Paper 1

• What is the rule for angles in the same segment of a circle?

  Angles in the same segment are equal.
• What is the 'bowtie theorem' related to?

  Angles in the same segment of a circle.
• What is the measure of an angle in a semicircle?

  90°
• How does the angle at the center relate to the angle at the circumference?

  The angle at the center is twice the angle at the circumference.
• What do opposite angles in a cyclic quadrilateral add up to?

  180°
• What are the properties of a cyclic quadrilateral?

  • Opposite angles add up to 180°
  • Angles subtended by the same arc are equal
  • The angle at the center is twice the angle at the circumference
• What is the relationship between a tangent and a radius at the point of contact?

  A tangent meets a radius at 90°.
• What is true about tangents from the same point?

  Tangents from the same point are equal in length.
• What does the alternate segment theorem state?

  Angles in alternate segments are equal.
• What does P(A') represent in a Venn diagram?

  Everything but A
• What does P(AUB) represent in a Venn diagram?

  Everything of A and B
• What does P(A∩B) represent in a Venn diagram?

  A intersect B
• What does P(A'∩B) represent in a Venn diagram?

  In B not in A
• What does P(A∩B)' represent in a Venn diagram?

  Everything apart from the intersect
• What does P(AUB)' represent in a Venn diagram?

  Not in A or B
• What are the steps to find the tangent to a circle?

  1. Find the gradient of a radius: $\Delta y =$$nse, \Delta x \text{ run}$
  2. Find the gradient of a tangent (reciprocal, negative)
  3. Substitute gradient of tangent into $y =$$mx +$$c$
  4. Substitute point into $y =$$mx +$$c$
• What is the formula for the gradient of a line?

  $\frac{y_2 - y_1}{x_2 - x_1}$
• What does SSS stand for in triangle congruence?

  Side, side, side
• What does ASA stand for in triangle congruence?

  Angle, side, angle
• What does SAS stand for in triangle congruence?

  Side, angle, side
• What is the condition for SAS in triangle congruence?

  Angle must be between two sides
• What does RHS stand for in triangle congruence?

  Right angle, hypotenuse, side
• How many figures are always used in bearings?

  Three figures
• In which direction are bearings measured?

  Clockwise from north
• What is the formula for COS A?

  $\cos A =$$\frac{b^2 + C^2 - a^2}{2bc}$
• What is the formula for \(A^2\) in relation to sides b and C?

  $A^2 =$$b^2 +$$C^2 - 2bc \cos A$
• What is the formula for the area of a sector?

  $\text{Area} =$$\pi r^2 \times \frac{\theta}{360}$
• What are the methods to prove triangle congruence?

  • SSS: Side, side, side
  • ASA: Angle, side, angle
  • SAS: Side, angle, side (angle between two sides)
  • RHS: Right angle, hypotenuse, side
• What are the key points about bearings?

  • Always have three figures
  • Measured clockwise
  • Measured from north
• What is the formula for the volume of a pyramid?

  Volume = $\frac{1}{3}$ times Area of base times Height
• What does the formula for the volume of a pyramid represent?

  It calculates the space inside the pyramid
• If the area of the base of a pyramid is 20 cm² and the height is 9 cm, what is the volume?

  Volume = $\frac{1}{3} \times 20 \times 9$
• How does the volume formula of a pyramid relate to that of a prism?

  Pyramid volume is one-third of prism volume