Diagnostic Test Algebra - Calculus Early Trascendentals 8th edition
Calculus Early Trascendentals 8th edition James Stewart
A. Diagnostic Test: Algebra
1. Evaluate each expression without using a calculator.
𝑎) 〖(−3)〗^4
𝑏) 〖−3〗^4
𝑐) 3^(−4)
𝑑) 5^23/5^21
𝑒)(2/3)^(−2)
2. Simplify each expression. Write your answer without negative exponents.
𝑎)√200−√32
𝑏)(3𝑎^3 𝑏^3 ) (4𝑎𝑏^2 )^2
3. Expand and simplify
𝑎)3(𝑥+6)+4(2𝑥−5)
𝑐) (√𝑎+√𝑏)(√𝑎−√𝑏)
𝑑) (2𝑥+3)^2
4. Factor each expression.
〖𝑎) 4𝑥〗^2−25
𝑏) 𝑥^3−〖3𝑥〗^2−4𝑥+12
5. Simplify the rational expresion
𝑎) (𝑥^2+3𝑥+2)/(𝑥^2−𝑥−2)
𝑏) (〖2𝑥〗^2−𝑥−1)/(𝑥^2−9)∙(𝑥+3)/(2𝑥+1)
6. Rationalize the expresión and simplify
𝑎)√10/(√5−2)
𝑏)(√(4+ℎ)−2)/ℎ
7. Rewrite by completing the square.
𝑎)〖 𝑥〗^2+𝑥+1
𝑏)〖 2𝑥〗^2−12𝑥+11
8. Solve the equation. (Find only the real solutions.)
𝑎) 𝑥+5=14−1/2 𝑥
𝑏) 2𝑥/(𝑥+1)=(2𝑥−1)/𝑥
9. Solve each inequality. Write your answer using interval notation
(10State whether each question is true or false.