GCE A-Level H2 Mathematics: Paper 2 practice
Practise paper 2 with the GCE A-Level H2 Mathematics question types and full mark budget. Work through the questions before opening feedback.
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Learning goals
- Determine function domains, ranges and admissible inputs
- Compose and invert functions with existence conditions
- Interpret and draw graphs of functions
- Transform graphs and relate representations
- Solve inequalities and represent their solution sets
- Formulate, use and interpret a mathematical model
- Express and use the general term of a sequence
- Find finite sums and analyse convergence of series
- Add vectors by ordered components
- Subtract vectors by ordered components
- Multiply a vector by a scalar
- Calculate the magnitude of a vector
- Produce a unit vector in a given direction
- Locate a point from a displacement parameter
- Find the directed displacement between two points
- Calculate the distance between two points
- Test all coordinates for point collinearity
- Locate an internally or externally dividing point from its ratio
- Explain vector geometry, position, displacement and ratio relationships
- Calculate a scalar product
- Calculate an ordered vector product
- Calculate the angle between directed vectors
- Find a signed scalar component along a direction
- Find the parallel vector component along a direction
- Find the perpendicular component's magnitude
- Justify the geometrical meanings and properties of vector products
- Produce a vector equation of a spatial line
- Produce independent Cartesian equalities for a spatial line
- Produce a vector equation of a plane
- Produce a Cartesian equation of a plane
- Distinguish coincident, parallel, intersecting and skew lines
- Classify a line's relationship with a plane
- Distinguish coincident, parallel and intersecting planes
- Produce the intersection line of two planes
- Find the foot of a perpendicular from a point to a line
- Find the perpendicular distance from a point to a line
- Find the foot of a perpendicular from a point to a plane
- Find the perpendicular distance from a point to a plane
- Find the unique intersection point of a line and a plane
- Find the smaller angle between spatial lines
- Find the smaller angle between planes
- Find the angle between a line and a plane
- Justify spatial vector relationships and parameter conditions
- Add complex numbers
- Subtract complex numbers
- Multiply complex numbers
- Divide by a nonzero complex number
- Find the conjugate of a complex number
- Calculate the modulus of a complex number
- Calculate a complex number's principal argument
- Find every distinct root of a real quadratic over the complex numbers
- Solve a unique linear complex equation, including a conjugate term
- Recover the remaining distinct roots of a real cubic or quartic from a non-real root
- Explain complex equality, the number system and real-coefficient root properties
- Represent and explain complex operations on an Argand diagram
- Relate a function to its derivative graphs
- Differentiate implicit and parametric relationships within stated scope
- Classify stationary points using justified derivative tests
- Find and interpret a tangent to a curve
- Find and interpret a normal to a curve
- Model and solve an optimisation problem
- Relate connected rates of change
- Use and derive bounded Maclaurin approximations
- Find antiderivatives within the permitted scope
- Select and apply permitted integration techniques
- Evaluate definite integrals
- Relate a definite integral to area under a curve
- Relate definite integrals to signed area and geometric area
- Use integrals to calculate volumes of revolution
- Formulate, solve and interpret separable differential equations
- Calculate event probabilities from an explicit sample space
- Distinguish independence from mutual exclusivity
- Calculate and interpret conditional probabilities
- Use counting principles, permutations and combinations
- Build a finite distribution from equally likely outcome counts
- Calculate an event probability from a finite distribution
- Calculate a finite discrete variable's expectation
- Calculate a finite discrete variable's second moment
- Calculate a finite discrete variable's variance
- Build a transformed finite distribution, combining equal values
- Calculate the expectation of a transformed finite variable
- Calculate the variance of a transformed finite variable
- Explain discrete models, probability constraints and moment interpretation
- Choose and use a binomial probability model
- Calculate an event probability in a specified binomial model
- Calculate a conditional probability in a specified binomial model
- Calculate the expectation of a specified binomial count
- Calculate the variance of a specified binomial count
- Recover the unique binomial parameters from exact moments
- Find the least trial count satisfying a binomial probability threshold
- Choose and use a normal probability model
- Calculate an event probability in a specified normal model
- Calculate a conditional probability in a specified normal model
- Recover a normal boundary from its specified tail probability
- Recover a normal mean from a probability and known variance
- Recover a normal variance from a probability and known mean
- Recover the unique normal mean and variance from two probabilities
- Calculate a linear combination's expectation from specified moments
- Calculate a linear combination's variance with justified dependence conditions
- Calculate a probability for a specified combination of normal variables
- Reason about sampling and sampling distributions
- Calculate a population-mean estimate from a specified independent sample
- Calculate an unbiased population-variance estimate from a specified independent sample
- Calculate an estimated standard error from a specified independent sample
- Calculate a sample mean's expectation from specified population moments
- Calculate a sample mean's variance from specified population moments
- Calculate a sample mean's standard error from specified population moments
- Calculate a sample-mean probability under a specified exact or approximate normal model
- Calculate a minimum sample size for specified normal-model precision
- Formulate and interpret a justified hypothesis test
- Calculate a signed population-mean test statistic under a stipulated normal-test model
- Calculate a population-mean test p-value for a prespecified alternative
- Calculate all standardised critical boundaries for a planned population-mean test
- Calculate all sample-mean critical boundaries for a planned known-variance normal test
- Determine a population-mean test decision using the unrounded planned p-value and level
- Fit and interpret correlation and regression models
- Calculate product-moment correlation from specified paired data
- Calculate complete ordered intercept and gradient from specified paired data
- Calculate original-response model prediction from specified paired data
- Calculate signed residual on the fitted response scale from specified paired data
- Calculate sum of squared residuals on the fitted response scale from specified paired data
- Calculate original-input solution of a specified fitted calibration model from specified paired data
- Calculate product-moment correlation from specified paired data and transformations
- Calculate complete ordered intercept and gradient from specified paired data and transformations
- Calculate original-response model prediction from specified paired data and transformations
- Calculate signed residual on the fitted response scale from specified paired data and transformations
- Calculate sum of squared residuals on the fitted response scale from specified paired data and transformations
- Calculate original-input solution of a specified fitted calibration model from specified paired data and transformations
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Mock exam
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- About 180 minutes.
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