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ZIMSEC · Form 6 · Upper 6 · Syllabus 6042

Pure Mathematics

7 topics7 with notes

Upper 6Writing A Level finals this year?Revision mode: every Pure Mathematics past paper by year, with marking schemes, and a checklist of the whole syllabus.
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  1. Trigonometry π radians = 180°. Arc length s = rθ; sector area = ½r²θ (θ in radians). Notes 1 PDF
  2. Differentiation Rules d/dx(xⁿ) = nxⁿ⁻¹; d/dx(eˣ) = eˣ; d/dx(ln x) = 1/x; d/dx(sin x) = cos x; d/dx(cos x)… Notes 1 PDF
  1. Integration ∫xⁿ dx = xⁿ⁺¹/(n + 1) + c (n ≠ −1); ∫1/x dx = ln|x| + c; ∫eᵃˣ dx = eᵃˣ/a + c; ∫sin ax dx = −cos ax / a + c; ∫cos ax dx = sin ax / a + c; ∫sec²x dx = tan x + c. Notes 1 PDF
  2. Differential equations A differential equation links a function with its derivatives. Notes 1 PDF
  3. Vectors Vectors in 3D: a = xi + yj + zk. Magnitude |a| = √(x² + y² + z²). A unit vector is a/|a|. Position vectors: AB = b − a. Notes 1 PDF
  4. Complex numbers i² = −1. A complex number z = x + iy has real part x and imaginary part y. The conjugate z* = x − iy. Notes 1 PDF
  5. Numerical methods If f(x) is continuous and f(a) and f(b) have opposite signs, a root lies between a and b. Notes 1 PDF