AS Pure Chapter 1: Algebraic Expressions

21 flashcards · Mathematics · by TheoTyson

1. Simplify ama^mam x ana^nan

   ama^mam x ana^nan = am+na^{m+n}am+n

2. Simplify ama^mam ÷ ana^nan

   ama^mam ÷ ana^nan = am−na^{m-n}am−n

3. Simplify (am)n(a^m)^n(am)n

   (am)n(a^m)^n(am)n = amna^{mn}amn

4. Expand (ab)n(ab)^n(ab)n

   (ab)n(ab)^n(ab)n = anbna^nb^nanbn

5. How do you find the product of two brackets?

   Multiply each term in the expression by each term in the other expression.

6. What is the form of a quadratic equation?

   ax2ax^2ax2 + bxbxbx + ccc Where a,ba, ba,b and ccc are real numbers and a≠0a \neq 0a=0

7. What is the difference of two squares (D.O.T.S.)?

   x2x^2x2 - y2y^2y2 = (x+y)(x−y)(x + y)(x-y)(x+y)(x−y)

8. Simplify a1ma^{\frac{1}{m}}am1​

   a1ma^{\frac{1}{m}}am1​ = am\sqrt[m]{a}ma ​

9. Simplify anma^{\frac{n}{m}}amn​

   anma^{\frac{n}{m}}amn​ = anm\sqrt[m]{a^n}man ​

10. Simplify a−ma^{-m}a−m

    a−ma^{-m}a−m = 1am\frac{1}{a^m}am1​

11. Simplify a0a^0a0

    a0a^0a0 = 111

12. What is a surd?

    If nnn is any integer that is not a square number, then any multiple of n\sqrt{n}n ​ is a surd.

13. What kind of numbers are surds?

    Surds are irrational numbers.

14. Expand ab\sqrt{ab}ab ​

    ab\sqrt{ab}ab ​ = a\sqrt{a}a ​ x b\sqrt{b}b ​

15. Expand ab\sqrt{\frac{a}{b}}ba​ ​

    ab\sqrt{\frac{a}{b}}ba​ ​ = ab\frac{\sqrt{a}}{\sqrt{b}}b ​a ​​

16. How do you rationalise 1a\frac{1}{\sqrt{a}}a ​1​ ?

    Multiply the numerator and denominator by a\sqrt{a}a ​

17. How do you rationalise 1a +b\frac{1}{a \, + \sqrt{b}}a+b ​1​ ?

    Multiply the numerator and denominator by a −ba \, - \sqrt{b}a−b ​

18. How do you rationalise 1a −b\frac{1}{a \, - \sqrt{b}}a−b ​1​ ?

    Multiply the numerator and denominator by a +b{a \, + \sqrt{b}}a+b ​

19. What does A⇒BA⇒BA⇒B mean?

    If A is true, then B is true.

20. What does A⇐BA⇐BA⇐B mean?

    If B is true, then A is true.

21. What does A⇔BA⇔BA⇔B mean?

    If A is true, then B is true, if A is false, then B is false.