Diagnostic Test Analytic Geometric

James Stewart, CALCULUS Concepts & Contexts 4th edition
 Download the Diagnostic Test of Analytic Geometric Solutions Step by Step
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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  

Diagnostic Test of Algebra Solutions Step by Step

James Stewart, CALCULUS Concepts & Contexts 4th edition 

 Download the Diagnostic Test of Algebra Solutions Step by Step 

"""Download HERE"""

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 } =

2. Simplify each expression. Write your answer without negative exponents.

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} =

9. Solve each inequality. Write your answer using interval notation.

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}} =