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AS & A-Level Question Bank

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Subjects:

Economics

The macro Economy

Economic growth, economic development and sustainability (4) National Income statistics (2) Employment/unemployment (3) Classification of countries (1)

Basic economic ideas and resource allocation

Externalities and market failure (7) Social costs and benefits; cost-benefit analysis (7)

The price system

Types of cost, revenue and profit, short-run and long-run production (2) Growth and survival of firms (1) Different market structures (1)

Government microeconomic intervention

Government failure in microeconomic intervention (1) Policies to achieve efficient resource allocation and correct market failure (1) Social costs and benefits; cost-benefit analysis (1)

Mathematics - furthe

Proof by induction

Proof by induction (22)

Matrix

Eigenvalues and eigenvectors (17) Diagonalise matrices (10) Matrix algebra (3) System of equations (1)

Equilibrium of rigid body

Objects in equilibrium (17) Toppling and sliding (13) Center of mass of rods (5) Moment (8) Composite objects (4) Center of mass of lamina (1) Center of mass of solids (1)

Rotation of a rigid body-Old Syl

Moment of Inertia (21) Parallel and perpendicular axes theorems (7) Equation of Angular Motion (9) Conservation of Energy for Rotational Rigid Body (8)

The binomial and geometric distributions

The geometric distribution (16) The binomial distribution (4)

Trigonometry

Trigonometry (44)

Integration

Integration by parts (21) Definite integration (43) Area problems (19) Integration of exponential functions (5) Integration by substitution (11) Integration using reduction formulae (4) Integration methods choosing (6) Volumes of revolution (9) Arc lengths and surface areas (7) Integration of sinx, cosx and sec2x and further trigonometric functions (18) Improper integrals (3) Integration formulae (4) Integration of $1/(x^2+a^2)$ (1)

Differential equations

Second order differential equations(homogeneous and inhomogeneous case) (13) Use of substitutions to transform differential equations (5) Solving differential equations (7) Forming a differential equation from a problem (3) Integrating factor and first order differential equations (1)

Simple Harmonic Motion-Old Syl

Definition of Simple Harmonic Motion and Period and Amplitude (20) Differential Equation and Simple Harmonic Motion (19) Approximation by Simple Harmonic Motion (3) Standard Simple Harmonic Motion Formula (15)

Momentum

Collision and convservation of momentum (39) Conservation of momentum (24) Multiple objects (5) Impulse (16) Oblique collisions (7) Kinetic energy (1) Momentum (1)

Circular motion

Angular speed and central force (7) Vertical circle (23) Radial and Transverse Components of Acceleration-Old Syl (4) Horizontal circle (1)

Vector

Find angle between two planes (5) Vector Equation of Line and Plane (4) The vector product (5) Find the distance between two skew lines (3) Find the distance from a point to a plane (3) Find angle between line and plane (1)

Complex Number

De Moivre’s theorem (11) The nth roots of a complex number (3) Powers of sine and cosine (5) Complex Summations (2) The modulus-argument form and exponential form (1) The complex plane and Argand diagrams (1)

Matrices

Matrix operations (16) Determinants (14) Inverse matrix (11) Matrix transformations (10) System of equations (4)

Chi-square test

Hypothesis of chi-square tests (1) Contingency table (1) Goodness of fit for discrete distribution (2) Goodness of fit for continuous distribution (2)

Polar Coordinate

The area of polar curve (14) Sketching polar curves (18) Application of polar coordinates (6) Convert between polar and Cartesian form (4)

Inferential statistics

Tests about mean by using normal or t-distribution (9) Confidence interval (18) Tests about difference in means by using normal or t-distribution (9) Paired t-tests (3)

Continuous random variables

Probability density function (13) Cumulative distribution function (13) Finding pdf and cdf of Y=g(x) (7) Expectation of function of continuous random variables (8)

Hookes law

Hookes law (5) Elastic potential energy (5) Work-energy principle (3)

Vectors

The vector euqation of a line (10) The angle between two lines (4) The distance between two skew lines (1) Position vectors (3) The scalar product (3) The distance from a point to a line (5) Vector Equation of Line and Plane (3) Find the distance from a point to a line (1) Intersection of two lines (6) The vector equation of a line (2) Intersection of two planes (1) Find the distance between two skew lines (1) Find angle between line and plane (1)

Differentiation

Parametric differentiation (3) Increasing and decreasing functions (1) Connected rates of change and its application (1) Derivatives of trigonometric functions (2) The product rule and quotient rule (2) Integration by parts (1) Implicit differentiation (3) Second derivatives (1) Stationary points and second derivatives (2) Maximum and minimum points (1) Derivatives and gradient functions (1) Derivatives of exponential and natural logarithmic functions (1)

Probability distributions

Continuous random variables (1) The normal distribution (1) Probability distributions (9) Expectation and variance of a discrete random variable (11) Discrete random variables (8)

Measrures of variation

Variance and standard deviation (2) The interquartile range (IQR) and percentiles (3)

Probability

Independent events and the multiplication law (4) Basic concepts in probability (4) Conditional probability (1)

Roots of polynomial equations

Cubics (12) Substitution (4) Quadratics (1)

The normal distribution

Continuous random variables (3) The normal distribution (4) Modelling with the normal distribution (4)

Measures of central tendency

The mean (6) The median (2) Variance and standard deviation (1)

Energy, work and power

Kinetic energy (5) Gravitational potential energy (4)

Complex numbers

Complex numbers and arithmetic operations (2) Solving equations with complex roots (3)

Summation of Series

The Summation Formula ∑r, ∑r 2 , ∑r 3 (7) Converging Series (9)

Algebra

Partial fractions (4) The modulus function and its graph (3) Solving modulus inequalities (2) Division of polynomials (2) The factor theorem and remainder theorem (2) Rearrange Formula (1)

Kinematics of motion in a straight line

Velocity as the derivative of displacement with respect to time (2) Acceleration as the derivative of velocity with respect to time (2) Displacement as the integral of velocity with respect to time (1)

Probability generating function

Probability generating function (1) Mean and variance by using pgf (1) Sum of independent random variables (1)

Linear motion under variable force

Acceleration with respect to displacement (1)

Nonparametric tests

Single sample sign test (1)

Projectile

Motion in the vertical plane (1) Trajectory (2)

Mathematics

Integration

Area problems (2) Volumes of revolution (1)

Differentiation

Tangents and normals (1) Derivatives and gradient functions (1) Connected rates of change and its application (1)

Series

Binomial expansions (1)

Trigonometry

Trigonometry (5)

Functions

Definition of functions (1)

Physics

Alternating currents

Rectification and smoothing (2) Characteristics of alternating currents (1)

Medical Physics

Production and use of ultrasound in diagnosis (1) Production and use of X-rays (1)

Motion in a circle

Kinematics of uniform circular motion (4) Centripetal acceleration and centripetal force (4)

Gravitational fields

Gravitational force between point masses (3) Gravitational field (4) Gravitational potential energy and Potential (3) Gravitational field of a point mass (1)

Energy, work and power

Work done by a force (1) Conservation of mechanical energy (1)

Capacitance

Capacitors and capacitance (1) Energy stored in a capacitor (1)

Momentum

Collision and convservation of momentum (4)

Magnetic fields

Concept of magnetic field (1) Force on a moving charge (1)
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