$$Introduction:$$

Hello! You have reached the "Great answers to learn from" page. This page is meant to be a collection of great answers that people could look back upon and learn from. Hopefully if you have a certain topic you want to learn about, you can some posts on that topic here!

For the most part, this thread is organized into "grade levels" of mathematics to make it easier to find what you want to learn about.

Finally, if you have anything you want to add to this post, go ahead and reply to it with what you want added, or you can message me and I'll add it to the proper section.

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This post was organised and up kept by NinjaDevo. I am very grateful to Ninja for his great efforts.

This is the address of Ninja's original: http://web2.0calc.com/questions/great-answers-to-learn-from

NinjaDevo is now too busy to upkeep the thread so I have transerred it into my name so that I can edit it as required.

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**Roots and exponents:**

• Simplifying.

http://web2.0calc.com/questions/3-sup3-radic-24-sup3-radic-375

http://web2.0calc.com/questions/can-anyone-do-square-roots

• Finding a root of a negative number

• Rationalising a denominator:

http://web2.0calc.com/questions/in-question-21-nbsp

• Exponets with negative bases:

**Fractions:**

• Dividing two fractions:

http://web2.0calc.com/questions/3-4-5-8

• Find the Least Common Denominator (LCD):

http://web2.0calc.com/questions/what-is-the-lcd-for-5-9-and-2-3

When can fraction be written as a terminating decimal. Great answer by CPhill. (26/11/14)

**Dealing with time in math, on a handheld calculator!**

http://web2.0calc.com/questions/what-is-21hours-and-58-minutes-subtracted-by-4-36-p-m-equal

**Directed numbers and plotting on a number line**

http://web2.0calc.com/questions/the-answer-to-the-expression-3-6-located-on-a-horizontal-number-line

**Is zero even or odd?**

http://web2.0calc.com/questions/0-is-a-nbsp-odd-number-or-even-number-why-please-explain

**Understanding different bases**

Converting base 10 to base 2

http://web2.0calc.com/questions/what-is-the-binary-representation-of-2015

**Ratio**

**Speed and rates:**

• Migrating elephants!

• Speed of a current

* Speed distance and trains (time for trains to pass each other)

http://web2.0calc.com/questions/i-came-across-this-question-and-didn-t-know-how-to-solve-it

* Speed of an escalator

* Speed of taps filling a pool

**Comparing numbers; the apparent brightness of stars!**

http://web2.0calc.com/questions/science-link-math-question

**Percentages:**

• Find a total when given a part

http://web2.0calc.com/questions/435-is-15-of-what-number

**Variant of Average:**

**Adding up all the numbers between two specific numbers:**

http://web2.0calc.com/questions/what-is-all-the-numbers-from-1-to-100-added-up

**Forever repeating decimal!**

http://web2.0calc.com/questions/0-99999

**Order of operations - multiplication before addition:**

http://web2.0calc.com/questions/3x60-5x9-2x2

**The basics of algebra:**

• What does "x" mean?

http://web2.0calc.com/questions/5x-21-2x-what-does-x-mean

• Solving for x by "balancing" out two sides of an equation:

http://web2.0calc.com/questions/solve-for-x-7

Solving a simple equation

http://web2.0calc.com/questions/solving-a-simple-equation

• Why would I use x^{2}?

http://web2.0calc.com/questions/what-does-x-squared-equal

**Algebra word problem examples:**

• Simultaneous equations:

http://web2.0calc.com/questions/how-old-they-are

• Set it up algebraicly, and solve!

http://web2.0calc.com/questions/i-know-the-answer-but-do-not-know-how-to-do-the-work

**Fractions and solving for x:**

http://web2.0calc.com/questions/if-then

http://web2.0calc.com/questions/solve-for-x-3-over-4-x-5-over-8-4x

**Three different techniques to this answer dealing with polynomials:**

http://web2.0calc.com/questions/5a-5-5a-5

**difficult indices (quadratic equation) question. (20/11/14)**

http://web2.0calc.com/questions/can-anyone-tell-me-what-are-the-steps-for-this

**Simplifying indices - they can be messy **

http://web2.0calc.com/questions/can-you-solve-this

**Simplifying indices - A pretty cool question (29/12/14)**

http://web2.0calc.com/questions/can-you-solve-this

**Making x the subject of a parabola**

http://web2.0calc.com/questions/factor_5 (15/12/14)

