Pre-Calculus Algebra Final Exam Review

11) A rectangular plot has area 126 yd^2 with a perimeter of 46 yd. What is the length of the longest side?

Honestly just test things out.

29) Divide. (36y^4 + 30y^3 + 5y - 1)/(6y^2 + 1)

Factor the numerator then cancel the common factor.

26) Use synthetic division to decide whether the given number k is a zero of the given polynomial function. 1; f(x) = -x^4 - 3x^2 - x + 9

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6) How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t) = 500e^(-.153t), where t is the time in years? Round your answer to the nearest hundredth year

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14) Write in logarithmic form. 4^(1/2)=2

For the equation a^b = c, use the form logva(c) = b.

19) Solve the equation. logvx(49) = - 2

For the equation logva(b) = c, use the form a^c = b then solve for x and eliminate false answers.

21) The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 900 square inches?

Honestly just test until you find it.

40) Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. 2 logvm(p) - 6 logvm(V)^2

Move all positive terms together, then the coefficients are powers inside the parentheses. If the log base is equal, multiply inside the parentheses or divide if one is negative.

1) The growth in population of a city can be seen using the formula p(t) = 10,472e^(0.004t), where t is the number of years. According to this formula, in how many years will the population reach 15,708? Round to the nearest tenth of a year.

Move everything to one side, then solve for t.

28) Solve the equation and express the solution in exact form. log(3 + x) - log(x - 3) = log3

Move log(x - 3) to the other side, then apply the rule log(a) + log(b) = log(ab), then apply the rule log(a) = log(b) is a = b, then solve for x.

24) For the pair of functions, find the indicated sum, difference, product, or quotient. f(x) = 6 - 7x, g(x) = -3x^2 + 7 Find (f + g)(x)

Add the two functions.

27) Solve the equation and express the solution in exact form. ln4x + ln3x = ln13

Apply rule ln(ab) = ln(a) + ln(b), then combine like terms, then isolate the variable and divide if necessary. Then apply rule ln(a) - ln(b) = ln(a/b), then apply rule ln(a/b/c) = ln(a/bc). Put in the form of (a/bc)^(1/2).

25) Use the change of base rule to find the logarithm to four decimal places. logv7.6(4.5)

Apply the base change rule logvb(X) = logvd(x)/logvd(b) then simplify.

22) Solve the equation in exact form. 4e^(2x) + 5e^x = 6

Apply the rule (a^b)^c = a^bc, then rewrite e^x as u, simplify, then use the quadratic formula to solve for u. Then replace the u on both answers with e^x, then multiply both sides by ln, removing the e.

18) Solve the equation. e^(x - 2) = (1/e^(6))^(x + 3)

Apply the rule 1/a^b = a^-b, then apply the rule (a^b)^c = a^bc, then eliminate the e's and solve for x.

20) Solve the equation. 4^(5 + 3x) =1/256

Apply the rule 1/a^b = a^-b, then simplify, then apply the rule (a^b)^c = a^bc, then apply the rule that if a^(f(x)) = a^(g(x)) then f(x) = g(x), then simplify.

43) Use properties of logarithms to evaluate the expression. logv10(0.01)^5

Apply the rule log(a)^b = blog(a), then solve the equation.

16) Solve the equation. (9x/(x - 9)) - (4/x) = 36/(x^(2) - 9x)

Combine expressions, then use the rule that if a/b = c/d then ad = bc. Move everything to one side, then use factoring to leave x's at a power of 1. Then solve for x. Eliminate answers of 0.

3) Which of the following is the same as 3log(4x) for x>0? A) log(12x) B) log12 + logx C) log(64x^(3)) D) log64 · logx^(3)

Raise the number inside the parentheses to the power of the number before log.

4) The growth in population of a city can be seen using the formula p(t) = 9779e^(0.004t), where t is the number of years. Use this formula to calculate the population after 10 years.

Replace t with the number of years, then solve.

17) Solve the equation. | 7x + 5 | - 4 = -2

Simplify the absolute value, then solve for x. Eliminate any false answers.

13) Solve the equation using the quadratic formula. (x + 5)(x - 4) = 5

Simplify the equation into the form of ax^2 + bx + c, then take the x's and put them into the formula (-b +-sqrt(b^(2) - 4ac)/2a, then simplify.

8) In the formula N = Ie^(kt), N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. There are currently 69 million cars in a certain country, increasing by 4.1% annually. How many years will it take for this country to have 95 million cars? Round to the nearest year.

Simplify the formula to N/l = e^kt then multiply both sides by ln.

23) Factor the polynomial by substitution. 12(p + 6)^2 + 13(p + 6) + 3

Simplify the polynomial, then honestly just test until you find it.

34) Solve the system by substitution. x - 3y = 6 x = 4y

Solve the first equation for x, then substitute the x in the second equation for the first answer, then solve that equation for y. Then substitute the y in either equation for the second answer, then solve that equation for x.

15) Solve the equation. sqrt(x + 3) = x - 3

Square both sides, then combine terms and use the quadratic formula to solve. Test the two answers to find the true answer.

2) Select the equation that describes the graph shown. A) y = x^(2) - 4 B) y = (x + 2)^(2)- 4 C) y = (x + 4)^(2) + 2 D) y = (x - 4)^(2) + 2

The number inside the parentheses is the point on the X axis, and the number outside is the point on the Y axis. If the number inside parentheses is negative, then the point is positive. If the number outside parentheses is positive, the point is positive.

30) Find a polynomial of least degree with only real coefficients and having the given zeros. 2 + i, 3

Use (x - a)(x - b)(x - c) with the variables other than x being zeroes. 2 + i is 2 + i and 2 - i.

45) Write the number in standard form a + bi.

Use an i to make the number inside the square root positive, then simplify inside the square root, factor the numerator, then divide,

10) How long will it take for $900 to grow to $14,700 at an interest rate of 5.7% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Use the formula A = Pe^rt then simplify and multiply both sides by ln.

12) What is the rate on an investment that doubles $3171 in 14 years? Assume interest is compounded quarterly.

Use the formula r = n((A/P)^(1/nt) - 1), where A = amount, P = initial amount, r = interest rate as a decimal, n = number of times interest is compounded in a year and t = time in years.

7) Find the required annual interest rate, to the nearest tenth of a percent, for $5200 to grow to $6500 if interest is compounded quarterly for 4 years.

Use the formula r = n((A/P)^(1/nt) - 1), where A = amount, P = initial amount, r = interest rate as a decimal, n = number of times interest is compounded in a year and t = time in years.

5) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x) = 4x^(2) - 312x + 49, where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

Write in the form of y = (-1/2)(b/a), then solve for y.