S3 Algebra Flashcards

1
Q

a2 - b2 =

A

(a+b)(a-b)

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2
Q

a2 + 2ab + b2 =

A

(a+b)2

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3
Q

a2 - 2ab + b2 =

A

(a-b)2

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4
Q

Under what conditions does x2 + px + q = (x+A)(x+B)?

A
  1. AB = q
  2. A + B = p (Ax + Bx on RHS = px on LHS)
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5
Q

a3 + b3 =

A

(a+b)(a2-ab+b2)

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6
Q

a3 - b3 =

A

(a-b)(a2+ab+b2)

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7
Q

If a ≠ 0, a(-n) =

A

1/an

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8
Q

If a ≠ 0, a0 =

A

1

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9
Q

If am = an, then

A

m=n

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10
Q

For numbers in scientific notation (a x 10b), what is the range of a?

A

1<=a<10
a can be a decimal but b must be an integer.

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11
Q

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)

A

4<2<3<5<1

2: -a/10n
3: a/10n
5: 5a x 10(n-1) < a x 10n

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12
Q

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)

A

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

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13
Q

What is the place value and value of digit of “3” in the number 1234?

A

place value: 101
value of digit: 30

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14
Q

Express 4+8+32 in binary system.

A

1011002

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15
Q

Express 100.012 in expanded form.

A

1 x 22 + 0 x 21 + 0 x 20 + 0 x 2(-1) + 1 x 2(-2)

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16
Q

How many digits are there in the binary representation of a number between 300010 and 400010?

A

12

211 = 2048 and 212 = 4096. Since any denary between 3000 and 4000 is between these two numbers, the largest term in its expanded form should be 1 x 211. Since the number of digits equals to the highest power of 2 plus 1, there are 12 digits in total.

17
Q

Convert 1101 0111 00012 to hexadecimal (base 16).

A

D7116
Since 24 = 16, each digit of the hexadecimal number corresponds to 4 digits in the binary number.
Last digit: a x 160, depends on last 4 digits of binary number = 110 = 116
Second digit: depends on middle 4 digits of binary number = 710 = 716
First digit: depends on first 4 digits of binary number = 1410, which is D16.

18
Q

Convert 23 30 11 024 to hexadecimal (base 16).

A

BC5216
Since 42 = 16, each digit in the hexadecimal number corresponds to 2 digits in the numbner in base 4.
Last digit: depends on last 2 digits of base 4 = 210 = 216
Second-last digit = 1 + 1 x 4 = 510 = 516
Second digit = 3 x 4 + 0 = 1210 = C16
First digit = 2 x 4 + 3 = 1110 = B16

19
Q

What is the meaning of principal, interest, and amount?

A

Principal: the money we deposit in a bank
Interest: the extra money paid by the bank
Amount: the sum of principal and interest
A = P + I

20
Q

What is the interest equation for simple interest?

A

I = P x R% x T
Interest = principal x annual interest rate (R%) x time (in years)

21
Q

What is the amount equation for simple interest?

A

A = P + I = P(1 + R% x T)

22
Q

What is the amount equation for compound interest compounded yearly?

A

A = P(1 + R%)n, where n equals the number of years.

23
Q

What is the amount equation for compound interest compounded every k weeks, with annual interest rate of R%? (assume that there are 52 weeks in a year)

A

A = P(1+(k x R%/52))52/k

24
Q

What are the definitions of growth factor and decay factor?

A

If a value increases at a constant rate of R% per period, (1+R%) is defined as the growth factor.
If a value decreases at a constant rate of R% per period, (1-R%) is defined as the decay factor.

25
Q

If a value P decreases at a constant rate of R% per period to an amount A, what are the depreciation and depreciation rate respectively?

A

Depreciation: original value - new value = P-A
Depreciation rate: depreciation/original value x 100% = R%

26
Q

What is the definition of Net Chargeable Income in taxation?

A

NCI = annual income - allowance

27
Q

Additive property of inequalities

A

if x>y, then x + c>y + c
(c can be a negative number)

28
Q

Multiplicative property of inequalities

A

if x>y and c>0, then xc>yc and x/c>y/c
if x>y and c<0, then xc<yc and x/c<y/c

29
Q

Transitive property of inequalities

A

if x>y and y>z, then x>z

30
Q

Reciprocal property of inequalities

A

if x>y>0, then 1/x<1/y (sign change)
if x<y<0, then 1/x>1/y (sign change)
if x<0<y, then 1/x<1/y (no sign change)

31
Q

Non-negative property of inequalities

A

If x>y>0, then xn>yn
If x<y<0, then x(2n) > y(2n), but x(2n-1) < y(2n-1)
If x<0<y, it depends on the absolute value of x and y.