**Simplifying root questions**

http://web2.0calc.com/questions/sqrt-a-2sqrt-a-4-5-7-sqrt-a-5

http://web2.0calc.com/questions/sqrt-6-sqrt-11-sqrt-6-sqrt-11

**Finding root using secant method.** Thanks Alan (29/12/14)

http://web2.0calc.com/questions/find-the-roots-of-the-equation-x2-4x-5-0-the-secant-method

**Floor and ceiling functions**

http://web2.0calc.com/questions/need-help-on-this-a-lot-thanks

http://web2.0calc.com/questions/the-function-nbsp-nbsp-is-defined-as-find-nbsp

**Binomial Expansions Advanced **

**http://web2.0calc.com/questions/what-is-the-coefficient-of-nbsp-nbsp-in-nbsp_2**

**SEQUENCES AND SERIES **

Sum of a Sequence - Really difficult

**POLYNOMIALS**

(There is a whole collection in here from 5/12/14)

http://web2.0calc.com/questions/polynomial-questions#rr0

**GRAPHING and FUNCTIONS**

Similar functions - I really liked this question (7/11/14)

This one really made me think - Melody (7/11/14)

This is similar to the above one but a bit easier.

http://web2.0calc.com/questions/the-function-nbsp-nbsp-satisfiesfor-all-nbsp-nbsp-nbsp-find-nbsp_1

Find the range of this function

http://web2.0calc.com/questions/letfind-the-range-of-nbsp-give-your-answer-as-an-interval-nbsp_1

This function question is not difficult - just unusual (7/11/14)

http://web2.0calc.com/questions/please-help-and-do-it-correctly

**Conic Sections:**

The original question is a degenerate conic BUT I have included info on other conics

This result is really weird graph. It has degenerated into two cross lines.

http://web2.0calc.com/questions/how-do-you-solve-this-please-help-me-2x-2-3y-2-5xy-and-3x-y-5

**Imaginary numbers:**

• Introduction to imaginary numbers

http://web2.0calc.com/questions/help-me-with-solving-this-equation-please

• Finding Complex Roots with imaginary numbers (Difficult)

http://web2.0calc.com/questions/how-do-i-solve-the-sqrt4-16-complex-numbers-4-different-roots

• Complex number proof that i^{i} is a real number:

http://web2.0calc.com/questions/puzzle-question-i-i

Log of complex number

http://web2.0calc.com/questions/ln-10-75-6-98i

**Difficult inequality solution**

http://web2.0calc.com/questions/how-can-i-solve-the-first-question-nbsp

**Solveing a nonlinear inequality. This one looks like a parabola!**

http://web2.0calc.com/questions/solve-the-nonlinear-inequality

**Well explained by heureka:**

http://web2.0calc.com/questions/5x-8-3x-3-whats-the-x

**Heureka just being awesome:**

http://web2.0calc.com/questions/solve-the-equation_1

**An example of scientific notation:**

**A more complicated algebra question answered by Alan**

http://web2.0calc.com/questions/x-2-xy-y-2-28-y-2-x-how-do-you-get-x-and-y

**Horizontal and slant Asymtotes (Advanced)**

http://web2.0calc.com/questions/horizontal-asymptote-of-y-x-2-6x-3-x-3

**Quadratic equations:**

• Complicated one:

http://web2.0calc.com/questions/please-help_40

• Solving with the quadratic formula:

http://web2.0calc.com/questions/help-me-with-solving-this-equation-please

• A little different than the usual quadratic questions:

http://web2.0calc.com/questions/x-7sqrt-x-10-0

**Finding the equation of a polynomial when you are given the roots:**

**Linear Representation (graphing the equation of a line) of a worded problem:**

**Completing the squares - This is a really interesting application of it. **

http://web2.0calc.com/questions/the-temperature-of-a-point-nbsp-nbsp-in-the-plane-is-given-by-the-expression-nbsp-what-is-the-temperature-of-the-coldest-point-in-the-pla_3

