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YOU are better than YOU think. Show yourself how: |
-/[]\- Logic
Mastery Do not leave here without it - Logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. |
-/[]\- After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6; For online automated help in senior high school maths & calculus, visit quickmath.com For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com With overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck. |
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Explore collaborative whiteboards from groupboard, twiddla or scriblink. |
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
100B =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 points) Use 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).
| www.whyslopes.com Algebra, Odds & Ends, |
Odd and Ends, Essays
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In Volume 2, Three Skills for Algebra, Chapters 8 to 14 and postscript What is a Variable point to a greater & clear use of words in algebra. Chapter 14 introduces a 4th skill for algebra, an elaboration of the third: - The direct and indirect use of formulas, numerically and algebraically, is unifying theme that should be mentioned aloud, with words, in each and every use of formula.