EDEXCEL MATH A LEVEL PURE MATH 1
FINAL PAPER QUESTIONS AND
SOLUTIONS
◉ Principal Value
Answer: When you use the inverse trig function on your
calculator, the angle you get is the principal value.
◉ Sine and Cosine Formulae
Answer: sin²(θ) + cos²(θ) = 1
tan(θ) = sin(θ) ÷ cos(θ)
◉ Triangle Law for Vector Addition
Answer: A→B + B→C = A→C
If A→B = a, B→C = b and A→C = c, then a + b = c
◉ Vector Rules
Answer: • P→Q = R→S, then line segments PQ and RS are equal in
length and are parallel.
• A→B = -(B→A)
• Any vector parallel to the vector a may be written as λa
,◉ Vector Magnitude
Answer: a = xi + yj → |a| = √(x² + y²)
◉ Unit Vector
Answer: In the direction of a, unit vector is
a ÷ |a|
◉ Position Vector
Answer: O→P = pi + qj
A→B = O→B - O→A
◉ First Derivative Formula
Answer:
◉ Differentiation Formula
Answer: dy/dx = anxⁿ⁻¹
◉ Function's Gradient
Answer: Increasing on the interval [a, b] if f'(x) ≥ 0 for all values of
a < x < b.
Decreasing on the interval [a, b] if
, f'(x) ≤ 0 for all values of a < x < b.
◉ Stationary Point
Answer: Any point on the curve y = f(x) where f'(x) = 0.
• if f''(a) > 0, the point is a local minimum.
• if f''(a) < 0, the point is a local maximum.
◉ Integration Formula
Answer: y = k/(n+1) x xⁿ⁺¹ + c
◉ Area of a Triangle
Answer: ½ x ab x sin(C)
◉ Differentiating eˣ
Answer: y = eᵏˣ → dy/dx = keᵏˣ
◉ Logarithm Format
Answer:
◉ Logarithm Laws
Answer:
◉ Natural Log (y = ln x)
FINAL PAPER QUESTIONS AND
SOLUTIONS
◉ Principal Value
Answer: When you use the inverse trig function on your
calculator, the angle you get is the principal value.
◉ Sine and Cosine Formulae
Answer: sin²(θ) + cos²(θ) = 1
tan(θ) = sin(θ) ÷ cos(θ)
◉ Triangle Law for Vector Addition
Answer: A→B + B→C = A→C
If A→B = a, B→C = b and A→C = c, then a + b = c
◉ Vector Rules
Answer: • P→Q = R→S, then line segments PQ and RS are equal in
length and are parallel.
• A→B = -(B→A)
• Any vector parallel to the vector a may be written as λa
,◉ Vector Magnitude
Answer: a = xi + yj → |a| = √(x² + y²)
◉ Unit Vector
Answer: In the direction of a, unit vector is
a ÷ |a|
◉ Position Vector
Answer: O→P = pi + qj
A→B = O→B - O→A
◉ First Derivative Formula
Answer:
◉ Differentiation Formula
Answer: dy/dx = anxⁿ⁻¹
◉ Function's Gradient
Answer: Increasing on the interval [a, b] if f'(x) ≥ 0 for all values of
a < x < b.
Decreasing on the interval [a, b] if
, f'(x) ≤ 0 for all values of a < x < b.
◉ Stationary Point
Answer: Any point on the curve y = f(x) where f'(x) = 0.
• if f''(a) > 0, the point is a local minimum.
• if f''(a) < 0, the point is a local maximum.
◉ Integration Formula
Answer: y = k/(n+1) x xⁿ⁺¹ + c
◉ Area of a Triangle
Answer: ½ x ab x sin(C)
◉ Differentiating eˣ
Answer: y = eᵏˣ → dy/dx = keᵏˣ
◉ Logarithm Format
Answer:
◉ Logarithm Laws
Answer:
◉ Natural Log (y = ln x)
