Algebra 2 Exam Review (^=exponent)
Simplify i^6
-1
Simplify (-2i)(5i)(-i)
-10i
Simplify (-8 + 5i) + (3-2i)
-5 + 3i
An exercise specialist has studied you exercise routine and says the formula, t = 1.85 square root of c + 10, expresses the amount of time, t, in minutest it takes you to burn c calories while exercising. a) Graph b) How long should it take to burn 100, 200, and 300 calories?
100 calories = 19.4 minutes 200 calories = 26.8 minutes 300 calories = 32.5 minutes
2 fourth root of 48 + 3 fourth root of 243
13 fourth root of 3
Find the square root of 400
20
Find the second term of (x + 3)^9
27x^8
Write log base 2 of 32 = 5 in exponential form
2^5 = 32
Write 1-2x+2x^3 in standard form. Then classify it by degree and number of terms.
2x^3-2x+1; cubic trinomial
Divide the fourth root of 243x^3 by the fourth root of 3x^7, then simplify
3/x
Write 3x^3-18x^2+27x in factored form
3x(x-3)^2
Find the fourth root of 256
4
Simplify the cubed root of 64x^9 y^11
4x^3 y^3 cubed root of y^2
Multiply the cubed roots of 50x^2 y^5 and 15x^3 y^1, then simplify
5xy^2 cubed root if 6x^2
Find the cube root of 216
6
State the number of terms in (2a + b)^5 and give the first two terms
6 terms; 32a^5 + 80a^4 b
(3 + the square root of 5)(1 + the square root of 5)
8 + 4 square root of 5
Determine the end behavior and the number of turning points of y = 3x^3 + 6x^2 - x + 12
End behavior: down, up; turning points: 2
Find the relative max and min of y = x^3 - x^2 - 9x + 9
Relative max: (-1.43, 16.9) Relative min: (2.2, -5.05)
Is x + 4 a factor of x^3 +3x^2 - 10x - 24?
Yes
Prove that ln of e = 1
e^1 = e
Without graphing, determine whether the y = 0.99(0.33)^x represents exponential growth or decay. Then find the y-intercept.
exponential decay; y-intercept = 0.99
Write 9^2 = 81 in logarithmic form
log base 9 of 81 = 2
Expand log6x^2 y^3
log6 + 2logx + 3logy
Write 2log4^2 + log2 + log2 as a single logarithm
log64
The coefficient of the second term in the expansion of (r + s)^n is 7. Find the value of n, and write the complete term.
n = 7; 7r^6 s^1
The term 126c^4d^5 appears in the expansion of (c + d)^n; what is n?
n = 9
(x^2 - 3x + 1) / (x - 4); use long division
x + 1 R5
Find the real zeroes of 2x^3 = 9x^2 - 2 by graphing
x = -0.45, 0.45, 4.45
Find the zeros of y = x(2x + 5)(x - 3)^3 and state the multiplicity
x = 0, 3, -5/2; multiplicity: 3
Solve 4lnx^4 = -2
x = 0.61
Solve 25^(3x+1) = 625
x = 1/3
Solve for x: (x - 2)^2/3 - 4 = 5
x = 29
Solve 5e^(2x+2) = 0.1
x = 3
Solve 2logx - log3 = 1
x = 5.48
Graph 6-4i on a number plane
x axis = real y axis = imaginary Over 6, down 4
(x^3 - 8x^2 + 17x - 10) / (x - 5); use synthetic dicision
x^2 - 3x + 2
Write the polynomial in standard form given the zeros; x = 0,1,2
x^3 - 3x^2 + 2x
(x^5 +1) / (x - 1)
x^4 + x^3 + x^2 + x + 1 R2
Expand (x + y)^7
x^7 + 7x^6 y + 21x^5 y^2 + 35x^4 y^3 + 35x^3 y^4 + 21x^2 y^5 + 7x y^6 + y^7
