EDEXCEL MATH A LEVEL PURE MATH 1
COMPREHENSIVE TEST PAPER WITH
SOLVED QUESTIONS
◉ cosx from first principles
Answer: re write as cos(x+h) - cosx/h
do addition formulae for cos,
factorise out to get cosx(cosh-1)/h - sinxsinh/h
sub in small angle identities
cosx(1-h^2/2-1)/h - sinxh/h
lim h--> left with -sinx
◉ Find f'(x) given that f(x) = coskx
Answer: f'(x) = -ksinkx
◉ Find f'(x) given that f(x) = e^x
Answer: f'(x) = e^x
◉ Find f'(x) given that f(x) = e^kx
Answer: f'(x) = ke^kx
◉ Find f'(x) given that f(x) = lnkx
, Answer: f'(x) = 1/x
◉ The equation of a straight line with the gradient and a point
Answer: y - y₁ = m(x - x₁) or y=mx+c
◉ The equation of a circle
Answer: x² + y² = r²
◉ The equation of a circle with centre at (a,b)
Answer: (x - a)² + (y - b)² = r²
◉ The Factor Theorem
Answer: If f(a) = 0, then (x - a) is a factor
◉ Cosine Rule
Answer: a² = b² + c² - 2bcCosA - for side length
OR
CosA = (b² + c² - a²) / (2bc) - for angle
◉ Sine Rule
Answer: a/SinA = b/SinB = c/SinC - for side length
OR
SinA/a = SinB/b = SinC/c - for angle
COMPREHENSIVE TEST PAPER WITH
SOLVED QUESTIONS
◉ cosx from first principles
Answer: re write as cos(x+h) - cosx/h
do addition formulae for cos,
factorise out to get cosx(cosh-1)/h - sinxsinh/h
sub in small angle identities
cosx(1-h^2/2-1)/h - sinxh/h
lim h--> left with -sinx
◉ Find f'(x) given that f(x) = coskx
Answer: f'(x) = -ksinkx
◉ Find f'(x) given that f(x) = e^x
Answer: f'(x) = e^x
◉ Find f'(x) given that f(x) = e^kx
Answer: f'(x) = ke^kx
◉ Find f'(x) given that f(x) = lnkx
, Answer: f'(x) = 1/x
◉ The equation of a straight line with the gradient and a point
Answer: y - y₁ = m(x - x₁) or y=mx+c
◉ The equation of a circle
Answer: x² + y² = r²
◉ The equation of a circle with centre at (a,b)
Answer: (x - a)² + (y - b)² = r²
◉ The Factor Theorem
Answer: If f(a) = 0, then (x - a) is a factor
◉ Cosine Rule
Answer: a² = b² + c² - 2bcCosA - for side length
OR
CosA = (b² + c² - a²) / (2bc) - for angle
◉ Sine Rule
Answer: a/SinA = b/SinB = c/SinC - for side length
OR
SinA/a = SinB/b = SinC/c - for angle
