 14

  1️⃣ Write down the equation: 3x + 5 = 14

  2️⃣ Subtract 5 from both sides: 3x = 9

  3️⃣ Divide both sides by 3: x = 3
• Match the term with its description in a linear equation:

  m ↔️ Gradient of the line

  c ↔️ y-intercept
• Steps to solve the equation 3x + 5 = 14

  1️⃣ Write down the equation: 3x + 5 = 14

  2️⃣ Subtract 5 from both sides: 3x = 9

  3️⃣ Divide both sides by 3: x = 3
• Match the term with its description in a linear equation:

  m ↔️ Gradient of the line

  c ↔️ y-intercept