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Some Algebra Practice questions          Back to Math 161

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  1. Evaluate each expression without using a calculator.  solution
  2. (a) (3)4   (b) 34   (c) 34   (d) 523521 (e) (23)2  (f) 163/4

  3. Simplify each expression. Write your answer without negative exponents. solution
  4. (a) 20032   (b) (3a3b3)(4ab2)2   (c) (3x3/2y3x2y1/2)2

  5. Expand and simplify. solution
  6. (a) 3(x+6)+4(2x5)   (b) (x+3)(4x5)   (c) (a+b)(ab)   (d) (2x+3)2  (e) (x+2)3

  7. Multiply or divide to simplify as a sum/difference of terms.  solution
  8. (a) x(x21)     (b) x+xx2     (c) t23t+3tt

  9. Factor the expression.  solution
  10. (a) x2+3x   (b) 2x3+4x   (c) x34x   (d) x3+9x   (e) x25x+6   (f) x2x6

  11. Factor the expression.   solution
  12. (a) x2+7x+3   (b) x2x6   (c) 6x2+x1   (d) 3x214x+8

     

    Solving Quadratic Equations (by factoring, completing square, formula)

     

  13. Solve the following equations.   solution
  14. (a) 11x2=0   (b) x1+3=5   (c) x+2=x   (d) |2x3|=4

  15. Simplify the rational expression. solution
  16. (a) x2+3x+2x2x2     (b) 2x2x1x29x+32x+1    (c) yxxy1y1x

  17. Simplify each expression.  solution
  18. (a) x39x2x6     (b) 12+h12h     (c) (5+h)225h

  19. Rationalize the numerator.  solution
  20. (a) 9+h3h    (b) x2x4

  21. Evaluate the difference quotient as indicated.
  22. (a) f(a+h)f(a)h   for   f(x)=x2solution

    (b) f(4+h)f(4)h   for   f(x)=xsolution

    (c) f(x+h)f(x)h   for   f(x)=1xsolution

  23. Decompse the rational function as a sum of partial fractions.   solution
  24. (a) 6x29     (b) x22xx1    (c) xx2+x2

  25. Compute the ratio |an+1an|, and simplify.   solution
  26. (a) an=(1)n12n+3     (b) an=(2)nn!    (c) an=(1)n11(2n+1)!