This year in Math 10 we were able to cover a wide variety of units that dealt with more complicated and challenging problems. The units we covered were Numbers, Exponents, Measurement, Trigonometry, Polynomials and Factoring, Relations and Functions, Linear Relations and Systems of Linear Equations.
For me Math 10 was a fun course that was challenging at certain times and had many ups and downs.
This post will cover my “Top 5” units we covered in Math 10 Foundations and Pre-Calculus, explaining what they were, what I learned and why I chose that unit.
AT NUMBER 5 WE HAVE: “MEASUREMENT”
In the measurement unit we continued on our previous knowledge and calculated the volume and surface area of a variety of 3D shapes, in Math 10 we learned how to calculate the surface area and volume for new 3D shapes like cones, pyramids, spheres and hemispheres. The measurement unit was important to me because it was one of the units that would be useful in real life situations. We learned how to calculate the capacity/volume and surface area of things like buildings and how much paint you would need to paint certain objects. We were also required to find the measurements of compound shapes and shapes split in half, Another thing we had to do is work backwards if it meant you were only given certain measurements. Overall I think this unit was very useful, It pushed my understanding of applying math to real life situation.
AT NUMBER 4 WE HAVE: “LINEAR RELATIONS/SLOPE”
This was a unit that bought in a whole bunch of math vocabulary, in this unit we learned how to interpret and turn equations into graphs, this would be useful when you have to interpret information on graphs, we learned about the 3 types of equations, slope-intercept form which is y=mx+b, slope point form which is y-y2=m(x-x2) and general form (useless) which is ax+by+c=0, we were taught how to switch from one type of equation to another and how to graph. One cool thing we got to do in this unit is use the program desmos to write our initials by making the equations. Although graphing and relations may be new this unit expanded on so many new concepts.
AT NUMBER 3 WE HAVE: “SYSTEMS OF LINEAR EQUATIONS”
Systems was a new but interesting unit that was introduced to me this year, a system is basically where you use 2 or more equations to find the point of intersection of 2 lines. Methods of solving systems:
Graphically- When solving a system graphically you must use your previous knowledge from the functions unit and convert both of the 2 equations to y-intercept form which is y=mx+b this will give you the slope and y-intercept to graph both lines and find the point of intersection.
Substitution Method- When you use the substitution method you want to isolate one of the variables in one of the equations. You want to choose the easiest way and “work smarter not harder”, so look for variables with a coefficient of 1 and avoid negatives this will also all help to avoid fractions. Once you have isolated one of the variables substitute the answer in to one of the variables. Soon you will figure out the missing variables if the system has a solution.
Elimination Method- When doing the elimination method your goal is to cancel out and make 0 pairs for 1 of the variables. In order to do this you need to find a common factor just like you would find a common denominator for fractions. Before doing this always remember adding is easier. Finally you will find both variables.
Finally remember when doing or using any of these methods verify/check your answers! When checking your answers for systems all you have to do is plug in both variable values and see if they give you the right answer. This unit was also a unit that greatly expanded my math vocab!
AT NUMBER 2 WE HAVE: “POLYNOMIALS AND FACTORING”
This unit may not be the most useful however it really tested and combined all of my algebra skills, I learned how to factor polynomials many different ways and change them back to the original form. In this unit the acronym that sums up everything is CDPEU (can divers pee easy under water (the answer is no)) these are the steps you take when factoring a polynomial, find common factors, difference of squares, pattern (x^2+x+c), easy and ugly. Why I put this as my top 5 is because factoring polynomials is important to know and learn because it is a major use of algebra, and can help you understand algebra better in the coming years like grade 11 and 12 math.
AT NUMBER 1 WE HAVE: “TRIGONOMETRY”
Trigonometry was one of those units that everyone thought would be challenging, it might have been the sound of the name or what they have heard. Once we started doing this unit it turned out to be one of the most enjoyable units. We learned how to solve a triangle and find the missing dimensions like angles and sides. A main acronym to sum things up is “SOH CAH TOA”, this is used to determine which equation to do when solving triangles.
BONUS: “MAKING OUR OWN VIDEO”
This was my first time making a math video and I thought it was really cool.