4. Multiply: (5x 2)(3x + 4) 6 y z 16 = 11. Simplify. All exponents must be positive. 12. Solve: 7z 3z = 8z Solve: -4(3 + 2m) m = -3m

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1 - - REVIEW PROBLEMS FOR INTERMEDIATE ALGEBRA ASSESSMENT TEST-Rev. Simplify and combine like terms: -8 ( 8) 9 ( ). Multiply: ( )( ). Multiply: (a )(a a 9). Multiply: ( )( ). y. 7 y 0 ( ) y 7. ( y ) 7a ( b c) 8. a( b c) Simplify. All eponents must be positive.. Solve: Solve: -( m) m -m. Solve for : Q y. Solve for : 8 -. Scott Hardy invested some money at % and $000 less than this amount at %. Find the amount invested at each rate if his total annual interest income is $,0. 7. A pharmacist needs 00 liters of a 0% alcohol solution. She has a 0% alcohol solution and an 80% alcohol solution that she can mi. How many liters of each does she need? 8. Two people need to sort a pile of bottles at the recycling center. Working alone, one person could do the entire job in 9 hours, and the other person could do the entire job in hours. How long would it take them to complete the job if they work together?

2 Solve the system: y 0 - y 0. Solve the system: y 8 7 8y. Steve and Ross must paint Steve s entire house. Steve bought gallons of paint and brushes at one store for $8. Ross bought gallons of paint and brush at another store for $. Assuming the price per gallon and cost per brush were the same at both stores, find what they paid per gallon for paint and the cost per brush.. Solve: q - q -. Solve: 0. Find the roots of the following equation by factoring: 0. Find the roots of the following equation using the quadratic formula: 0. Find the roots of the following equation: ( )( ) - 7. Solve: y - 7 y 8. Solve: m - m 8 9. Rationalie the denominator and simplify: 0. Multiply and combine like terms: ( ). Multiply and combine like terms: ( ) ( ). Evaluate the following epression if and y -. y y. Find the distance between the point (-, -) and the point (, -).

3 . Divide: 8m m m m - -. Divide: (p p 7) (p ). What quadrant is the point (-,0) in? 7. Reduce, if possible: 7 8. Multiply: p p p 8p 8 p 0 p p q pq 9. Divide: 8p q p 0. Divide: (y y) y y y. Combine: t - t. Combine: y y r. Combine: 0r rs s r r rs s. Simplify:. Sketch the graph of the line y.

4 - -. If the slope, m, of line is, and the y- intercept is at (0, ), what is the equation of the line? Epress the answer in slope-intercept form. 7. What is the slope of the line between the two points (, -) and (-, -)? 8. What is the equation of the line with slope and containing point (, -)? Epress the answer in standard form. 9. What is the equation of the line which goes through the two points (, ) and (-, 0)? Epress the answer in standard form. 0. Sketch the graph of the line y -.. Solve. Solve - <.!. Solve - >

5 - - SOLUTIONS FOR INTERMEDIATE ALGEBRA ASSESSMENT TEST. 8 ( 8) 9 ( ) Use the distributive law to remove parentheses: -8 9 Combine like terms: - 8. Multiply vertically to easily line up like terms: Multiply vertically as in #. a a 9 a 8a a 8a a 8a 7 8a 7 answer: 8a 7. Multiply using the acronym FOIL (firsts, outsides, insides, lasts) ( )( ) When dividing, the base stays the same and you subtract eponents negative eponents then go to the denominator: y y 7 y y

6 When raising a power to a power, you multiply eponents. Any non-ero epression raised to the ero power is. 0 ) ( ) ( y y 0 y y 9 y 8. ( ) ( ) c b a c b a 7 ) ( c b a c b c b ) ( works eactly like. Just as, c b c b ) ( (b c) or (b c) means the th root of to the th power: ) (. Remember, to raise a power to a power, multiply eponents. The - must go to the numerator and become : When multiplying, add eponents. When dividing, subtract eponents Combine like terms: Add to both sides: 7 7 Add 7 to both sides: 0 Divide both sides by : 0

7 . ( m) m -m Use the distributive law to remove parentheses: - 8m m -m - 9m -m Add 9m to both sides: - m Divide both sides by : - m. Q y Add y to both sides in order to isolate the term containing the unknown, : Q y Divide both sides by : Q y. 8 - Rewrite and 8 as powers of : ( ) ( ) - When raising a power to a power, you multiply eponents: -9 Hence, Let the amount of money invested at %. 000 the amount of money invested at %. Then,..( 000) 0 Multiply each term by 00 to remove decimal points: ( 000), ,000 8,000 8,000 He invested $8,000 at % and $,000 at %

