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When you subscribe, clicking on any of the items in the list below will take you to one or more example problems for the selected task. If you're still lost you can click to view the lesson that discusses that task.
Algebraic Methods
| Factorise an expression |
| Solve a quadratic equation |
| Simplify an algebraic fraction |
| Simplify a compound fraction |
| Solve a linear equation |
| Simplify a surdic expression |
| Solve an equation involving surds |
| Compare two surds |
| Express a rational fraction as a decimal |
| Express a decimal as a rational fraction |
Functions
| Find the domain/range of a relation |
| Test if a function is even or odd |
| Compose two functions |
| Find the zeroes of a function |
| Find the inverse of a function |
| Find the transformations that produced a function |
| Find a function given a set of transformations |
| Sketch a function given its formula |
Linear Functions
| Solve linear simultaneous equations |
| Find equation of a line using point and gradient |
| Find equation of a line using gradient and intercept |
| Use Mid-point and distance formulas to prove geometrical properties |
| >Use gradients to prove geometrical properties |
| Find intersection point of two lines |
| Find a line through the intersection point of two other lines |
Quadratic Functions
| Solve simultaneous quadratic equations |
| Find intersection of quadratic and linear equation |
| Find properties of a quadratic from sum and product of roots |
| Find properties of a quadratic from the discriminant |
| Find properties of a quadratic from its equation |
| Find the zeroes of a quadratic |
| Find the features of a quadratic from its equation |
| Find the equation of a quadratic given its features |
Other Functions
| Sketch a cubic given x-intercepts |
| Sketch a cubic given its equation |
| Use Absolute Value Identities |
| Sketch an Absolute Value Functon |
| Solve an Absolute Value Equation |
| Sketch a hyperbola given its equation |
| Find properties of a circle from its equation |
| Find intersection of a circle and a line |
Trigonometry
| Find a side of a right angled triangle given a side and an angle |
| Find an angle of a right angled triangle given two sides |
| Find a trigonometric ratio given another |
| Find a trigonometric ratio using related angles |
| Use the sine rule to find a side |
| Use the sine rule to find an angle |
| Use the cosine rule to find a side |
| Use the cosine rule to find an angle |
| Find a side, given an angle of elevation/depression |
| Find a true bearing, given angles/sides |
| Find a side, given angle/sides in three dimensions |
| Find an angle, given angle/sides in three dimensions |
Trigonometric Functions
| Find area of a region defined by circles/radiuses/chords |
| Find perimeter of a region defined by circles/radiuses/chords |
| Find properties of a region defined by circles/radiuses/chords |
| Solve simple trigonometric equatons |
| Find equation of trigonometric function from sketch |
| Sketch trigonometric function from equation/properties |
| Sketch trigonometric function from description of properties |
| Sketch trigonometric function from transformations |
| Simplify trigonometric expressions using trigonometric identities |
| Solve a trigonometric equation involving two trigonometric functions |
| Solve a trigonometric equation involving one trigonometric function |
| Solve a trigonometric equation using a quadratic substition |
Differentiation
| Differentiate from first principles |
| Find the limit of an expression |
| Test a function for continuity |
| Differentiate powers |
| Differentiate composites |
| Differentiate products |
| Differentiate quotients |
| Sketch a derivative given its function |
| Find the equation of a tangent to a curve |
| Find the equation of a normal to a curve |
| Find a rate given an expression for Quantity |
| Find velocity given displacement |
| Find acceleration given displacement |
Exponential and logarithm
| Simplify expression involving logs |
| Solve equations with unknown in the exponent |
| Solve equation with unknown as a log |
| Differentiate an exponential |
| Graph an exponential using transformations |
| Differentiate a logarithm |
| Graph a log function using transformations |
| Asset depreciation using exponential decay |
| Radioactive half life and exponential decay |
| Solve equation involving logs |
Probability
| Translate English to set properties |
| Translate english to sample and event spaces |
| Translate english to statements about probability |
| Calculate conditional probability using the sample space definition |
| Calculate conditional probability using the probability definition |
| Calculate probability of independent events using enumeration |
