218 results for "root".
-
Question in MfEP Progress Quizzes
Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.
-
Question in MfEP Progress Quizzes
Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.
-
Question in MfEP Progress Quizzes
This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.
The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.
-
Question in Skills Audits for Maths and Stats
Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation
-
Question in Skills Audits for Maths and Stats
Factorise three quadratic equations of the form $x^2+bx+c$.
The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.
-
Question in MESH
Simple questions on square numbers, square roots, cube number, cube roots and prime numbers.
-
Question in How-tos
The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.
When there's only one root, the student can only fill in one of the answer fields.
This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.
The marking corresponds to this table:
There is one root There are two roots Student gives one correct root 100% 50%, "The root you gave is correct, but there is another one." Student gives two correct roots impossible 100% Student gives one incorrect root 0% 0% Student gives one incorrect, one correct root 50% "One of the numbers you gave is not a root". 50% "One of the numbers you gave is not a root". Student gives two incorrect roots 0% 0% -
Question in HELM books
Rearrange a formula with a square root to make a variable under the root the subject.
-
Question in HELM books
Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.
-
Question in HELM books
evaluate sqrt(x/z) where x and z are random positive decimals.
-
Question in Functions
Given a randomised square root function select the possible ways of writing the domain of the function.
-
Question in Musa's workspace
A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.
-
Question in Musa's workspace
A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.
-
Question in Musa's workspace
Factorise three quadratic equations of the form $x^2+bx+c$.
The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.
-
Question in Yvonne's workspace
Factorise three quadratic equations of the form $x^2+bx+c$.
The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.
-
Question in Content created by Newcastle University
Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.
-
Question in Yvonne's workspace
Factorise three quadratic equations of the form $x^2+bx+c$.
The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.
-
Question in Content created by Newcastle University
Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.
-
Question in Shaheen's workspace
No description given
-
Question in WM175 ASSESSMENT 1
Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.
-
Question in MASH Bath: Question Bank
Determining the number of real roots a quadratic equation has by evaluating and interpreting the discriminant.
-
Question in Ed's workspace
Factorise three quadratic equations of the form $x^2+bx+c$.
The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.
-
Question in Ed's workspace
Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation
-
Question in Ed's workspace
Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation
-
Ugur's copy of Ugur's copy of Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$ Ready to useQuestion in Ugur's workspace
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 in NCL MAS2707
Consider a binary tree with $2^n$ nodes.
We give generators for the isomorphisms of the tree: at each non-leaf vertex, swap the branches descending from that node.
- What is the action of a given word?
- Write a word which produces the required isomorphism
- Which generators commute?
- What is the order of each generator?
- Write one of the (non-root) generators in terms of the others.
- Which permutations of the leaves are possible?
- What is the order of the group of isomorphisms?
- What is the order of the quotient group obtained by identifying all the leaves of one branch?
-
Question in NC Math 4
No description given
-
Exam (2 questions) in .Algebra
Identify co-efficients, then use quadratic formula to find roots.
All set to be distinct and real. Some can be non-integer (0.5 steps)
-
Question in .Algebra
Solve quadratic equations (non-simple case, two real, discrete integer roots) using the formula.
-
Question in .Algebra
Solve quadratic equations (non-simple case, two real, discrete roots) using the formula. Some, random, non integer roots.