OCR a-level maths
with question and
answers 2025/2026
- correct answers(a+bx)^n = a^n (1+bx)^n and is valid where |x|<b
- correct answersa fraction can be split into partial fractions. each of these can then be
binomially expanded
- correct answersa resultant force acting on an object will cause the object to accelerate in the
same direction as the resultant force
- correct answersalgebraic fractions can be separated into partial fractions which can be
integrated
- correct answersfor a two-tailed test the critical region is split at either end of the distribution
- correct answersfor a two-tailed test, halve the significance level at each end you are testing
- correct answersfunctions can either be one-to-one or many-to-one
- correct answersif ∠PRQ = 90° then R lies on the circle with diameter PQ
,- correct answersif x is small the first few terms in a binomial expansion can be used to find an
approximate value for a complicated expression
- correct answersintegration by parts formula is given
- correct answersintegration by substitution can be used to simplify the integral by changing the
variable
- correct answersseries can be shown using sigma notation
- correct answersthe binomial expansion of (1+x)^n is valid when |x|<1, n∈ℝ
- correct answerstrigonometric identities can be used to integrate expressions. this allows an
expression that cannot be integrated to be replaced by expressions that can
- correct answerswhen integrating an algebraic fraction by substitution u is often the
denominator
- correct answersyou should only use the regression line to make predictions for values of the
dependent variable that are within the range of the given data
- acceleration
- due to gravity (a=g) - correct answersthe vertical motion of a projectile is modelled as having
constant what?
- always resists the motion
- Fmax is the maximum value of friction
,- Fmax = µR where µ is the coefficient of friction and R is the reaction force - correct
answersfriction in mechanics µ
- defines each term of a sequence as a function of the previous term
- to find the members of the sequence substitute in n=1, n=2 ... using the previous terms given -
correct answersrecurrence relation of form Un+1 = f(Un)
- horizontal component is UcosA
- vertical component is UsinA - correct answersif a particle is projected with an initial velocity of
U, at an angle of A above the horizontal what are the horizontal and vertical components of the
initial velocity?
- if f(x) = uv
- f'(x)= uv' + u'v - correct answersproduct rule
- if it is at rest and the resultant force acting on the particle is zero - correct answerswhen is a
particle or rigid body in static equilibrium?
- it is periodic
- means that the terms repeat in a cycle
- k = the order of the sequence (how often the terms repeat) - correct answersif Un+k = Un for
all n ∈ ℕ, what is true of the sequence
- P(X<Q1) = 0.25
-inverse normal function on calculator can be used to show that Q1 =89.88
- mean is 100
- 100-89.88 = 10.12
-Q1 is 10.12 from the mean
, -Q3 will also be 10.12 from the mean as the normal distribution is symmetrical
-so IQR = 2*10.12 = 20.24 - correct answersX~N(100,15^2) how would you calculate the IQR?
