Fully comprehensive math worksheets with detailed solutions and other math resources for students of all abilities and levels (KS2, KS3, SATs, 11+, GCSEs, iGCSEs, A-Levels, Scottish Highers and Advanced Highers, International Baccalaureate, BTECs or even university or college degree level).
Fully comprehensive math worksheets with detailed solutions and other math resources for students of all abilities and levels (KS2, KS3, SATs, 11+, GCSEs, iGCSEs, A-Levels, Scottish Highers and Advanced Highers, International Baccalaureate, BTECs or even university or college degree level).
A worksheet on factorials. The exercises require to evaluate expressions involving factorials, simplify expressions with factorials and solve equations involving factorials. Detailed solutions are included.
A worksheet on expanding and simplifying expressions using the identities for the square of a sum or a difference of two terms, the cube of a sum or a difference of two terms and the difference of two squares. It included some more demanding exercises that require to prove new identities or evaluate the value of given expressions using the identities. Solutions are included.
A review worksheet on the equation of a straight line and simultaneous equations. The exercises require to find the midpoint of a line segment and the distance between two points, to find the relative position of two given lines, find the equation of a line passing through a given point and parallel to a given line, use graphs of lines to find the solution of simultaneous equations, solve simultaneous equations algebraically and solve word problems using simultaneous equations. Detailed solutions are included.
Three introductory worksheets on negative rational numbers. The exercises require to order a given set of numbers, compare pairs of given numbers, find missing numbers in a given sequence.
Solutions are included.
An introductory worksheet on exponential functions. The exercises include stating whether a given function is exponential or not, evaluating an exponential function at some values, determining the constant term of an exponential function given a point on its graph and sketching exponential functions. Solutions are provided.
Three worksheets on the following topics
Introduction to Logarithms: The exercises require converting expressions from exponential to logarithmic form, evaluating given logarithms and solving equations involving logarithms or exponential equations.
Properties of Logarithms: The exercises require using the basic properties of logarithms, product rule,
division rule, power rule/exponential rule and change of base rule.
Logarithmic Function: he exercises require to sketch graphs of such functions, find their domain and the functions which are symmetric to them about the line y=x.
Detailed solutions are included.
Three worksheets on the following basic properties of logarithms:
log_a 1=0
log_a a=1
log_a a^x=x
a^{log_a x}=x
product rule
division rule
power rule/exponential rule
change of base rule
Detailed solutions are included.
A worksheet on logarithmic functions. The exercises require to sketch graphs of such functions, find their domain and the functions which are symmetric to them about the line y=x.
Detailed solutions are included.
An introductory worksheet on logarithms. The exercises require converting expressions from exponential to logarithmic form, evaluating given logarithms and solving equations involving logarithms or exponential equations.
Detailed solutions are included.
A worksheet on factorizing algebraic expressions (quadratics included), simplifying algebraic expressions, performing the four operations between algebraic fractions, solving equations and word problems using factorization. detailed solutions are included.
Three worksheets on factorials. The exercises require to evaluate expressions involving factorials, simplify expressions with factorials and solve equations involving factorials. Detailed solutions are included.
A worksheet on the basic properties of logarithms: product rule,
division rule, power rule/exponential rule and change of base rule.
Detailed solutions are included.
A collection of three worksheets on addition, subtraction, multiplication and division of integers and addition and subtraction of positive and negative fractions. Detailed solutions are included.
An introductory worksheet on differentiating simple functions from first principles using the definition of the derivative at x0 as the limit of the quotient f(x)-f(x0)/x-x0 at this point. Detailed solutions are included.
An introductory worksheet on differentiating functions from first principles using the definition of the derivative as the limit of the quotient f(x+h)-f(x)/h as h tends to zero. Detailed solutions are included.
A worksheet on differentiating using the basic rules for functions that are constant, powers of a variable or sums of powers of a variable, products of a constant and another function, products or quotients of two functions. Detailed solutions are provided. Good for GCSE/IGCSE students.
A worksheet on using differentiation in order to determine the gradient (and the equation) of the tangent of a function at a given point. Detailed solutions are provided. Good for GCSE/IGCSE students.
A worksheet on finding the domain or the range of a given function (including the cases of polynomial functions, rational functions and functions with square roots). Detailed solutions are included.
