Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3.
_Why_Slopes_&_More_Math_1995

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1. Arithmetic Videos  11-2008
2.  Algebra Videos (to appear)
3. Solving Linear Equations  04-2005
4.- Fractions-Rates-Proprtns-Units-2006
5.-Algebra-Odds-&-Ends-HS-level-2001
6.-Euclidean-Geometry/Complex No.s
7.  Analytic Geometry/Functions 2006
8.  Number Theory. 2006-7
9.  Complex Numbers More 2001.  10  Exponents & Radicals Exactly 2008
11. Calculus  2005
12.Real  Analysis 1995
13. Electric Circuits Etc  2007
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Mathematics How TOs & site 
content guides  08- 2008
1. Arithmetic
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
  15. Problems: Algebra Test  Back ] Area Intro ] Next ]    

 

Problems on Quadratics, Straight Lines, Polynomials, Logs and Exponentials

1. (10 points) Express A and B as simplified, improper fraction:  For the calculation of A, cancel common factors in numerators and denominators before multiplication. For the calculation of B, use the least common denominator.

A =  25
27
. 81
100
 B =   3
26
 + 7
10

For A and B, there is 1 point for right answer and 4 points for following instruction on how to arrive at the answer. Show work!  If you use a calculator (not recommended), show the reasoning needed to arrive at your solution without its use.

2. (10 points)  Use algebra to find the intersection point of the two lines  

y = ¾x - ¼
y = ¼x + 2

3.  (4 points) (a) Find the slope of the straight line K if K is perpendicular to a line L with slope 2.
     (6 points) (b)  Find the slope and an equation for a straight line T which passes through [3,5] and [8, 20].        
                            Express the equation in slope intercept form y= m x + b

4.  (10 points) Compute product (x4+3x3+6x2 + 3x + 1)(x2 + 2x + 1) using  a column  method. 

5.  (10 pointsUse the polynomial long division to find polynomials a(x) (the quotient) and r(x) (the remainder)  such that 

x4+3x3+6x2 + 4x + 2= a(x)(x2 + 2x + 1) + r(x)

with degree (r(x)) < 2. 

6.   (2 points)  (i)  Use the ln(x) button on your calculator to fill in the table (or a copy of it) 

x

1/6 0.2 0.25 1/3 0.5   1 2 3 4 5 6

ln(x)

         

0

         

     (3 points)  (i) Use the ex button on your calculator to complete in the table (or a copy of it). 

x

-1.792

-1.61 -1.39 -1.099 -0.693   0 0.693 1.099 1.39 1.61 1.79
exp(x)

 

       

1

         

   (5 points)   (iii) Draw  the straight line y = x from [-2,-2] to [6,6] on graph paper.  Then on the same graph, use the above points to sketch graph of y = ln(x) for x in the interval [1/6, 6] and  y = exp(x) =  ex  for x in the interval [-1.79, 1.79]. Label all curves.  

7. (3 points) (i) Solve x2-5x+ 4 =0 using factorization by inspection. Show all ways for 4 to equal  the product AB of two integers A and B.  
    (3 points) (ii) Solve x2-5x+4 = 0  with the quadratic formula. Show work.
    (4 points) (iii) Solve x2 - 5x + 4 =0  starting with the method of completing the square. Show work.

8.  (4 points)  (i) Find the x- and y-intercepts of  the quadratic y =  x2-5x+4 and the straight line y =  -2x + 8 with the x- and y-axes. Hint: See 7(ii) or (iii).
     (3 points) 
(ii) Sketch the curves  y =  x2-5x+4 and y =  -2x + 8. Identify the axis of symmetry for the quadratic. Label axes  and all intercepts.
     (3 points) (iii) Find the coordinates of the intersection points for the  quadratic y =  x2-5x+4 and  line y =  -2x + 8.  Show reasoning.  Hint:  x2-3x-4  = (x-4)(x+1). 

Algebra, Odds & Ends,

1. Hints for Exams
2A. Exact Arithmetic
2B. Fractions Briefly
3. What is a Variable?
4.. Square Roots
5. Straight Lines
6. Problem Solving Methods
7. Trig and Complex No.
8. Complex Applet
9. History of No.s
10. ln(x) and exp(x)
13. Rename the > Sign
14. Problems: Quadratics
15. Problems: Algebra Test
16. Problems: Linear Eqns I
17. Problems: Linear Eqns II
18. Problem Solving Hints
20. Independent Variables
21. Why Logic
22. Why Math
23. The 15 Times Table
24.  The  20 Times Table
25. Algebra Formulas
26. On Learning Maths
27. Maths in Biology
28. Navigation +Time
29 Quibble-What is Algebra
30. Logic in Maths


Odd and Ends, Essays

Constant Retirement Rate
Road Safety
3 Strikes Law in California.
Math HOW-TOs
9 Steps in Maths

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Caution: Site advice is approximately correct, for some circumstances, not all. Site How-TOs are logically developed, but not tried and tested. That leaves room for thought and refinement..

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