8 Let amount of 0% alcohol solution. y amount of 80% alcohol solution. Equate amount of solution: y 00 Equate amount of alcohol:.0.80y.0(00) or 0 80y 0(00) If y 00, then y (00 ) She needs 0 liters of the 0% solution and 0 liters of the 80% solution. 8. First person takes 9 hours. Second person takes hours. Together they take hours. Equate what can be done in hour. 9 Multiply both sides by the L. C. D. 8: or Together it would take hours. 9. y 0 - y Multiply the top equation by and the bottom by so that the terms will be eliminated. 9y 0 - y y y Substitute y in the first equation: ()

9 0. y 8 7 8y In the second equation add 8y to both sides to get it in standard form: y 8 8y 7 Multiply the top equation by : - 8y - 8y That cannot happen. The lines are parallel and the system is inconsistent.. Let g price for one gallon of paint Let b price for one brush g b 8 g b In the second equation: b g. Substitute this into the top equation: g ( g) 8 g 0g 8-7g 8-7g -8 g b g () 0 A gallon of pain costs $; one brush costs $.. q q - - Multiply both sides by to eliminate the denominators: (q ) (q ) -() 8q q - q 7 - q - q -

10 Factor out the common factor of : ( ) 0 The product of two factors is 0, and hence one of the factors is 0: 0 or 0. 0 Add to both sides so that 0 is on one side of the equation: 0 0 Factor the left hand side: ( 0) ( ) 0 The product of two factors is 0, and hence one of the factors is 0: 0 or Add 0 to both sides so that 0 is on one side of the equation: 0 0 The quadratic formula says that in the quadratic equation a b c 0, b ± b a ac In the given equation, then, a, b, and c -0 ± ()( 0) () ± 9 80 ± 89

11 . ( )( ) First multiply the binomials: - Add to both sides: 0 Factor: ( )( ) 0 0 or 0 7. y y - 7 Multiply both sides by : 7y y y y 8. m - m 8 Factor the denominators, wherever possible: m - ( m ) Multiply both sides by the L. C. D. of (m ): () -(m ) -m -m - m 9. Multiply numerator and denominator by :

12 ( ) ( )( ) 9 9. ( ) - ( ) From problem #0 ( ) 9 Then, ( ) ( )( ) ( ) ( ) 9 ( ) 9 8. y y If and y -, then the problem becomes: () (-) ()(-) (9)(-) ()() The distance between points (, y ) and (, y ) is given by the formula: d ( ) ( y y) The given points are (-, -) and (, -) ; y ; y Notice that ( ) 0 y y ( ) Therefore, d m m m m 8m m m m m m m m. p- p p 7 p p 7 p 0 p p 7 p -

13 . Quadrant II ( )( ) p p p p 8 p 8 0 p ( p (p )( p )( p ) ( p )( p ) ( p ) ) p p q pq 9. 8p q p To divide fraction, invert the divisor and multiply: p p p q p 0 p 8p q pq q 0. To divide fractions, invert the divisor and multiply: y y y ( y y) ( y y) y y y ( y )( y ) y( y ) y( y )( y ) y.. t t Note that - t (-)(t - ). The problem can then be written: t ( )( t ) 8 The two negatives become positive: t t t y y The L. C. D. is (y )(y ): ( y ) ( y )( y ) ( y ) ( y )( y ) y y ( y )( y ) 8y (y ) or ( y )( y ) ( y )( y )

14 r r. 0r rs s r rs s - - Factor the denominators: r r (r s)(r s) (r s)( r s) The L. C. D. is (r s)(r - s)(r s) r( r s) r(r s) (r s)(r s)( r s) (r s)( r s)(r r (r s) rs 0r rs r rs s)(r s)( r s) (r s)(r s)( r s). In the numerator, the L. C. D. is and it becomes: Similarly, the denominator is: Invert the denominator, and multiply:. y One way to sketch this is to plot points and then connect the points. ) If 0, then y -. ) If, then y -. ) If, then y.

15 - -. Slope-intercept form is y m b where m is the slope and b is the y-intercept. This problem states that the slope is and the y-intercept in at (0, ). Hence, the equation is: y 7. Slope is defined to be: change in y y y m change in Given the point (, -) and (-, -): ( ) m ( ) 8. The point-slope form of an equation is: m( - ) y - y Given m and the point (, -), the equation is: ( ) y ( ) y Multiply by : y y Pts: (, ) and (-, 0) The slope, m, ( ) Using point (-, 0) and the point-slope form from problem 8: ( ) y 0 y y y - 0. Since y is always equal to, the graph is a horiontal line units below the -ais.

16 - -. Solve Since a square root is involved, square both sides: Then you get - 8. Set 0 getting Factor the ( ) ( ) quadratic getting (-7)(-) 0. Solving you get 7 or. 7 checks but does not, so the answer is 7.. Solve - < For absolute value with less than, there are two cases: - < and - > -. Solving the first gives < ; solving the second gives > -. Therefore - < <.!. - > Subtract from both sides gives - >. Divide both sides by - giving < -. Remember, when you multiply or divide an inequality by a negative, the inequality reverses.