Xiaodan Leng

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Solving for a geometric series

Solving for a geometric series

Solving for a geometric series

Find the sum of the first n terms of a Geometric progression

Find the nth term of a Geometric progression

Find the sum of the first n terms of an arithmetic progression

Find the nth term of an Arithmetic progression

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Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Simplify logarithmic expressions using rules on logarithms.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Recognising the equation of a circle.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

A parabolic graph is given. The question is to determine the equation of the graph. Non-calculator. Advice is given.

A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point. Non-calculator. Advice is given.

A quartic graph is given. The question is to determine whether the gradient is positive or negative at various values of x. Non-calculator. Advice is given.