- Study guides, Class notes & Summaries

What is the gradient of a curve at a given point defined as? - Answer The gradient of the tangent to the curve at that point What is the formula of first principles? - Answer lim as h ->0 f(x + h) - f(x) / h What are different notations used to describe the gradient function (derivative)? - Answer dy/dx for y = ... f'(x) for when f(x) = ... What is the gradient function? - Answer dy/dx What is the gradient function of x^n? - Answer nx^n-1 What is the gradient...

Straight line vector equation - Answer r = a + lambda b B is direction vector Lambda is a scalar Cartesian form of a vector - Answer x - a1 / b1 = y - a2 / b2 = z - a3 / b3 Equation of a plane - Answer r = a + lambda b + mu c A = position vector of a point in the plane B and c = non parallel non zero vectors in the plane Lambda and mu are scalars Cartesian equation of a plane - Answer ax + by + cz = d, (a) (b) is the normal vector (c) Scalar product - Ans...

How to find a midpoint of a line segment - Answer Average the x and y coordinates of its end points; (x1+x2/2),(y1+y2/2) What's a line segment - Answer A finite part of a straight line with two distinctive end points What's it helpful to do in coordinate geometry? - Answer Draw a sketch showing the info given in the question What's the perpendicular bisector of line AB? - Answer The straight line perpendicular to AB and that also passes through its midpoint What ...

Quadratic Formula - Answer x = -b±(√b²-4ac)/2a Straight Line Equation - Answer y-y₁ = m(x-x₁) Line Length Equation - Answer √(x₂-x₁)²+(y₂-y₁)² Sine Rule (Lengths) - Answer a/sinA = b/sinB = c/sinC Sine Rule (Angles) - Answer sinA/a = sinB/b = sinC/c Cosine Rule (Lengths) - Answer a² = b²+c²-2bc(cosA) Cosine Rule (Angles) - Answer cosA = (b²+c²-a²)/2bc Midpoint for lines - endpoints (x₁, y₁) & (x₂, y₂) - Answer (x₁+x...

What is the 1st set in a mathematical modelling process? - Answer Setup mathematical model, assumptions and variables What is the 2nd step in a mathematical modelling process? - Answer Solve and interpret What is the 3rd step in a mathematical modelling process? - Answer Ask is your answer reasonable? If the answer to the 3rd step in the mathematical modelling process is yes then what is the 4th? - Answer Reconsider assumption If the answer to the 3rd step in the mathemat...

State cosine rule for length - Answer a² = b² + c² - 2bc cosA State cosine rule for angle - Answer cosA = (b² + c² - a²) / 2bc State sine rule for length - Answer a / sinA = b / sinB = c / sinC State sine rule for angle - Answer sinA / a = sinB / b = sinC / c State formula for area of a triangle given an angle - Answer 0.5 ab sinC If you are given an angle from the sine rule, explain how to determine a possible second solution - Answer 180 - angle Draw t...

aᵐ x aⁿ = aᵐ ÷ aⁿ = (aᵐ)ⁿ = (ab)ⁿ = - Answer aᵐ⁺ⁿ aᵐ⁻ⁿ aᵐⁿ aⁿbⁿ (a + b + c)(d + e + f) = - Answer ad + ae + af + bd + be + bf + cd + ce + cf State the form of a quadratic equation - Answer ax² + bx + c where a ≠ 0 Factorise x² - y² - Answer (x + y)(x - y) xⁿ/ᵐ = x⁻ᵐ = x⁰ = - Answer ᵐ√xⁿ 1/xᵐ 1 √(ab) = √(a/b) = - Answer √a x √b √a/√b Explain how to rationalise fractions - Ans...

Census - Answer Every member of the population Sample - Answer A selection of observations taken from a subset of the population which is used to find out information about the population as a whole Simple random sampling - Answer Random sampling- everyone the sample has a equal chance of being selected. E.g. each person given a number and then the numbers are chosen from random Systematic sampling - Answer Random sampling- the required elements are chosen at regular interva...

(Yr1) Expanding (a+B) ^n using the binomial expansion formula? - Answer (3-2x)^8 Find the binomial expansions up to x^2 1.) 8C0 x(-2x)x(3^8) + 8C1x(-2x)x(3^7) + 8C2x(-2x)^2x(3^6) 2. (1 + 2x)^30 up to x^3 =30C0x(2x) + 30C1x(2x) + 30C2x(2x)^2 xeg( 1^28)+ 30C3x(2x)^3 Powers (x) go up Coefficient (eg 1) goes down Binomial expansion formula when n(power) is a negative number or a fraction - Answer (1+x)^n = 1 + nx + n(n-1)/2 (x^2) + n(n-1)(n-2)/3 (x^3) +... Example (1+x)^-3 up...

Population - Answer The whole set of items that are of interest Census - Answer Observes or measures every member of a population Advantages of a census - Answer It should give a completely accurate result Disadvantage of a census - Answer Time consuming and expensive Hard to process large quantity of data Sample - Answer A selection of observations taken from a subset of the population which is used to find out information about the population as a whole Advantage...