Mathematics Archives - Page 5 of 5

07Mar 2014 by Vincent Summers No Comments

Secondary School Math Problems Plus Solutions

[caption id="attachment_5613" align="alignright" width="480"] Fractal[/caption] For some, it's actually fun when they come across secondary school math problems plus solutions. It's because they are no longer accountable, since they graduated years ago. Math Problems Plus Solutions Problem 1: Find the slope intercept form of the line passing through the point (– 1, 5) and parallel to the line – 6x – 7y = – 3. The line given is rewritten (in slope-intercept form, y = mx + b) as y = – 6/7 x + 3/7 Thus the slope m = – 6/7 Now two lines are parallel if they have the same slope. So, y = – 6/7 x + b is the formula for the new line, with the intercept not yet solved. We do so by inserting…

07Mar 2014 by Vincent Summers No Comments

Eight Middle and High School Math Problems with Solutions

Mathematics

Not only current students. but old-timers as well will find these middle and high school math problems informative. Middle and High School Math Problem 1: Leaves from a tree were reported by four different European students to be 2.9 cm, 3.33 cm, 3.9 cm, and 3.12 cm in length. List the numbers in order of decreasing length. For the beginner, the easiest way to evaluate which of these number is smaller and which is larger, is to make the number of digits to the right of the decimal the same. Now the maximum number of such digits here is two. Adding zeros to the right of the last digit does not change a number’s value. When that is done, the numbers become: 2.90, 3.33, 3.90 and 3.12 In decreasing order,…

04Mar 2014 by Vincent Summers 2 Comments

Sample High School Math Problems with Answers

Mathematics

[caption id="attachment_5578" align="alignright" width="440"] Fractal - CCA Share Alike 3.0 Unported by Wolfgang Beyer[/caption] Want some sample high school math problems with answers? Well then here you go! High School Math Problems Problem 1: A change purse has 100 nickels and dimes. The total value of the coins is $7. How many coins of each type does the purse contain? If the number of nickels is N and the number of dimes is D, then 5N + 10D = 700 (the 5, 10 and 700 representing the number of cents) However, N + D = 100 (the number of nickels plus the number of dimes equals 100) So, solving for N for both equations, we get as the result N = – 2D + 140 and N = 100 – D…

24Feb 2014 by Vincent Summers No Comments

Math Equations for Parallel and Perpendicular Lines

Mathematics

It's fun and very instructive to figure out the math equations for parallel and perpendicular lines. The basic mathematical equation for a line is, ax + by = c Here are three examples of line equations: 2x + 3y = 6 4x – 2y = –5 –x/3 + 2.47y = √3 Slope-Intercept Form One of the most useful formats for the equation of a line is the slope-intercept form. That form is written, y = mx + b The variables here are x and y. The letters m and b are constants that represent the rise or tilt of the line (slope, m) and the point at which the line crosses the y-axis (intercept, b). So the first of the three equations for a line listed above is written in…

21Feb 2014 by Vincent Summers 1 Comment

Determining the Equation for a Line from Two Points

Mathematics

Lines can be drawn in three dimensions, but most analytical geometry courses stick to lines in two dimensions, generally using the Cartesian or XY coordinate system. The generic equation for a line may follow the form: y = mx + b where m is the slope (measure of tilt or steep-ness) of the line, while b is its intercept or intersection with the y-axis. Equation for a Line from Two Points A line can be determined and an equation derived from two points. In the Cartesian system, for instance, take two points, (2 , 3) and (– 1 , 5). The first number in each pair represents the x-value of a point and the second number in each pair represents the y-value. Writing these points into the general equation y…

04Nov 2013 by Vincent Summers 2 Comments

The Bee, Fibonacci, and Genealogy

Mathematics

The Bee, Fibonacci and Genealogy -By Ellen Hetland Fenwick. Bees are strange creatures. There are three “sexes” of bees... Drone: Male born of a Queen. No male parent. Not sterile. Queen: Female born of a Queen & a Drone. Fed Royal Jelly. Not Sterile. Worker: Female born of a Queen & a Drone. Not fed Royal Jelly. Sterile. This makes for a most unusual genealogy. Let’s examine the first six generations. Gen 0: Our Male: Drone Gen 1: His parent: Queen Gen 2: Her Parents: Queen, Drone Gen 3: Their parents: Queen, Drone, Queen Gen 4: Their parents: Queen, Drone, Queen, Queen, Drone Gen 5: Their Parents: Queen, Drone, Queen, Queen, Drone, Queen, Drone, Queen The total number of individuals in our male bee’s line for each generation is shown below: But…

30Oct 2013 by Vincent Summers No Comments

Questioning Examination Questions

Mathematics

[caption id="attachment_5170" align="alignright" width="480"] Professor lecturing at a blackboard[/caption] You are to undergo testing. You look at your test paper and see many examination questions... Many useful equations are arrived at by solving differential equations—for instance, the equation for the acceleration experienced by a falling object. This kind of activity involves some mathematical expertise and lots of care. When I was working in industry, my partner told me that he suspected that there was an error in arriving at the navigation equations from its differential equations. He asked me to monitor his work as he solved the equations anew. Mathematicians Do It Too I know that when a mathematician (yes, even a good one) does math, he makes mistakes. I truly believe that he tends to get the easy stuff…

12Jul 2013 by Vincent Summers 1 Comment

I’ve Got Your Number

Mathematics

[caption id="attachment_3965" align="alignright" width="380"] Paul Erdos - GNU Free Documentation License 1.2 by Kmhkmh[/caption] The next time someone says, I've got your number, pay close attention. There was a play on Broadway called “Six Degrees of Separation.” The premise is as follows: given any persons, A and H, there exist at most six other persons B, C, D, E, F and G such that A has met B, B has met C, C has met D, D has met E, E has met F, F has met G, G has met H. Mathematicians think five degrees of separation are sufficient; they call this theory the “Handshake Conjecture.” Mathematicians also have the concept of The Paul Erdos Number. Your Erdos number is one if you have co-authored a paper with Erdos.…

12Jul 2013 by Vincent Summers 1 Comment

Geometry Stop the World – I Want to Get Off

Mathematics

[caption id="attachment_3951" align="alignright" width="440"] Space Time Curvature - GNU Free Documentation License Version 1.2 by Johnstone[/caption] Many of us had to take plane geometry in high school. If you remember it was, “Theorem, Proof, Theorem, Proof...” What kind of ammunition did you use for the proof of a theorem? The axioms and previously proven theorems. I know, I know. Some of you want to forget the anguish. But I want you to recall the fifth axiom... Plane Geometry - Diagram 1 Look at Diagram 1. directly below. Line a is parallel to line b. That is lines a and b don’t meet. Axiom V: Through the point where line t meets line a there is no other line that can be drawn parallel to b. Now it took about 2,000…

11Mar 2013 by Vincent Summers No Comments

Distance, Velocity, and Acceleration

Mathematics, Physics

[caption id="attachment_3512" align="alignright" width="440"] Porsche 911 image - CCA 2 Generic[/caption] Do you know the relationships between distance, velocity, and acceleration? In learning about a matter, the primary obstacle is likely to be understanding the concept of it. For instance, as a young teen, I was introduced to algebra. Algebra is the first form of mathematics that contains not only numbers, but letters as well. Numbers are constant (after all, 3 is three), but letters are used to indicate variance in value, i.e. they are variables. Distance The concept of distance is so very simple, it is taken for granted. But should it be? Some young ones may not fully comprehend the concept of distance. That being said, we will assume here that the reader and his or her pupil…