area of sector (where θ is in radians) ½r²θ angles in 3D vectors cosθₓ =x/|a| cosθᵧ =y/|a| cosθ₂ =z/|a| this is where vector a makes an angle θ with the x/y/z axis (because x/y/z would be the adjacent and a the hypotenuse) Expanding (a + bx)ⁿ (a + bx)ⁿ = aⁿ(1 + (b/a)x)ⁿ cosine rule a² = b² +c² -2bc cosA rule for parametric integration ∫y dx = ∫(y dx/dt)dt as (dx/dt) x dt would cancel out to give you ∫y dx

Chapter 1.1 - Index Laws: What is a base? The number having the power applied to it Chapter 1.1 - Index Laws: What is an index, power or exponent? The operation being applied to the base Chapter 1.1 - Index Laws: What is the result when multiplying the same bases of different powers? You add the powers E.g a^m x a^n = a^m+n

1 + tan2θ = sec2θ cot2θ + 1 = cosec2θ = cosec2θ Sin2θ 2sinθcosθ Cos2θ cos²θ-sin²θ 2cos²θ-1 1-2sin²θ Tan2θ 2tanθ / (1 - tan²θ)

1 + tan2θ = sec2θ cot2θ + 1 = cosec2θ = cosec2θ Sin2θ 2sinθcosθ Cos2θ cos²θ-sin²θ 2cos²θ-1 1-2sin²θ Tan2θ 2tanθ / (1 - tan²θ)

1 + tan2θ = sec2θ cot2θ + 1 = cosec2θ = cosec2θ Sin2θ 2sinθcosθ Cos2θ cos²θ-sin²θ 2cos²θ-1 1-2sin²θ

nswer all questions. • • • • • • Try to answer every question. • Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. • Show your working in any calculation questions and include units in your answer where appropriate. Answer the questions in the spaces provided – there may be more space than you need.

If det M = 0 then M is a ... Singular matrix. What are the steps of inverting a 3 x 3 matrix? 1. Find the determinant of the matrix. 2. Form the matrix of the minors of the matrix. 3. Form the matrix of cofactors. 4. Write down the transpose, C^T, of the matrix of cofactors. 5. A^-1 = 1/detA x C^T If det M ≠ 0 then M is a ... Non-singular matrix. For a matrix to have an inverse it must be ... Non-singular

Laws of indices for powers of the same base -a^m x a^n = a^m+n -a^m / a^n = a^m-n -(a^m)^n = a^mn -(ab)^n = a^n b^n Laws of indices for any rational power -a^1/m = m √a -a^n/m = m √a^n -a^-m = 1/a^m

Use Fill in the boxes black ink or ball-point pen. at the top of this page with your name, •• centre number and candidate number. Answer Show your working in any calculation questions and include units in your answer all questions. • where appropriate. Answer the questions in the spaces provided – there may be more space than you need. Information •• The total mark for this paper is 80. The marks for each question are shown in brackets

Pearson Edexcel Level 3 Maths Pure Paper 1 2022 Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for algebraic manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. Instructions • Use black ink or ball-point pen. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). • Answer all questions and ensure that your answers to parts of questions are clearly lab...