Bill Foster's content - Numbas at mathcentre.ac.uk

204 results authored by Bill Foster - search across all users.

Linear Inequality : direct input (Bill)
Draft
Question in Bill's workspace by Bill Foster

Solve $p - t < \text{or}> q$
Truth tables 0 (v2)
Ready to use
Question in Bill's workspace by Bill Foster

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$ .

For example $\neg q \to \neg p$ .
Truth tables 3 (v2)
Ready to use
Question in Bill's workspace by Bill Foster

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}(e \operatorname{op5} f)$ where each of $a, \;b,\;c,\;d,\;e,\;f$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4},\;\operatorname{op5}$ one of $\lor,\;\land,\;\to$ .

For example: $((q \lor \neg p) \to (p \land \neg q)) \to (p \lor q)$
Truth tables 2 (v2)
Ready to use
Question in Bill's workspace by Bill Foster

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e$ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$ .

For example: $((q \lor \neg p) \to (p \land \neg q)) \lor \neg q$
Truth tables 1(v2)
Ready to use
Question in Bill's workspace by Bill Foster

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$ .

For example: $(p \lor \neg q) \land(q \to \neg p)$ .
Truth tables 4 (v2)
Ready to use
Question in Bill's workspace by Bill Foster

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e$ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;r,\;\neg p,\;\neg q,\;\neg r$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$ .

For example: $((q \lor \neg r) \to (p \land \neg q)) \land \neg r$
Solving equations. (Video)
Ready to use
Question in Bill's workspace by Bill Foster

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Simultaneous Equations with integers as solutions.
Ready to use
Question in Bill's workspace by Bill Foster

A simultaneous equations question with integers only
Simultaneous linear equations (variables)
Ready to use
Question in Bill's workspace by Bill Foster

Shows how to define variables to stop degenerate examples.
Solve a pair of linear equations using a matrix
Ready to use
Question in Bill's workspace by Bill Foster and 1 other

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
Sequences and Limits 1.1
Ready to use
Question in Bill's workspace by Bill Foster

Seven standard elementary limits of sequences.
Sequences and Limits 1.2
Ready to use
Question in Bill's workspace by Bill Foster

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$ . Find $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \lt 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$ .
Sequences and Limits 1.3
Ready to use
Question in Bill's workspace by Bill Foster

$x_n=\frac{an+b}{cn+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \lt 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ .
set1
Ready to use
Question in Bill's workspace by Bill Foster

Given a set in predicate form i.e. $A=\{x|P(x)\}$ , find and input the elements of the set.
set2
Ready to use
Question in Bill's workspace by Bill Foster

Given a set $A$ , elements of which may also be sets, determine if the given elements or subsets are in $A$ .
set3
Ready to use
Question in Bill's workspace by Bill Foster

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.
set4
Ready to use
Question in Bill's workspace by Bill Foster

Enumerate elements of a set given in predicate form.

For example, find all elements of $A=\{x\in\mathbb{Z}\;|\;\;|2x-5|<4\}$ .
SFY0004 Implicit 1
Ready to use
Question in Bill's workspace by Bill Foster

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$ .
SFY0004 Implicit 2
Ready to use
Question in Bill's workspace by Bill Foster

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$ .

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.
Quantifiers 2
Ready to use
Question in Bill's workspace by Bill Foster

English sentences which are propositions are given and for each the appropriate statement involving quantifiers is to be chosen.
Quantifiers 3
Ready to use
Question in Bill's workspace by Bill Foster

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.
Quantifiers1
Ready to use
Question in Bill's workspace by Bill Foster

English sentences are given and for each the appropriate statement involving quantifiers is to be chosen. Also choose whether the statements are true or false.
Recursively defined sequences.
Ready to use
Question in Bill's workspace by Bill Foster

a) Given a recursively defined sequence $t(n)$ , find $t(n)$ as a function of $n$ .

b) Given a sequence $s(n),\;n \in \mathbb{N}$ , find a recursive definition of $s(n)$
Predicates and sets
Ready to use
Exam (5 questions) in Bill's workspace by Bill Foster

Various questions on predicates and sets.
Predicates
Ready to use
Question in Bill's workspace by Bill Foster

Given sentences involving propositions translate into logical expressions.
Propositions (v2)
Ready to use
Question in Bill's workspace by Bill Foster

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.
Paired t-test after treatment.
Ready to use
Question in Bill's workspace by Bill Foster and 1 other

Paired t-test to see if there is a difference between responses after treatment.
Max and Min 1 and 2
Ready to use
Question in Bill's workspace by Bill Foster and 1 other

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$ . Find stationary points, local and global maxima and minima of $g$ on $I$
Max and Min 3
Ready to use
Question in Bill's workspace by Bill Foster

$I$ compact interval, $g:I\rightarrow I$ , $g(x)=(x-a)(x-b)^2$ . Stationary points in interval. Find local and global maxima and minima of $g$ on $I$ .
Max and Min 4
Ready to use
Question in Bill's workspace by Bill Foster

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$ . Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min?

Bill Foster

Show results for Show results for

Refine by Refine by

Status

Tags

Usage rights

Ability Level

Topics