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What is the Pythagorean Theorem formula and what does it calculate?
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a^2 + b^2 = c^2; It calculates the length of a side in a right-angled triangle.
Describe how to solve for BC in a trigonometric ratio problem where sin(52) = 8.6/BC.
Rearrange the equation to solve for BC: BC = 8.6/sin(52)
How do you calculate the intersection and union of two sets?
Intersection: Common elements in both sets. Union: All unique elements from both sets combined.
How do you calculate the original price if given a reduced price and percentage reduction?
Original Price = Reduced Price / (1 - Reduction Percent/100)
If Y is inversely proportional to X^2 and K = 32, how do you find Y when X = 4?
Y = K/X^2 = 32/16 = 2
How do you find the first common multiple of two numbers, for example, 4 and 17?
The first common multiple is the least number divisible by both, calculated here as 68 for 4 and 17.
What is the relationship between the gradients of perpendicular lines?
The product of the gradients of perpendicular lines is -1.
What are the main formulas for transformations and provide an example for enlargement?
Reflection, Rotation, Translation, Enlargement. Example: If a shape is enlarged by a scale factor of 2, each side length is multiplied by 2.
Explain the concept of speed, distance, and time using an example where the speed is 18 km/h and time is 55 minutes.
Convert time to hours: 55/60. Then, Distance = Speed * Time = 18 * (55/60) = 16.5 km
What is the rule for the sum of interior angles of a polygon?
Sum of Interior Angles = (N - 2) * 180°
What is the formula for calculating the upper bound given a nearest measurement?
Upper bound = Value + (Nearest measurement / 2)
What is the formula to find the sum of exterior angles in any polygon?
The sum of exterior angles in any polygon is always 360°.
How do you find the arc length of a sector?
Arc Length = (Central Angle/360) * 2πr
What is the formula for Simple Interest?
I = PRT
What is the unit conversion for exchange rates and how would you convert $80 to Japanese Yen given $1 = 24.3 Yen?
Multiply the amount in dollars by the exchange rate: 80 * 24.3 = 1944 Yen
What is the formula for Compound Interest?
A = P(1 + r)^t
When given a polynomial for differentiation, such as 6x^2 - 3, how would you differentiate it?
The derivative of 6x^2 - 3 is 12x.
Give an example of how to find the line equation that is parallel to another given line equation.
Parallel lines have the same gradient (M). Given Y = MX + C, any line with the same M will be parallel.
Solve the equation: 11X - 3X = -7 - 5
X = -2.75
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