## Friday, July 9, 2010

### Diagnostic Test Analytic Geometric

James Stewart, CALCULUS Concepts & Contexts 4th edition

1 Find an equation for the line that passes through the point (2, -5) and
( a ) has slope -3.
( b ) is parallel to the x-axis.
( c ) is parallel to the y-axis.
( d ) is parallel to the line 2 x  - 4 y =  3 .

2. Find an equation for the circle that has center (-1, 4) and passes through the point (3, -2).
3. Find the center and radius of the circle with equation: x^{2} + y^{2} - 6x + 10y + 9 = 0

4. Let A (-7, 4) and B (5, -12) be points in the plane.
( a ) Find the slope of the line that contains A and B.
( b ) Find an equation of the line that passes through A and B. What are the intercepts?
( c ) Find the midpoint of the segment AB.
( d ) Find the length of the segment AB. ( e ) Find an equation of the perpendicular bisector of AB. ( f ) Find and equation of the circle for which AB is a diameter. 5. Sketch the region in the xy-plane defined by the equation or inequalities. (a) -1 leslant y leslant 3 ( b ) absolute value of x less than 4 and absolute value of y less than 2. ( c ) Do not appear in the exam complete. ( d ) Do not appear in the exam complete. ( e ) Do not appear in the exam complete. ( f ) 9x^2 + 16y^2 = 144

## Sunday, July 4, 2010

### Diagnostic Test of Algebra Solutions Step by Step

James Stewart, CALCULUS Concepts & Contexts 4th edition

1. Evaluate each expression without using a calculator.

a) (-3) ^4 =
b) -3^4 =
c) 3^-4 =
d) {5^{23}} over {5^{21}} =
e) ({2} over {3} )^{-2} =
f) 16^{-3 / 4 } =

a) sqrt{200} - sqrt{32} =
b) (3a^{3}b^{3}) (4ab^{2})^{2} =
c) ({3x^{3 / 2 }y^{3}} over {x^{2} y^{-1 /2 }} )^{-2} =

3. Expand and simplify.
a) 3(x + 6) + 4(2x - 5) =
b) (x + 3)(4x - 5) =
c) (sqrt{a} + sqrt{b}) (sqrt{a} - sqrt{b}) =
d) (2x + 3) ^{2} =
e) (x + 2)^{3} =

4. Factor each expression.
a) (4x^{2} - 25) =
b) 2x^{2} + 5x -12 =
c) x^{3} - 3x^{2} - 4x + 12 =
d) x^{4} + 27x =
e) 3x^{{3} over {2}} - 9x^{{1} over {2}} + 6x^-{{1} over {2}} =
f) x^{3} y - 4xy =

5. Simplify the rational expression.
a) {x^{2} + 3x + 2} over {x^{2} - x - 2} =
b) {2x^{2} - x - 1} over {x^{2} - 9} cdot {{x + 3} over {2x + 1}} =
c) {x^{2}} over {x^{2} - 4} - {{x + 1} over {x + 2}} =
d) {{y} over {x} - {x} over {y}} over {{1} over {y} - {1} over {x}} =

6. Rationalize the expression and simplify.
a) {sqrt{10} } over {sqrt{5} - 2} =
b) {sqrt{4 + h} - 2} over {h} =

7. Rewrite by completing the square.
a) x^{2} + x + 1 =
b) 2x^{2} - 12x + 11 =

8. Solve the equation. (Find only the real solutions.)
a)   x + 5 = 14 - 1 / 2
b)  {2x} over {x + 1} = {2x - 1} over {x}
c)  x^{2} - x - 12 =
d) 2x^{2} + 4x + 1 =
e) x^{4} - 3x^2 + 2 = 0
f) 3 lline x - 4 rline = 10
g) 2x(4 - x)^-({1} over {2}) - 3 sqrt{4 - x} =

a) -4 <>
b)  x^2 <>
c)  x (x - 1)(x + 2) > 0
d) lline x - 4 rline <>
e) {2x - 3} over {x + 1}

10. State whether each equation is true or false.
a) ( p + q )^2 = p^2 + q^2 =
b) sqrt{ab} = sqrt{a} sqrt{b} =
c) sqrt{a^2 + b^2} = a + b
d) {1 + TC} over {C} = 1 + T =
e) {1} over {x - y} = {1} over {x} - {1} over {y} =
f) {{1} over {x} } over {{a} over {x} - {b} over {x}} =