21-12

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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long subtraction 21−12

Solution

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Solution steps

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21−12

Line up the numbers

	2	1
−	1	2

Subtract each column of digits, starting from the right and working left
If the digit being subtracted is larger than the digit above it, 'borrow' a digit from the next column to the left.

In the bolded column, subtract the second digit from the first

	2	1
−	1	2

The bottom number is larger than the upper number. Try to 'borrow' a digit from the left.

Borrow 1 from 2. The remainder is 1

	1	10
	2	1
−	1	2

Add 1 ten to 1: 10+1=11

	1	11
	2	1
−	1	2

In the bolded column, subtract the second digit from the first: 11−2=9

	1	11
	2	1
−	1	2

In the bolded column, subtract the second digit from the first: 1−1=0

	1	11
	2	1
−	1	2

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Notebook

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

21-12

Solution

Solution steps

Number Line