Exercises for Question Type 2: Proving starting from the right-hand side

Question 1

Skill question

Starting from the left-hand side, prove that $\frac{1}{\frac{1}{a} + \frac{1}{b}} = \frac{ab}{a + b}$ .

[3]

Question 2

Skill question

Starting from the right-hand side, prove that $a^{m} \cdot a^{n} = a^{m + n}$ where $a \neq = 0$ and $m, n$ are positive integers.

[2]

Question 3

Skill question

Starting from the right-hand side, prove that $\frac{1}{a} + \frac{1}{b} = \frac{a + b}{ab}$ .

[2]

Question 4

Skill question

Starting from the right-hand side, prove that $lo g_{b} a = \frac{ln a}{ln b}$ for $a, b > 0$ , $b \neq = 1$ .

[3]

Question 5

Skill question

Starting from the right-hand side, prove that $1 + r + r^{2} + \dots + r^{n} = \frac{r ^{n + 1} - 1}{r - 1}$ for $r \neq = 1$ .

[3]

Question 6

Skill question

Starting from the right-hand side, prove that $(a + b)^{2} = a^{2} + 2 ab + b^{2}$ .

[2]

IB Mathematics Analysis and Approaches Question Type 2: Proving Starting from the Right-hand Side Exercises