Author: 132-cvankoughnett

This week in math, I got confused rationalizing radicals with an irrational binomial denominator. I would only multiply the top or even multiply the whole denominator again, instead of both the top and bottom by the conjugate of the denominator, so the radical was not eliminated. It is important to know how to properly rationalize radicals because it brings expressions to standard form, making them easier to work with in equations. One mistake I made was with the expression: ​ I attempted to simply multiply top and bottom by ​ But then I had to expand a binomial square in the denominator, and I still had radicals, so the expression was ugly and not fully simplified. To properly rationalize a denominator like this, I need to multiply the Numerator and Denominator both by the Conjugate: ​ With this you would then ese the difference of squares formula: So the final simplified … Continue reading PC 11 – Week 6 – Rationalizing

My best mistake of the week was simplifying a rational expression incorrectly by not factoring first. I canceled out too soon and thought i was done, but I left out important steps that need to be done in order to simplify it. -Question with Error The error I made was in the question: I attempted to cancel out the x right away: That was wrong because I split the numerator and denominator into separate terms instead of factoring the whole expressions. The way to do it is to factor the numerator and denominator: Numerator is: x^2 − 9 = (x−3)(x+3) Denominator: x^2 – x – 6 = (x -3)(x + 2) With this the expression becomes: Now I need to cancel the common factor: -What I Learned I learned that … Continue reading PC 11 – Week 12 – Rational Expressions

This week, my biggest mistake in math was using the Cosine Law when I should have used the Sine Law. I had been given two angles and one side (AAS), but I had forgotten that Cosine Law is used in different types of triangle problems. This gave a confusing and wrong answer. -Question with Mistake The question was: “In triangle ABC, angle A = 40°, angle B = 65°, and side a = 10 cm. Find side b.” I wrongly tried to use the Cosine Law: b^2 = c^2 + a^2 – 2ac x Cos(B) But I didn‘t even have side c, so I was trying to put in values I didn‘t have. I got stuck and ended … Continue reading PC 11 – Week 17 – Cosine and Sine law

This week, the greatest mistake I made in math was not understanding the vertex from a quadratic function. Specifically, when it came to the sign inside the parentheses. I made the mistake of when a quadratic is written as y = a(x – b)² + c, the x-coordinate of the vertex is positive b, not negative b. This led to me constantly getting the wrong answer.  Example: When I had a function: y = 2(x – 5) ² + 3, I looked at the expression (x – 5) and assumed the x-value for the vertex was –5. So, I put … Continue reading PC 11 – Week 9 – Quadratic equations

My greatest mistake this week was working with completing the square when doing a quadratic equation. I fist though that when solving the square I was supposed to take     (½b) ² then make C equal that number.   For example: in the equation: x² – 4x – 7 = 0  I started off by taking half of –4 which is –2, then squaring it to get 4. From there I thought I had to make –7 equal 4. So, I added 11 making my equation:  (x –2) ² + 11 = 0  This gave me the wrong equation which led to … Continue reading PC 11 – Week 7 – Quadratic equations

  This week I made a mistake solving the equation 2√(2x – 1)- 10 = 20. My mistake was not isolating x properly, and skipping over important steps. To solve this equation, the first thing you need to do is isolate the square root. You do this by adding 10 to both sides, which gets: 2√(2x – 1) = 30 After that you can get rid of the 2 in front of the root by dividing 30 by 2. The mistake I made here was trying to divide both sides by 2, when you only need to divide the right … Continue reading PC 11 – Week 5 – Radical Equations

My greatest mistake this week was rationalizing radicals. I was making the mistake of multiplying on the numerator, while I was supposed to multiplying the both the numerator and denominator, this way you get rid of the irrational number on the bottom Example 1: With this question, I made the mistake of multiplying the top by denominator but not the bottom What I should have done is multiplying both the numerator and the denominator by 5 over root 3  Now the denominator is a rational number Example 2: With this question I made the same mistake, by only multiplying the top … Continue reading PC 11 – Week 4 – Rationalizing