Synthetic
Division
Logarithms
Exponents
Factoring
Evaluate Trigonometric Functions
100
What does 3X^3-2X^2-7X+6 divided by X+1 break down to?
3X^2-5X-2+8/X+1 Paulo Ruffini came up with this method in 1809 to avoid the tedious work it took to divide
100
write 4^5=1024 in logarithmic form
log (base 4) 1024=5 John Napier created logarithms in 1614
100
Simplify: (2a^3)^2
4a^6 Exponents were first used in the 15th century by a man named Nicolas Chuquet
100
Factor: X^2+4X-32
(X-4)(X+8) Factoring is called factorising in the UK
100
Convert: 5pi divided by 3 to degrees without the unit circle
300 degrees Hipparchus produced the first known table of chords in 140 BC
200
What does 2X^3-5X-7 divided by X-2 break down to?
2X^2+4X+3-1/X-2 Ruffini's rule is a special case of sythnetic division in which the divisor polynomial has the form X-A
200
solve for X: log(base 5) X=2
X=25 The invention of logarithms helped fueled the scientific revolution, by cutting time scientists spent doing arithmetic
200
Simplify: 2X^4 multiplied by 3X^3
6X^7 Until about 400 years ago no one used exponents
200
Factor: 3X^2-3X-90
3(X+5)(X-6)
200
Solve: cos^2(45 degrees)-sin(30 degrees)
0
300
What does 2X^3+7X^2-6X-8 divided by X+4 break down to?
2X^2-X-6
300
Calculate: Log100/Log10
X=2
300
If x=-3 and y=7 find the value of X^2Y^3
3087 Then they decided it would be easier to use exponents to save themselves time from writing it out so many times
300
Factor: 24X^2Y+34XY+12
2Y(3X+2)(4X+3)
300
Solve: 2sin^2(60 degrees)-tan(45 degrees) divided by 3sin(45 degrees)
2 square root 2 divided by 3
400
What does 5X^3-3X^2-6 divided by X-1 break down to?
5X^2+2X+2-4/X-1
400
calculate: (hint: use base function in your calculator) log(base 3) 234
X=4.966
400
Simplify: (2X^3)(8X^5) divided by 4X^6
4X^2
400
Factor: 9X^2+12X+4
(3X+2)(3X+2)
400
Solve: 1 divided by (cos(33 degrees))^2 - (tan(33 degrees))^2 (hint Pythagorean identity)
1 Thales of Miletus recorded the first known history of sin, cos, and tan
500
What does 3X^3-5X^2+4X+2 divided by 3X+1 break down to?
3X^2-6X+6
500
Express as a single log: 3log(base 5) X + log(base 5) Y - 2log(base 5) W
log(base 5) X^3Y/W^2
500
Simplify: 9X^4-27X^6 divided by 3X^3
3X(1-3x^2)
500
Factor: 15X^2+14X-8
(5X-2)(3X+4)
500
Change: 4pi divided by 3 to degrees without a calculator (hint pi/180)
240 degrees
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