220 results for "formula".

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• Question
Formulate a recurrence relation (= difference equation) and solve this recurrence relation.
• Question

A question testing the application of the Area of a Triangle formula when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

• Question

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

rebelmaths

• Algebra 1
Exam (3 questions)
In this practice test you can work on simple equations and also solving quadratics using the formula. You should give all answers to 2 decimal places.
• Question

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

• Exam (3 questions)

Apply formulas to calculate the areas of various shapes.

• Question

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

• Exam (5 questions)

Identify parts of statistical formulas, and answer questions about how changing one variable affects the statistic.

• Question

Given three linear combinations of four i.i.d. variables, find the expectation and variance of these estimators of the mean $\mu$. Which are unbiased and efficient?

• Question

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$.

• Question

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

• Question

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

• Question

$Y \sim \operatorname{Poisson}(p)$. Find $P(Y=a)$, $P(Y \gt b)$, $E[Y],\;\operatorname{Var}(Y)$.

• Question

Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

• Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

• Question

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

• Question

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

• Question

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

• Question

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

• Question

Substitute given values into formulas.

• Question

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

• Question

Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.

• Question

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.

• Question

Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

• Question

Given a formula for a sequence, calculate a given term.

• Question

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

• Question

Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.

Each part is broken into steps, with the formula given.

• Question

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif

• Question

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• Question

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.