190 results for "into".

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• Question

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.

• Question

Substitute values into formulae for the area or volume of various geometric objects.

• Question

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

• Numbas demo: video
Question in Demos

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

• Question in How-tos

Demonstrates that the marking algorithm for "match text pattern" parts doesn't put quotes around substituted strings any more.

• Question in How-tos

A table showing how to substitute raw LaTeX code into question text.

NOTE: You probably don't want to do this! There's usually a more robust way, where you get Numbas to make the expression for you.

• Question in How-tos
This question contains a single "match text pattern" part which accepts anything you type into it.
• Question in How-tos

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

• Question

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

• Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

• Input 2 PSY
Draft
Question

Details on inputting numbers into Numbas.

• Question

Independent events in probability. Choose whether given three given pairs of events are independent or not.

• Question

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA

• Question

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.

• Question

Calculate definite integrals: $\int_0^\infty\;e^{-ax}\,dx$, $\int_1^2\;\frac{1}{x^{b}}\,dx$, $\; \int_0^{\pi}\;\cos\left(\frac{x}{2n}\right)\,dx$

• Question

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

• Question

Inputting algebraic expressions into Numbas.

• Details on inputting numbers into Numbas.

• Question

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

• Question

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

• Question

Transform a second order ODE into 2D non-autonomous and 3D autonomous dynamical systems of ODEs.

• Transform a second order ODE into 2D non-autonomous and 3D autonomous dynamical systems of ODEs.

• Question

What is the value of the expression given a choice of n?

• Question

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.

• Question

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

• Question

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors.

• Question

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.

• Question

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number.

• Decimals to fractions