- s = Ut + 0.5at^2
- y = Usinαt -0.5gt^2
- t = x / Ucosα = x/u Secα
- y = Usinα(x/cosα) - 0.5g(x/U secα)^2
- y = xtanα - gx^U^2 Sec^2 U
- y = xtanα - g/2U^2 x^2 sec^2α
- y = xtanα - g/2u^2 x^2(tan^2α + 1)
- y = xtanα - gx^2 ((1 + tan^2α) / 2U^2) - correct answersfinding the equation of trajectory for a
particle
- Sn = a(1-r^n) / 1-r
- Sn = a(r^n - 1) / r-1
where r does not equal 1 - correct answersformula of first n terms of a geometric sequence
- Sn = n/2 (2a + (n-1)d)
- Sn = n/2 (a + l) where a is the first term and l is the last term - correct answersformula of an
arithmetic series
- the sum of the values tend towards a specific number
- it is only convergent if |r|<1 - correct answersconvergent sequence
- the weight acts straight downwards
- the reaction force is at a right angle to the plane - correct answers- direction of forces for a
particle on an inclined plane
with question and
answers 2025/2026
- correct answers(a+bx)^n = a^n (1+bx)^n and is valid where |x|<b
- correct answersa fraction can be split into partial fractions. each of these can then be
binomially expanded
- correct answersa resultant force acting on an object will cause the object to accelerate in the
same direction as the resultant force
- correct answersalgebraic fractions can be separated into partial fractions which can be
integrated
- correct answersfor a two-tailed test the critical region is split at either end of the distribution
- correct answersfor a two-tailed test, halve the significance level at each end you are testing
- correct answersfunctions can either be one-to-one or many-to-one
- correct answersif ∠PRQ = 90° then R lies on the circle with diameter PQ
,- correct answersif x is small the first few terms in a binomial expansion can be used to find an
approximate value for a complicated expression
- correct answersintegration by parts formula is given
- correct answersintegration by substitution can be used to simplify the integral by changing the
variable
- correct answersseries can be shown using sigma notation
- correct answersthe binomial expansion of (1+x)^n is valid when |x|<1, n∈ℝ
- correct answerstrigonometric identities can be used to integrate expressions. this allows an
expression that cannot be integrated to be replaced by expressions that can
- correct answerswhen integrating an algebraic fraction by substitution u is often the
denominator
- correct answersyou should only use the regression line to make predictions for values of the
dependent variable that are within the range of the given data
- acceleration
- due to gravity (a=g) - correct answersthe vertical motion of a projectile is modelled as having
constant what?
- always resists the motion
- Fmax is the maximum value of friction
,- Fmax = µR where µ is the coefficient of friction and R is the reaction force - correct
answersfriction in mechanics µ
- defines each term of a sequence as a function of the previous term
- to find the members of the sequence substitute in n=1, n=2 ... using the previous terms given -
correct answersrecurrence relation of form Un+1 = f(Un)
- horizontal component is UcosA
- vertical component is UsinA - correct answersif a particle is projected with an initial velocity of
U, at an angle of A above the horizontal what are the horizontal and vertical components of the
initial velocity?
- if f(x) = uv
- f'(x)= uv' + u'v - correct answersproduct rule
- if it is at rest and the resultant force acting on the particle is zero - correct answerswhen is a
particle or rigid body in static equilibrium?
- it is periodic
- means that the terms repeat in a cycle
- k = the order of the sequence (how often the terms repeat) - correct answersif Un+k = Un for
all n ∈ ℕ, what is true of the sequence
- P(X<Q1) = 0.25
-inverse normal function on calculator can be used to show that Q1 =89.88
- mean is 100
- 100-89.88 = 10.12
-Q1 is 10.12 from the mean
, -Q3 will also be 10.12 from the mean as the normal distribution is symmetrical
-so IQR = 2*10.12 = 20.24 - correct answersX~N(100,15^2) how would you calculate the IQR?
- s = Ut + 0.5at^2
- y = Usinαt -0.5gt^2
- t = x / Ucosα = x/u Secα
- y = Usinα(x/cosα) - 0.5g(x/U secα)^2
- y = xtanα - gx^U^2 Sec^2 U
- y = xtanα - g/2U^2 x^2 sec^2α
- y = xtanα - g/2u^2 x^2(tan^2α + 1)
- y = xtanα - gx^2 ((1 + tan^2α) / 2U^2) - correct answersfinding the equation of trajectory for a
particle
- Sn = a(1-r^n) / 1-r
- Sn = a(r^n - 1) / r-1
where r does not equal 1 - correct answersformula of first n terms of a geometric sequence
- Sn = n/2 (2a + (n-1)d)
- Sn = n/2 (a + l) where a is the first term and l is the last term - correct answersformula of an
arithmetic series
- the sum of the values tend towards a specific number
- it is only convergent if |r|<1 - correct answersconvergent sequence
- the weight acts straight downwards
- the reaction force is at a right angle to the plane - correct answers- direction of forces for a
particle on an inclined plane
