Practice finding parallel and perpendicular lines to a given line.

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Indices

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Two questions on solving systems of simultaneous equations.

Rearrange equations to make $x$ the subject.

Integration by Substitution

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Basic indefinite integrals, Basic definite integrals, integration by substitution

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Basic indefinite integrals, Basic definite integrals, integration by substitution

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Integration by Substitution

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Integration by Substitution

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Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

Definite Integrals

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Ratio Questions

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A student selects a card from a deck of 52 and rolls a dice once.

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Laplace from tables: e^(at), cos(bt), sin(bt).

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Laplace from tables: e^(at), cos(bt), sin(bt).

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Laplace of constants and powers of t

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Substitute the numeric or algebraic definition of a variable into different expressions. 

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

A student selects a card from a deck of 52 and rolls a dice once.

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Differential equations.

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Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

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Partial Fractions

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Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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