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Logarithms: Solving equations 2
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Question in Bill's workspace by Bill Foster

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.
Logarithms: Solving equations 1
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Question in Bill's workspace by Bill Foster

Solve for $x$ : $\log_{a}(x+b)- \log_{a}(x+c)=d$
Regression1
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Question in Bill's workspace by Bill Foster

Find a regression equation.
Regression2
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Question in Bill's workspace by Bill Foster

Find a regression equation.
Indefinite integral by substitution
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Indefinite integral by substitution
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$
Indefinite integral by substitution
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$
Indefinite integral by substitution
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Indefinite integral by substitution
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$ . Solution involves inverse trigonometric functions.
Indefinite integral
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Question in Bill's workspace by Bill Foster

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$ .
Indefinite integral
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Indefinite integral
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Indefinite integral
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .
Leicester: Integration 3
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx$ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx$

Also two other questions on integrating by parts.
Independent two sample t-test.
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Question in Bill's workspace by Bill Foster

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.
Hyperbolic Functions 2
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Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Hyperbolic Functions 4
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Question in Bill's workspace by Bill Foster

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Hyperbolic Functions 3
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Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$
Hyperbolic Functions 1
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Question in Bill's workspace by Bill Foster

Solve for $x$ : $a\cosh(x)+b\sinh(x)=c$ . There are two solutions for this example.
Dividing polynomials 2
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Question in Bill's workspace by Bill Foster

Algebraic manipulation/simplification.

Simplify $\displaystyle \frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.
Solving equations
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Question in Bill's workspace by Bill Foster

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .
Simplify Expression
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Question in Bill's workspace by Bill Foster

Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$ .
Expansion of two brackets: Linear and Quadratic
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Question in Bill's workspace by Bill Foster

Expand $(pw+q)(aw^2+bw+c)$ .
Expansion of two brackets: Quadratic and Quadratic
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Question in Bill's workspace by Bill Foster

Expand $(az^2+bz+c)(dz^2+pz+q)$ .
Expansion of two brackets: Quadratic and Linear
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Question in Bill's workspace by Bill Foster

Expand $(az^2+bz+c)(pz+q)$ .
Expansion of two brackets: Linear 2
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Question in Bill's workspace by Bill Foster

Expand $(ax+b)(cx+d)$ .
Expansion of two brackets: Linear 1
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Question in Bill's workspace by Bill Foster

Expand $ax(cx+d)$ and expand $(rx+s)(px)$
Expansion of three brackets: (Video)
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Question in Bill's workspace by Bill Foster

Expand $(ay+b)(cy+d)(py+q)$ .

Includes a video expanding three brackets, however uses the variable $x$ rather than $y$ .
Simplify Algebraic Expressions
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Question in Bill's workspace by Bill Foster

Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$ . Answer is a multiple of $x$ .
Simplify Algebraic Expressions: 2 unknowns
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Question in Bill's workspace by Bill Foster

Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$ . Answer is a multiple of $xy$ .

Bill Foster

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