**What is a logarithm? (thanks to anonymous)**

http://www.mathsisfun.com/algebra/logarithms.html

**Half life problem:**

**Solving for x when x is raised to a power:**

http://web2.0calc.com/questions/can-t-seem-to-get-this-equation-solved

**Finding why an equation with logs equals zero - two different approaches:**

http://web2.0calc.com/questions/why-does-log-2ab-log-5-a-log10b-0

**Radioactive decay!**

**This certainly looks like a more difficult logarithmic equation to me!**

http://web2.0calc.com/questions/difficult-logarithmic-equation-without-a-calculator

**Harder logarithm problem. Three people got the same answer, so it should be right!**

http://web2.0calc.com/questions/log-3-6-log-9-6-log-4-6-log-18-6

**Triangles! Great picture and explanation by CPhill**

**Finding the circumference from the diameter:**

http://web2.0calc.com/questions/circumference-of-pipe-diameter-3090mm

**Height of a triangle, the Pythagorean theorem!**

**Heron's formula to find the area of a triangle:**

**Volume of a sphere:**

**Word problems:**

•** Hay bales (cylinder):**

**• Wagon wheels (circumference of a circle):**

http://web2.0calc.com/questions/neeeed-help-on-this

**Finding the 4th side of a quadrilateral that is circumscribed by a circle. **

**An interesting trapezium area question.** Thanks Chris

**Unusual area question**

**An interesting co-ordinate geometry question.**

http://web2.0calc.com/questions/equation-to-circles

Inscribed equilateral triangle in a circle

http://web2.0calc.com/questions/length-of-an-equilateral-traingle-within-a-circle

Finding the area of a segment of a circle. (19/5/15)

Difficult triangle question (Thanks Heureka 25/6/15)

http://web2.0calc.com/questions/triangle_2

http://web2.0calc.com/questions/in-triangle-abc-point-d-is-on-side-bc-bd-2-dc-cosdac-cosc-ac-bc

**Z scores:**

**Permutations where some objects are not unique:**

http://web2.0calc.com/questions/permutations_2

**Collections of probability threads**

http://web2.0calc.com/questions/probability-melody

**Introductory set theory:**

**Here is one for middle level trig students to have a go at - I have not actually finished it.**

http://web2.0calc.com/questions/3-sin-2x-3-1-2-sin-2x

**Verifying the identity**

http://web2.0calc.com/questions/verify-the-identity-cot-theta-sec-theta-csc-theta

**Why is Sinθ approximately equal to θ for very small values of θ **

http://web2.0calc.com/questions/why-is-sin-of-theta-appromately-equal-to-theta

**How do you choose the correct trigonometric ratio (sin, cos or tan) to use?**

**Finding an angle on a right sided triangle:**

http://web2.0calc.com/questions/i-need-help-finding-the-angle-of-a-right-sided-triangle#rr2

**Unusual trig. equation (solve for θ**)

http://web2.0calc.com/questions/sin-3-cos-26-solve-for

**Changing radians to degrees:**

http://web2.0calc.com/questions/how-do-turn-radians-to-degrees

**Bearings and vectors:**

**Bearings speed and vectors Great Question!**

http://web2.0calc.com/questions/a-coast-guard-cutter-detects-an-unidentified-ship-at-20-0km-in-the-direction-15-0-degrees-east-of-north-the-ship-is-traveling-at-26-0km-h-o

**Velocities - Looks like a great answer from Alan:**

**Light rays!**

**Some more trig. questions:**

http://web2.0calc.com/questions/8-sec2-x-4-tan2-x-12-0

http://web2.0calc.com/questions/3cosx-4sinx-1

**Area of a triangle - not straight forward and Heron's formula:**

http://web2.0calc.com/questions/2-neigbouring-triangles-with-no-right-angles-with-very-little-information-find-the-area-of-them-combined_1

**High level Trig:**

**University level Trigonometry:**

http://web2.0calc.com/questions/how-to-know-when-the-function-is-continuous

**Difficult sine and cosine rule problem:**

http://web2.0calc.com/questions/i-get-no-diea

**Tricky trig limit**

http://web2.0calc.com/questions/how-to-evaluate-the-lim-x-pi-4-1-tan-x-sec-2x

**Equation with inverse trigonometry** (Gret answer from Heureka)

http://web2.0calc.com/questions/what-is-x-if-the-equation-is-2-tan-1-x-160-tan-1-x-60

**Another great length question. - Great pre-runner to calculus 28/12/14**

http://web2.0calc.com/questions/lim-t-0-tan-12t-sin-4t (7/12/14 Trig)

Limiting sum of a series - uses a differential (14/5/15)

How far will the bullet travel?