| Calculate probability of independent events using a tree diagram |
| Calculate probability of non-independent events using a tree diagram |
| Calculate probability of non-independent events using enumeration |
Discrete Probability distributions
| Construct a probability distribution for a random variable |
| Use properties of the probability distribution associated with a random variable |
| Calculate sample mean and sample variance of a sample |
| Calculate sample mean and sample variance of a sample generated by simulaton |
| Calculate mean and variance of a discrete probability distribution |
| Use properties of a discrete probability distribution |
| Use properties of a uniform distribution |
| Use properties of a Bernoulli distribution |
Graphing Techniques
| Find the transformations that produced a function |
| Sketch a trigonometric function |
| Solve a linear inequation |
| Solve an inequation graphically |
Differentiating Standard functions
| Differentiate trigonometric functions |
| Differentiate exponential functions |
| Differentiate logarithmic functions |
Applications of Differentiation
| Find extreme values of a function on an interval |
| Find maxima and minima of a function on an interval |
| Find intervals where a function is increasing or decreasing |
| Find the inflection points of a function |
| Find the nature of the stationary points of a function |
| Find the nature of the inflection points of a function |
| Sketch a function using derivatives |
| Solve maxima and minima problems |
Integration
| Find antiderivatives of powers and sums of powers |
| Find antiderivatives of trigonometric functions |
| Find antiderivatives of reciprocal functions |
| Find antiderivatives of exponential functions |
| Find the area under a curve using lower rectangles |
| Evaluate a definite integral |
| Find the area under a curve using definite integrals |
| Find the area between a curve and the y axis |
| Find the net change given a rate |
| Given a velocity, find the displacement |
| Given acceleration, find the velocity |
| Approximate a definite integral using the trapezoid rule |
| Find an approximation to an irregular area using the trapezoid rule |
Financial Mathematics
| Find an effective rate given nominal rate |
| Find the time to achieve a given future value |
| Find an effective rate given time and future value |
| Find the future value of an annuity using the recurrence relation |
| Find the future value of a reducing balance loan using the recurrence relation |
| Find the future value of an annuity using a spreadsheet function |
| Find the future value of an annuity using an annuity table |
| Construct a reducing balance loan table |
| Find the present value of an annuity using a present value table |
| Find properties of an arithmetic series given some terms |
| Find the sum of some terms of an arithmetic series |
| Find an expression for the nth term of an arithmetic series |
| Find the number of terms in an arithmetic series given some terms |
| Use properties of arithmetic series to solve problems |
| Find properties of a geometric series given some terms |
| Find the sum of some terms of a geometric series |
| Use properties of geometric series to solve problems |
| Find the future value of an annuity using series |
| Find the payment amount on a loan using series |
| Find the contribution amount to achieve a given value on an annuity using series |
Descriptive Statistics
| Construct a frequency table |
| Construct a stem and leaf plot |
| Construct a frequency histogram |
| Construct a cumulative frequency histogram |
| Construct a relative frequency histogram |
| Determine the skew of a dataset |
| Find the mean and standard deviation of a dataset |
| Find the interquartile range of a dataset |
| Construct a box plot |
Bivariate Data Analysis
| Construct a scatter plot |
| Calculate the correlation coefficient |
| Construct a best fit line by eye |
| Construct a least squares best fit line |
Continuous Probability Distributions
| Confirm a function is a probability distribution |
| Calculate the mean and variance of a continuous probability distribution |
| Find a probability distribution given the cumulative distribution |
| Find a probability given the score in a normal distribution |
| Find a score given a percentile in a normal distribution |
| Find a probability given the score in a normal distribution using a spreadsheet function |
| Find a score given a percentile in a normal distribution using a spreadsheet function |
More on Functions
| Sketch a graph of y = |f(x)| |
| Sketch a graph of y = 1/f(x) |
| Sketch a graph of y2 = f(x) |
| Find the inverse of a function |
| Sketch the inverse of a function |
