Maths theory - general

• How can the expression $x^2 +$$8x +$$18$ be rewritten in the form of $(x+a)^2 +$$b$?


  $(x+4)^2 +$$2$
• What is the value of $a$ when rewriting $x^2 +$$8x +$$18$?


  4
• How can the expression $x^2 - 6x - 7$ be rewritten in the form of $(x+a)^2 +$$b$?


  $(x-3)^2 - 16$
• What is the value of $a$ when rewriting $x^2 - 6x - 7$?


  • 3
• How can the expression $x^2 - 3x +$$1$ be rewritten in the form of $(x+a)^2 +$$b$?


  $(x - \frac{3}{2})^2 - \frac{5}{4}$
• What is the value of $a$ when rewriting $x^2 - 3x +$$1$?


  • \frac{3}{2}
• What are the steps to solve the quadratic equation $x^2 +$$6x +$$1 =$$0$?


  Set $(x+3)^2 - 8 =$$0$ and solve for $x$.
• What is the formula for a straight line?

  $y =$$mx +$$c$
• What does $m$ represent in the straight line formula?


  Gradient
• What does $c$ represent in the straight line formula?


  1. intercept
• What are the three important rules for bearings?

  • Always measure the angle starting from North
  • Always measure the angle clockwise from North
  • Bearings are always three digits
• What is the formula for arc length?

  $\text{Arc length} =$$\frac{\theta}{360} \times 2\pi r$
• What is the formula for the area of a sector?

  $\text{Area of a Sector} =$$\frac{\theta}{360} \times \pi r^2$
• What is the first circle theorem?

  The angle subtended at the circumference in a semi-circle is 90 degrees.
• What is the second circle theorem?

  The angle subtended at the center of a circle is twice the angle subtended at the circumference via the same arc.
• What is the third circle theorem?

  Angles at the circumference via the same arc are equal.
• What is the fourth circle theorem?

  Opposite angles in a cyclic quadrilateral are supplementary.
• What is the formula for the area of a parallelogram?

  $A =$$b \times h$
• What is the formula for the area of a trapezium?

  $A =$$\frac{(a+b)}{2} \times h$
• What is the formula for circumference?

  $C =$$2\pi r \text{ or } C =$$\pi d$
• What is the formula for the area of a circle?

  $A =$$\pi r^2$
• What is the formula for the volume of a prism?

  $\text{Volume} =$$\text{cross-sectional area} \times \text{height}$
• What is the formula for the volume of a cylinder?

  $V =$$\pi r^2 h$
• What is the formula for the volume of a pyramid?

  $V =$$\frac{1}{3} \times \text{area of base} \times \text{height}$
• What is Pythagoras' theorem?

  $a^2 +$$b^2 =$$c^2$
• What is the sine rule in trigonometry?

  It relates the lengths of sides of a triangle to the sines of its angles.
• What is the cosine rule in trigonometry?

  $a^2 =$$b^2 +$$c^2 - 2bc \cos A$
• What is the formula for the area of a triangle using trigonometry?

  $A =$$\frac{1}{2} ab \sin C$
• What is the quadratic formula?

  $x =$$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• What is the probability rule for the union of two events A and B?

  $P(A \text{ or } B) =$$P(A) +$$P(B) - P(A \text{ and } B)$
• What is the formula for the curved surface area of a cone?

  $\text{Curved SA} =$$\pi r l$
• What is the formula for the volume of a cone?

  $V =$$\frac{1}{3} \pi r^2 h$
• What is the formula for the surface area of a sphere?

  $SA =$$4\pi r^2$
• What is the formula for the volume of a sphere?

  $V =$$\frac{4}{3} \pi r^3$