**Unusual Calculus/Cordinate geometry question:**

http://web2.0calc.com/questions/find-the-most-left-and-right-tangent

**Advanced calculus (thanks to Alan)**

http://web2.0calc.com/questions/help-please_27

http://web2.0calc.com/questions/differenciate-y-arcsec-x-2-1-x-2-1-and-y-squaroot-of-1-3tan-2-theta (Alan)

http://web2.0calc.com/questions/integrate-2cos3x-3sinx-sin-3x-dx-and-tan-5x-csc-5x-dx (Melody and Heureka) I used the reduction formula here :)

**Integration with substitutions - answer is inverse trig** (CPhill and Heureka 6/2/15)

http://web2.0calc.com/questions/integration_3

**Trig integration (best with substitution)** 20/6/15

http://web2.0calc.com/questions/integrate-cos-1x-2-1-x-2-1-2

http://web2.0calc.com/questions/integral_4

**Newton's method of approximating roots.**

**Partial Fractions - a technique needed for some integration problems**

http://web2.0calc.com/questions/partial-fractions

**Integrating log functions (19/11/14 Heureka)**

http://web2.0calc.com/questions/how-to-find-integral-of-logarithmic-functions

**Integration by parts (19/10/14) Melody**

http://web2.0calc.com/questions/integrate-the-inverse-sine-of-x---by-parts

http://web2.0calc.com/questions/integral-of-xe-square-root-of-x-dx

http://web2.0calc.com/questions/integral-problem (Melody and Alan 8/12/14)

**Difficult:**

• Compare Renting to Buying - Annuities

http://web2.0calc.com/questions/need-done-if-possible

Finding the present value of a bond.

http://web2.0calc.com/questions/valuation-corporate-bond_1

**Forces explained by Alan**

http://web2.0calc.com/questions/finding-friction-coefficient-from-kinetic-energy

http://web2.0calc.com/questions/2d-forces-equation#r0

Electrical Resistance (24/4/15)

http://web2.0calc.com/questions/resistant#r15

**Vectors:**

• Vector forces:

http://web2.0calc.com/questions/collinear-resolving-angles-of-a-parallelogram

• Converting to vector units:

http://web2.0calc.com/questions/how-to-turn-into-vector-units

• Magnitude of vector forces:

http://web2.0calc.com/questions/u-6i-j-and-v-10i-j-find-the-manitude-of-u-v

• Another vector problem:

**Distance/displacement:**

http://web2.0calc.com/questions/total-distance

**Misc. physics problems:**

http://web2.0calc.com/questions/nbsp_3

**Complex numbers**

Graphical solutions to the 12 root of 1

http://web2.0calc.com/questions/how-do-you-represent-the-twelfth-root-of-unity-graphically

**Some thinking puzzle problems:**

http://web2.0calc.com/questions/a-drinking-problem

How slow is the clock? I really liked this problem! (4/5/15)

**Plain Interesting Facts**

http://web2.0calc.com/questions/a-girl-was-eight-years-old-on-her-first-birthday-how-could-that-be

**Plain interesting Questions**

Optimization - Soap bubbles - problem

Melody Oct 18, 2014

#2**+5 **

**Thanks MathsGod1**,

It is a good thread, it has not been added to for a long time because NinjaDeva can no longer do it and I don't have time. It is a pity but i do include a little more threads in the "reference Material" to make up a little.

Ninja used to help me a lot - I continue to be very appreciative of all the effort he put in :)

Melody Apr 13, 2015

#3**0 **

**Probability**

Boolean Contour map. (really cool)

1) https://web2.0calc.com/questions/a-line-segment-of-length-5-is-broken-at-two-random

2) https://web2.0calc.com/questions/probability-and-geometry

Melody Oct 9, 2017