Math Exam 3

Posted byjonseyPosted in5th grade english
  1. Write the following numbers or expressions:
    a) s t s 3 s 4 t s s simplified with powers = s⋅t⋅s3⋅s4⋅t⋅s⋅s=s10t2
  2. b) 16,400,000 = 1.64×107
  3. c) 8.4 × 10−6 = 0.0000084
    in scientific notation
    in decimal notation
  4. Evaluate the following expression with the correct order of operations:
    27 + 4(3 + 10 ÷ 2 ‒ 2) − 2 × 32 = 33
  5. Use the distributive rule to find the following product:
    (3x ‒ 2)(x2 + 3x − 1) = 3x3+7x2−9x+2
  6. (x + 1)(2x − 6)(x − 8) = 0 = -1 3 8
  7. Write down the quadratic formula: x=−b±b2−4ac2a
  8. Karen has $48 in fivedollar bills and singles. Write a linear equation in
    standard form to show how many of each she might have. Use f for five
    dollar bills and s for singles. 5f+s=48
  9. So far in this class we have seen some polynomials that can be factored by
    inspection, and we have learned techniques for factoring more difficult
    polynomials such as completing the square, common factors, associating,
    and splitting the middle term. Factor each of the following polynomials
    completely using the technique of your choice. Then write down the solution
    set. If the polynomial is prime, use the quadratic formula to find the solution
    set, and leave the radical in the solution set (do not evaluate the radical). a) b) c) d) 5×2 + 35x − 40 = 0 x2 − 7x − 10 = 0 18×2 ‒ 23x ‒ 6 = 0 9×2 − 49 = 0 = 3 2 and 2′ 9
  10. Answer the following questions about the graph below.
    a) What is the slope of the line that is plotted? m=y2−y1x2−x1
  11. b) Write down the equation for the line. use slope–intercept form y=mx+b, plug in a point to solve for b.
  12. c) Graph the following equation on the same graph: y = x 2 − 7 = To graph y=x2−7, plot a parabola opening up with vertex at (0,−7).
  13. d) Use the graph to find the solution to the set of two simultaneous
    equations. The solution to the system is the point(s) where the line and parabola intersect.
  14. e) Use one of the other techniques you learned for simultaneous
    equations to show another way to find the solution set. Algebraically, you’d solve the system by substitution:
  15. If the line is y=mx+b, then solve mx+b=x2−7 to find intersection points.
  16. Solve the following quadratic equation by completing the square:
    x2 ‒ 10x + 21 = 0 = 3, 7
  17. Explain in words what the following graphs would look like:
    a) A pair of simultaneous linear equations with a unique solution. Two straight lines that intersect at exactly one point.
    b) A pair of inconsistent simultaneous linear equations. The lines have different slopes.
    c) A pair of equivalent simultaneous linear equations. On the graph, you see a clear crossing point: that point is the solution.

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