A2 Pure Chapter 1: Algebraic Methods

6 flashcards · Mathematics · by TheoTyson

1. What is proof by contradiction?

   Start by assuming it is not true, and then follow logical steps to show it leads to a contradiction or impossibility.

2. In what form can rational numbers be written? And what form can irrational numbers not be written?

   ab\frac{a}{b}ba​ , where a,b∈Na, b \in \mathbb{N}a,b∈N

3. How can Y(x+1)(x+2)(x+3)\frac{Y}{(x+1)(x+2)(x+3)}(x+1)(x+2)(x+3)Y​ be rewritten?

   Y(x+1)(x+2)(x+3)=Ax+1+Bx+2+Cx+3\frac{Y}{(x+1)(x+2)(x+3)} = \frac{A}{x+1} + \frac{B}{x+2} + \frac{C}{x+3}(x+1)(x+2)(x+3)Y​=x+1A​+x+2B​+x+3C​

4. How can Y(x+1)(x+2)2\frac{Y}{(x+1)(x+2)^2}(x+1)(x+2)2Y​ be rewritten?

   Y(x+1)(x+2)2=Ax+1+Bx+2+C(x+2)2\frac{Y}{(x+1)(x+2)^2} = \frac{A}{x+1} + \frac{B}{x+2} + \frac{C}{(x+2)^2}(x+1)(x+2)2Y​=x+1A​+x+2B​+(x+2)2C​

5. What identifies an improper algebraic fraction?

   The numerator has a degree greater than or equal to the denominator.

6. How do you split an improper fraction into partial fractions?

   Algebraic long division or F(x)=Q(x)\text{F}(x) = \text{Q}(x)F(x)=Q(x) x divisor+remainder\text{divisor} + \text{remainder}divisor+remainder