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Mathematics 098 fourth test review problems √ ab + b2 = a + b for all positive numbers a and b. √ 2. True or False: x2 = x for all positive and negative real numbers x. 3. Simplify: (in part (c) you may need to use the imaginary unit i) 1. True or False: (a) √ y8 (b) √ 32 (c) √ s −64 (d) 3 x 5 (e) x24 8y 6 2 4. Use radical notation to rewrite each expression. Simplify if possible. (a) 5x1/3 (b) − 82/3 6. Simplify: 5. Use a fractional exponent to rewrite the expression √ 4 x3 q − 20x8 y 7 8. Simplify: 2 1 1 − x y 7. Multiply & simplify √ √ 2 x+ y 9. Use long division or synthetic division to simplify: 3x2 − 4x + 7 x−2 10. Find a line equation for the line which has slope equal to 3/4 and which passes through the point (x, y) = (3, −6). 11. Reduce: 5−x x2 − 25 12. Simplify: 4x2 2 3x − 1 − + 4x + 1 2x + 1 13. Solve the absolute value inequality |x − 40| < 3 14. Find all the solutions of (a) √ 2x − 5 = 3 (d) m12 = 1.5 (b) √ x = −6 (e) x17/12 = 2 (c) (f) x−3 =4 2x + 1 √ 3 2x − 5 = −2 page two 15. The pressure P of a gas varies inversely with the volume V of the container holding the gas. If the pressure P = 8 atmospheres when the volume V = 3 cubic centimeters, calculate the pressure P when the volume is V = 4 cubic centimeters. 16. Find all the solutions of (a) ex = 12 (b) 10 log(x/10) = 55 17. What is the domain of f (x) = x3 5−x ? − 10x2 + 25x