550 results for "expression".
-
Question in MASH Bath: Question Bank
Knowing the half-life of Carbon-14 and the initial mass of Carbon-14 when a tree was cut (a) write an expression that describes the relationship between the remaining mass and time, (b) calculate the remaining mass after $t$ years, and (c) given the remaining mass calculate how many years ago the tree was cut down.
-
Question in MASH Bath: Question Bank
The relationship between the frequency of an allele A, $x$, at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A, $w$, is described by the function $w=ax^2+x(b-x)+c(b-x)^2$ . The aims are (a) ti simplify the algebraic expression, (b) calculate the fitness of a population with a given allele A frequency, and (c) calculate the allele A frequency when the fitness of the population is given.
-
Question in Skills Audits for Maths and Stats
Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$.
-
Question in Skills Audits for Maths and Stats
Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.
-
Question in Skills Audits for Maths and Stats
Differentiate a polynomial expression involving coefficients and, negative and fractional indices.
-
Question in Skills Audits for Maths and Stats
Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.
-
Question in Skills Audits for Maths and Stats
Simplifying first is essential in terms of managing expressions that might need factorising.
-
Question in Skills Audits for Maths and Stats
A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).
-
Question in Skills Audits for Maths and Stats
Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.
-
Question in Skills Audits for Maths and Stats
Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.
-
Question in Skills Audits for Maths and Stats
Substitute values into an algebraic expression and calculate the result.
-
Question in Skills Audits for Maths and Stats
Fiind the Highest Common Factor of two algebraic expressions involving a coefficient and powers of $x$ and $y$.
-
Question in Skills Audits for Maths and Stats
Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4
-
Question in Skills Audits for Maths and Stats
Filling in the blanks from the answer to a simplified expression involving indices.
-
Question in Skills Audits for Maths and Stats
Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.
-
Question in Skills Audits for Maths and Stats
Simplifying expressions from $\frac{x^mx^n}{x^p}$ to $x^{m+n-p}$.
-
Question in How-tos
A mathematical expression part with a pattern restriction to ensure that the student has extracted the highest common factor of two terms.
The answer must be of the form $a(b+cx)$, where $b$ and $c$ are coprime.
-
Question in HELM books
evaluate a function with randomised alphanumeric expressions as inputs.
-
Question in How-tos
A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.
If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.
-
Question in Demos
Examples of the following custom part types: Yes/no, List of numbers, Give a numerical input for an expression, Number entry modulo.
-
Question in Demos
This shows how to take an expression given by the student and plot the implicit curve of points where it equals zero.
-
Question in Demos
This question shows a JSXGraph diagram above a mathematical expression input, containing a plot of the expression the student enters.
-
Question in HELM books
Simplify, if possible,
(a) $\frac{2}{3}x^2 + \frac{x^2}{3}$, (b) $0.5x^2 + \frac{3}{4}x^2 - \frac{11}{2}x$, (c) $3x^3 - 11x + 3yx + 11$, and (d) $-4\alpha x^2 + \beta x^2$ where $\alpha$ and $\beta$ are constants.The numbers and letters are all randomised.
Part of HELM Book 1.3
-
Question in Odds and Ends
Used in a LANTITE workshop.
-
Question in Ugur's workspace
Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.
-
Exam (7 questions) in Introduction to Calculus
Apply the factor and remainder theorems to manipulate polynomial expressions
-
Question in HELM books
Explain why one variable is a factor but the other is not. Factorise the expression, whose factor is alphanumeric. Part of HELM Book 1.3
-
Question in HELM books
Factorise a 2-term expression where the gcd can be alphanumeric. Part of HELM Book 1.3
-
Question in HELM books
Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4
-
Question in HELM books
Factorise a 2-term expression by pulling out a numeric gcd. Part of HELM Book 1.3