Math

Question 1

ab + ac

Answer 1

a(b + c)

Question 2

a² + 2ab + b

Answer 2

(a+b)²

Question 3

a² - 2ab + b²

Answer 3

(a - b)²

Question 4

a² - b²

Answer 4

(a - b)(a + b)

Question 5

Area of triangle

Answer 5

Area = 1/2 (base)(height)

Question 6

Isoscelese Triangle

Answer 6

Two equal sides with two equal angles

Question 7

Special Right Triangles

Answer 7

3: 4:5
5: 12:13

30, 60, 90

1: rt3:2
1. here, the shortest side is half the hypotenuse

45, 45, 90

1. sides are always 1:1:sqr2

Question 8

Area of Parallelogram

Answer 8

Area = (base)(height)

Question 9

Area of Trapezoid

Answer 9

Area = (average of parallel sides) x (height)

Question 10

Circumference of Circle

Answer 10

Area = 2πr

Area = πd

Question 11

Area of Circle

Answer 11

Area = πr²

Question 12

Original Whole; before percent increase/decrease

Answer 12

Decrease:

(1 - .x) x (original) = given

Increase:

ex: 15% increase over x = 1.15x

Question 13

Simple Interest

Answer 13

interest = (principal) x (int rate) x (time)

Question 14

Compound Interest

Answer 14

final = (principal) x (1 + Int rate / C) ^^(time)(C)

C = num of times compounded

Question 15

Remainder

Answer 15

Ex: remainder of 12 ÷ 7 is 5

Question 16

Weighted Average

Answer 16

(Weight 1)(X₁) + (W₂)(X₂)

divided by

(Weight 1) + (weight 2)

Question 17

Combined Work

Answer 17

Question 18

Combined Ratio

Answer 18

multiply one or both ratios until the term they have in common is the same. Then combine and remove the like term.

Question 19

Dilution or Mixing

Answer 19

(percent dif b/w weaker and desired) x (amount of weaker) = (percent diff b/w stronger and desired) x (amound of stronger)

Question 20

Group problem involving both or neither

Answer 20

group 1 + group 2 + neither - both = Total

Of the 120 students, 65 study french, 51 spanish, and 53 neither. How many study both french and spanish?

65 + 51 + 53 - both = 120

169 - both = 120

both = 49

Question 21

Standard Deviation

Answer 21

1. Find the average of the set
2. Find Diff b/w mean and each value in set
3. Square each of the diff
4. Find the avg of the squared differences
5. Take the positive square root of the averages

Question 22

Multiplying values with exponents

Answer 22

(x^a)(x^b) = x^a+b

2³ x 2⁴ = 2⁷

Question 23

Dividing Values With Exponents

Answer 23

like multiplying but substract exponents

5⁶/ 5² = 5⁴

Question 24

Add Roots

Answer 24

Combine like roots only

ex: sq2 plus 3*sq2 = 4*sq2

Question 25

Sequence

Answer 25

What is the diff b/w the fifth and fourth terms in the sequence 0, 4, 18, … whose nth term is n²(n-1)?

n₅ = 5²(5-1) = 25(4) = 100

n₄ = 4²(4-1) = 16(3) = 48

So, the difference b/w 4th and 5th terms is;

100 - 48 = 52

Question 26

Max and Min lengths for a side of a triangle

Answer 26

Range is somewhere between the difference and the sum of the known lengths.

eg: given a triangle with sides 7 and 3

the third side is greater than the difference and less than the sum.

7-3 = 4

7 + 3 = 10

4 < x < 10

Question 27

One angle or the sum of all angles of a Regular Polygon

Answer 27

((n - 2) x 180) / n

n = number of sides

ex: pentagon; n= 5

Question 28

Arc Length

Answer 28

(n/360) x 2πr

Question 29

Area of a sector

Answer 29

(n/360) x πr²

Question 30

Volume of cylinder

Answer 30

V = (area of base) x height

V = πr²h

Question 31

Cylinder Surface Area

Answer 31

2πr² + 2πrh

Question 32

Permutation

(The number of ways to arrange elements sequentially)

Answer 32

n! / (n-k)!

n = # in larger group

k = # you are arranging

ex: There are 5 runners, only 3 can place. How many possible outcomes?

n = 5; k = 3

Answer: 60

Question 33

Combination

(if the order or arrangement of the smaller group does not matter)

Answer 33

n! / (k!(n-k)!)

n = # in larger group

k = num you are choosing

e: how many diff ways can you choose 3 delegate from 8 candidates?

n = 8; k = 3

Question 34

Exponent raised to an exponent

Answer 34

(x^a)^b = x^ab

(3⁴)⁵ = 3²⁰

Question 35

Fractional Powers

Answer 35

(x-2)^1/2 = x^(-2)(1/2) = x^-1 = 1/x