H1 Mathematics Checklist
Graphing techniques

Sketch the shapes of the graphs such as logarithm, exponential, trigonometric and rational functions.

Identify the features of each graph such as asymptotes, intercepts, turning points.

Finding intersection of graphs either using GC or algebraic method.
Inequalities, Quadratic and Simultaneous Equations

Solve an inequality using number line method (for rational functions).

Solve an inequality using graphical method.

Solve basic inequalities involving exponential, logarithm, surds, etc using either graphical or algebraic approach.

Read a context and formulate simultaneous equations to solve for unknown.

Use discriminant to determine the number of roots for a quadratic equation.
Logarithm and exponential

Apply properties of logarithm to simplify or solve equations, such as
2. Apply laws of indices to simplify or solve equations, such as
3. Perform change of base and convert from logarithm form to exponential form and vice versa.
4. Perform substitution to solve an equation involving exponential or logarithmic terms.
Differentiation

Determine whether a graph is increasing or decreasing using f '(x).

Determine the concavity of a graph using f "(x).

Use differentiation to find the maximum or minimum of a quantity.

Find tangent of a curve.

Use differentiation to calculate connected rate of change.
Integration

Solve integral using standard formulas.

Use integration to evaluate area involving single or two curves with respect to x and y axes.
Permutation and combination

Able to apply multiplication (sequential steps) and addition rule (cases) correctly.

Able to identify if a question is about permutation or combination.

Know when and how to apply the formula
correctly.
4. Apply special techniques such as "insertion method", "complement method" and "grouping method"
for special permutation situation.
Probability

Identify the correct type of events such as "complement", "union", "intersection", "conditional", "independent" and "mutually exclusive" events and their respective formulas.

Identify the correct strategy to solve the probability problem as as "P&C", "Tree diagram", "Venn Diagram" and "Frequency Table".
Discrete Random Variables

Apply probability concepts and present the probability distribution in a table format.

Calculate the expectation, E(X) and variance Var(X) of a discrete probability distribution.

Apply properties of E(X) and Var(X) such as
Binomial Distribution

Determine if a random variable has a binomial distribution using the conditions for a binomial distribution.

Solve probability problems involving binomial distribution using GC (binompdf, binomcdf) or the binomial pdf formula
3. Calculate the expectation E(X), variance Var(X) and the mode of a binomial distribution.
Normal Distribution

Calculate probability problems involving normal distribution using GC (normalcdf, invnorm).

Know when to convert a nonstandard normal random variable to the standard normal random variable, Z using the formula
3. Evaluate the distribution, mean and variance for a linear combination of normal random variables.
Distribution of sample mean

Know the conditions when is the distribution of the sample mean,
(a) normal, (b) approximately normal (CLT) or (c) neither.
2. Know how to calculate the mean and variance of and calculate probabilities involving
and normal distribution.
Hypothesis Tests

Write the appropriate null and alternative hypothesis statements.

Know the definitions of "level of significance" and "p value".

Know how to calculate the value of test statistic and critical value.

Carry out the hypothesis test (Z test) using p value method or critical value method.

Write appropriate conclusion statements for the hypothesis test.
Linear Regression and Correlation

Use GC and plot scatter diagram and comment on the relationship between two sets of data.

Compute the correlation coefficient and comment on the linear relationship between two sets of data.

Explain, in context, if a linear model is suitable and hence obtain the equation of the least squared regression line.

Explain, in context, the meaning of "a" and "b" in the regression line equation y = a + bx.

Carry out estimation using the equation of the regression line and comment whether the estimate is reliable or not.

Convert a nonlinear equation for the relationship between two variables into a linear one.