notes photos

• What is the expanded form of $(x+7)^2 +$$6(x^2 - 10)$?


  $(x+7)(x+7) +$$6x^2 - 60$
• What is the value of the discriminant for <latex{b=6, a=4, c=4}</latex>?

  <latex{36 - 64 = -28}</latex>
• What is the vertex form of a quadratic equation?

  <latex{y = (x + p)^2 + q}</latex>
• What is the vertex of the equation <latex{y = (x - 3)^2 + 2}</latex>?

  (3, 2)
• What is the formula for the cosine rule?

  • <latex{a^2 = b^2 + c^2 - 2bc \cos A}</latex>
  • Used to find a side when two sides and the included angle are known
• How do you calculate <latex{D = (1500x^8) + 12500}</latex>?

  <latex{D = 12000 + 12500}</latex>
• What is the result of <latex{D = 12000 + 12500}</latex>?

  <latex{D = 24500}</latex>
• What is the formula for the area of a triangle using the cosine rule?

  <latex{Area = \frac{1}{2}ab \sin C}</latex>
• How do you find side <latex{a}</latex> using the cosine rule?

  <latex{a^2 = b^2 + c^2 - 2bc \cos A}</latex>
• How do you calculate <latex{a^2}</latex> when given <latex{b=6, c=5, \text{and } C=60^\circ}</latex>?


  <latex{a^2 = 36 + 25 - 60 \cdot \frac{1}{2}}</latex>
• What is the value of <latex{a}</latex> when <latex{a^2 = 49}</latex>?

  <latex{a = 7}</latex>
• What is the process of rationalizing the denominator?

  Eliminate the square root from the denominator
• What is the simplified form of <latex{\frac{12\sqrt{15} + 3}{15}}?</latex>

  <latex{4\sqrt{15}}</latex>
• What is the formula for the slope-intercept form of a line?

  <latex{y - b = m(x - a)}</latex>
• What is the equation of the line with slope <latex{m=1500}</latex> and y-intercept <latex{b=20000}</latex>?

  <latex{y = 1500x + 12500}</latex>
• What is the formula for the area of a sector?

  <latex{Area = \frac{\theta}{360} \pi r^2}</latex>
• How do you calculate the arc length of a sector?

  <latex{Arc Length = \frac{\theta}{360} \times 2\pi r}</latex>
• What is the relationship between the angle and the area of a sector?

  Area increases with larger angles
• What is the formula for the sine rule?

  <latex{\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}}</latex>
• How do you find angle <latex{A}</latex> using the sine rule?

  <latex{A = \sin^{-1}\left(\frac{a \sin B}{b}\right)}</latex>
• How do you solve for <latex{x}</latex> in the equation <latex{17 \sin x + 1 = 9}</latex>?

  <latex{\sin x = \frac{8}{17}}</latex>
• What is the value of <latex{\sin^{-1}\left(\frac{8}{17}\right)}</latex>?

  <latex{x = 28.07^\circ}</latex>
• What is the significance of the upper quartile?

  It represents the 75th percentile of data
• How do you calculate the shaded area in a sector?

  Use the formula for area of a sector
• What is the formula for the circumference of a circle?

  <latex{C = 2\pi r}</latex>
• How do you find the area of a circle?

  <latex{Area = \pi r^2}</latex>
• How do you calculate the angle of a sector?

  <latex{\theta = \frac{360 \times \text{Area}}{\pi r^2}}</latex>
• How do you determine the relationship between arc length and angle?

  Arc length is proportional to angle
• What is the formula for the sine of an angle?

  <latex{\sin A = \frac{\text{opposite}}{\text{hypotenuse}}}</latex>
• How do you find the value of <latex{a}</latex> in the equation <latex{a \sin 110 = 22 \sin 40}</latex>?

  <latex{a = \frac{22 \sin 40}{\sin 110}}</latex>
• What is the value of <latex{a}</latex> when <latex{a = 22 \sin 40 / \sin 110}</latex>?

  <latex{a \approx 15.05}</latex>
• What is the formula for the area of a triangle?

  <latex{Area = \frac{1}{2} \times \text{base} \times \text{height}}</latex>
• How do you find the height of a triangle using sine?

  <latex{h = a \sin B}</latex>
• How do you determine the dimensions of a triangle given two sides and an angle?

  Use the sine and cosine rules
• What is the formula for the tangent of an angle?

  <latex{\tan A = \frac{\text{opposite}}{\text{adjacent}}}</latex>
• How do you find the value of <latex{x}</latex> in the equation <latex{5x + 11 - 30 \geq 90x}</latex>?

  <latex{-25 \geq 4x}</latex>
• What is the result of $2784(100-167898)$?


  116%
• What is the expression for $y(y-6)$?


  y squared minus 6y
• What is the result of $(y+3)(6)$?


  6y + 18
• What is the value of $V$ given $V =$$139.4519$?


  140 cm³