S3 Algebra Flashcards
a2 - b2 =
(a+b)(a-b)
a2 + 2ab + b2 =
(a+b)2
a2 - 2ab + b2 =
(a-b)2
Under what conditions does x2 + px + q = (x+A)(x+B)?
- AB = q
- A + B = p (Ax + Bx on RHS = px on LHS)
a3 + b3 =
(a+b)(a2-ab+b2)
a3 - b3 =
(a-b)(a2+ab+b2)
If a ≠ 0, a(-n) =
1/an
If a ≠ 0, a0 =
1
If am = an, then
m=n
For numbers in scientific notation (a x 10b), what is the range of a?
1<=a<10
a can be a decimal but b must be an integer.
For positive a and positive integral n, arrange the following in ascending order:
1. a x 10n
2. (-a) x 10(-n)
3. a x 10(-n)
4. (-a) x 10n
5. 5a x 10 (n-1)
4<2<3<5<1
2: -a/10n
3: a/10n
5: 5a x 10(n-1) < a x 10n
For positive a, b>1 and positive integral m>n, arrange the following in ascending order:
1. (a x 10m) x (b x 10n)
2. (a x 10n) / (b x 10m)
3. -(a x 10n) / (b x 10m)
4. -(a x 10m) / (b x 10n)
4<3<2<1
1: a x b x 10(m+n)
2: a/(b x 10(m-n))
3: -a/(b x 10(m-n))
4: -(a x 10(m-n)) /b
What is the place value and value of digit of “3” in the number 1234?
place value: 101
value of digit: 30
Express 4+8+32 in binary system.
1011002
Express 100.012 in expanded form.
1 x 22 + 0 x 21 + 0 x 20 + 0 x 2(-1) + 1 x 2(-2)