| Sketch a curve from its parametric equations |
| Find the cartesian equation of a curve from its parametric equations |
Polynomials
| Divide one polynomial by another |
| Use polynomial properties |
| Use polynomial identities |
| Use Remainder and Factor theorems |
| Use Sums and Products of Zeroes |
| Use Properties of repeated zeroes |
| Find approximations to zeroes |
Trigonometric Functions and Identities
| Evaluate expressions involving inverse trigonometric functions |
| Sketch inverse trigonometric functions |
| Prove trigonometric identities involving compound angles |
| Prove trigonometric identities using t-formulas |
| Evaluate trigonometric ratios using t-formulas |
| Convert expressions involving products of trigonometric ratios to expressions involving sums |
| Convert expressions involving sums of trigonometric ratios to expressions involving products |
| Solve equations involving sums of trigonometric ratios |
Rates of Change
| Use properties of rates |
| Verify a solution of a rate equation |
| Find properties of rate equations |
| Find a related rate |
Combinatorics
| Find a coefficient in a binomial expansion |
| Expand a binomial up to a given term |
| Find the greatest coefficient in a binomial expansion |
| Find the greatest term in a binomial expansion |
| Prove a binomial identity using substitution |
| Prove a binomial identity by differentiation |
| Prove a binomial identity by integration |
Counting and Probability
| Count an ordered selection |
| Count ordered selections with constraints |
| Count a circular arrangement |
| Count an unordered selection |
| Apply the pigeonhole principle |
| Apply counting of unordered selections to probability |
| Apply counting of ordered selections to probability |
| Apply counting of circular arrangements to probability |
More Inequalities
| Solve a rational inequality |
| Solve a rational inequality where the unknown is a factor |
| Solve an absolute value inequality |
| Solve a rational absolute value inequality |
Proof
| Prove a summation formula by induction |
| Prove divisibility by induction |
| Prove an inequality by induction |
Trigonometric Equations
| Solve a trigonometric equation involving compound angles |
| Solve a trigonometric equation involving reciprocal functions |
| Solve a trigonometric equation involving two trigonometric functions |
| Solve a trigonometric equation using the auxiliary angle method |
| Solve a trigonometric equation using the t formula method |
| Find the general solution to a trigonometric equation |
More Calculus
| Differentiate an expression by expanding it |
| Integrate an expression by rewriting it |
| Integrate a trigonometric expression using the rule for the power of a composite |
| Integrate a trigonometric expression using a compound angle identity |
| Integrate a trigonometric expression by expanding it |
| Integrate an expression using a substitution of the form u=f(x) |
| Integrate an expression using a substitution of the form x=f(u) |
| Differentiate an expression involving inverse trig functions |
| Evaluate integrals related to inverse trig functions |
| Find a volume by rotation about the x axis |
| Find a volume by rotation about the y axis |
| Integrate an expression involving derivatives of inverse trig functions |
| Find the area between two curves |
Differential Equations
| Verify a function is a solution to a differential equation |
| Solve a simple differential equation |
| Plot the direction field of a differential equation |
| Solve a separable differential equation |
| Solve a linear differential equation |
| Solve a logistic differential equation |
Vectors
| Find the components of a vector defined by two points |
| Find the magnitude and direction of a vector defined by two points |
| Add and subtract vectors using components |
| Prove properties of vectors using components |
| Add and subtract vectors using unit vectors |
| Find the magnitude and direction of a vector defined by unit vectors |
| Compute the scalar product of vectors |
| Project one vector onto another |
| Find a vector component |
| Decompose a vector into vector components |
| Find forces using vector components |
| Find the range of a projectile |
| Find the time of flight of a projectile |
| Find the maximum height of a projectile |
Binomial Distribution
| Find a binomial distribution |
| Find the mean and variance of a binomial distribution |
| Find the probability of an outcome of a binomial experiment |
| Find the most likely outcome of a binomial experiment |
| Find the probability of at least k successes in a binomial experiment |
| Find the probability of at most k successes in a binomial experiment |
| Use the Normal approximation to the Binomial |
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