AQA A LEVEL MATHS COMPREHENSIVE EXAM
2026 QUESTIONS WITH SOLUTIONS GRADED
A+
◉ If y = cos x, what is dy/dx? Answer: dy/dx = -sin x
◉ Equation for distance between two points. Answer: SQRT( (x2-x1)^2
+(y2-y1)^2)
◉ Midpoint formula. Answer: (x₁+x₂)/2, (y₁+y₂)/2
◉ If y = sin x, what is dy/dx? Answer: dy/dx = cos x
◉ integral of e^x dx. Answer: e^x + C
◉ Integral of 1/x dx. Answer: ln|x| + C
◉ integral of sin x dx. Answer: -cos x + C
◉ cot x =. Answer: 1/tan x
, ◉ sec x =. Answer: 1/cos x
◉ integral of cos x dx. Answer: sin x + C
◉ cosec x =. Answer: 1/sin x
◉ Mutually exclusive events. Answer: events that cannot happen at the
same time (circles don't overlap on a venn diagram)
P (A U B) = P(A) + P(B)
P (A n B) = 0
◉ area of a sector of a circle (radians). Answer: A= 1/2 r^2 θ
◉ arc length (radians). Answer: l= rθ
◉ inverse functions. Answer: 1. start with y = f(x)
2. rearrange to get x the subject in terms of y
3. give f^-1(x) by replacing ys with xs
◉ degrees to radians conversion. Answer: multiply by π/180
2026 QUESTIONS WITH SOLUTIONS GRADED
A+
◉ If y = cos x, what is dy/dx? Answer: dy/dx = -sin x
◉ Equation for distance between two points. Answer: SQRT( (x2-x1)^2
+(y2-y1)^2)
◉ Midpoint formula. Answer: (x₁+x₂)/2, (y₁+y₂)/2
◉ If y = sin x, what is dy/dx? Answer: dy/dx = cos x
◉ integral of e^x dx. Answer: e^x + C
◉ Integral of 1/x dx. Answer: ln|x| + C
◉ integral of sin x dx. Answer: -cos x + C
◉ cot x =. Answer: 1/tan x
, ◉ sec x =. Answer: 1/cos x
◉ integral of cos x dx. Answer: sin x + C
◉ cosec x =. Answer: 1/sin x
◉ Mutually exclusive events. Answer: events that cannot happen at the
same time (circles don't overlap on a venn diagram)
P (A U B) = P(A) + P(B)
P (A n B) = 0
◉ area of a sector of a circle (radians). Answer: A= 1/2 r^2 θ
◉ arc length (radians). Answer: l= rθ
◉ inverse functions. Answer: 1. start with y = f(x)
2. rearrange to get x the subject in terms of y
3. give f^-1(x) by replacing ys with xs
◉ degrees to radians conversion. Answer: multiply by π/180
