Algebra word problems using area and perimeter.

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Calculating wages using algebraic equations

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Another transposition question, which requires (basic) factorisation.

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rearranging the Michelas-Menten equation to make the substrate the subject.

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Indefinite Integrals

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4 questions on integrating by parts.

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

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Definite Integrals

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5 indefinite integrals containing exponential functions

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Indefinite Integrals

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Antiderivatives

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Definite Intgerals

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Find the general solution of $y''+2py'+(p^2-q^2)y=x$ in the form  $Ae^{ax}+Be^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral.

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Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

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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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Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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This is a homework assignment. Students may complete this assignment during a maths lesson with the support from the teacher. 

• Passing mark 60%
• Difficulty level 3 Moderat/Average (C+, B-, B Level).

Practice of basic transpositions. Doesn't include roots

Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.

Antiderivatives

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

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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

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Match the question with the correct formula.

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Laplace of constants and powers of t

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