ch 5 review CCA CPM

exponents

100

(10x²y^-8)⁰

1

(anything to the power of 0 equals 1)

200

-5x^-4y⁶

-5y⁶/x⁴

300

(4x10⁸)(2x10^-6)

8x10²

400

(2x²)⁴/8x¹⁰

2/x²

500

(12x10¹⁵)/(6x10^-7)

2x10²²

sequences

100

Is the sequence geometric or arithmetic? give its sequence generator

-4, -1, 2, 5, 8

arithmetic, sequence generator= +3

200

Is the sequence geometric or arithmetic? give its sequence generator

-2, 6, -18, -54

geometric, sequence generator= multiply by -3

300

Give the first three terms for t(n) = -2n + 10

8, 6, 4

(use equation and plug n=1 for the first term and repeat for n=2 and n=3)

400

What are the next three terms for the sequence: 12, 10.5, 9, 7.5

6, 4.5, 3

500

Is 150 a sequence value in the sequence -7, -3, 1, 5

No

(the equation t(n)=4n-11 models the sequence, solve equation for n: 15=4n-11, n= 40.25, n can only be positive integers) 

Systems of equations

100

x-2y=4

-x-6y=4

(2, -1)

(solve using elimination)

200

4x+2y=10

x=y+13

(6, -7)

(Solve using substitution)

300

y=4x-9

y=x-3

(2, -1)

(solve using equal values method or substitution)

400

x+7y=0

2x-8y=22

(7, -1)

(if you use elimination you must multiply top equation  by -2 so the x's match, or you can subtract 7y from top equation to get x=-7y and use substitution)

500

4x=-13+y

3x+2y=4

(-2, 5)

(can use substitution if you change the first equation to y=4x+13 (added 13 to both sides to get y alone) or can use elimination if you move y to the left side in the first equation 4x-y=-13 then multiply this by 2 -> 8x-2y=-26)

multiplying binomials

100

Multiply (x-1)(2x+3)

2x² + x -3

(use generic rectangle to multiply)

200

(3x-1)(3x+1)

9x² - 1

(use generic rectangle)

300

(x- 4)²

x²-8x +16

[(x-4)²=(x-4)(x-4) use generic rectangle to multiply]

400

(x+3y)(2x+5y)

2x² +11xy +15y²

(use generic rectangle)

500

(x-y)²

x²-2xy+y² 

[(x-y)²=(x-y)(x-y) use generic rectangle to multiply]

Linear Equations

100

Write the linear equation for a line with a slope of -2 and goes through the point (0, 5)

y = -2x+5

(use y = mx+b, we were given the slope and the y-intercept in the problem) 

200

Write the equation of a line with a slope of 3 and goes through the point (2, 7)

y = 3x +1

(use y=mx+b, given m (slope) plug the point given into x & y and solve or b)

300

Write the equation of a line that has a slope of -1/2 and goes through the point (2, -4)

y=-1/2x - 3

(use y=mx+b, given m(slope) and plug the point given into x & y and solve for b)

400

write the equation of a line that goes through the point (-2, -9) and (3,1)

y = 2x - 5 

(find the slope m=(y-y)/(x-x), the plug into y=mx+b and plug in one point given into x & y and solve for b)

500

Write the equation of a line that goes through the points (3,1) and (6, 0) 

y = -1/3x + 2 

(find slope m=(y-y)/(x-x) then use y-mx+b and plug in m and one point for x & y and solve for b)