Download february review due monday 3/2

Name___________________________________________ Algebra Enriched
February Break Mid-Year Review
Due Date: 2/27/09
Part I: Answer all questions in this part. Write your answers on the line provided. Each
correct answer will receive 2 points. No partial credit will be given.
1) Which line is parallel to the line y = 4x – 2?
A) 12x – 4y = 8
B) 4y – 16x = 10
1)_________
C) 5y – 25x = – 10
D) – x + 4y = – 8
2) Marilyn paid $172 for a coat that was on sale for 20% off the original price. What was the original
price of the coat?
A) $192
B) $344
C) $215
D) $860
2)_________
3) Subtract ( 9x3 + 7x - 3x2 ) from ( 2x3 - 9x2 + 5x)
A) –7x3 – 16x2 + 8x
B) 7x3 + 2x + 6x2
3)_________
C) –7x6 – 6x4 – 2x4
4) Which graph represents the solution set for 2x – 4  8 and
D) –7x3 –6x2 –2x
x + 5  3?
4)_________
A)
B)
C)
D)
5) The expression (2x3 – 3)2 is equivalent to:
A) 4x6 + 9
C) 4x6 – 12x3 + 9
B) 4x9 – 12x3 + 9
D) 4x6 – 12x3 – 9
5)_________
6) The expression 32  93 is equivalent to
A) 38
B) 312
C) 275
D) 276
6)_________
7) The set of odd integers is closed under which operation?
A) addition
8) If
B) division
7)_________
C) multiplication
D) none
x > x , then x could be
A) 0
B) 2
C)
1
2
D) –2
8)_________
9) Which function has the values f(–3) = –11 and f(2) = –1?
B) f(x) = –2x + 3
A) f(x) = x - 8
9)_________
C) f(x) = 1/3x – 10
D) f(x) = 2x – 5
10) When 63x3 – 18x2 – 9x is divided by (–9x) the result is:
A) –7x3 + 2x
B) –7x2 + 2x – 1
C) –7x2 + 2x + 1
D) 7x2 + 2x +1
11) Which expression is equivalent to (–2a)( –4a2b3c)2(–5a4b3c6)2?
A) – 40a13b12c14
B) 800a11b10c11
10)________
11)________
D) – 800a14b12c14
C) 400a11b10c10
12) Evaluate -3m2 - n2 if m = –.15 and n = .45
A) 0
B) –
135
1000
C) –
27
100
D)
27
200
12)________
13) If four-fifths of a number is 12 less than twice the number, what is the number?
A) –30
B) 15
C) 7.5
13)________
D) 10
14) Which equation is equivalent to 2x + 3y = 15?
A) 3x + 2y = 15
B) 2x = 3y + 15
C) y = 2/3x + 5
D) y = –2/3x + 5
14)________
15) The measures of the angles in a triangle are in the ratio of 1:2:6. Find the number of degrees in the
largest angle of the triangle.
A) 20º
B) 40º
C) 90º
D) 120º
16) Which equation represents a direct variation?
A) –2x = 3y
B) 5y – x = 4
15)________
16)________
C) 12x – 3 = 4y
D) 5x – 2y + 3 = 0
17) At a concert, $720 was collected for hot dogs, hamburgers, and soft drinks. All three items sold
for $1.00 each. Twice as many hot dogs were sold as hamburgers. Three times as many soft drinks
were sold as hamburgers. The number of soft drinks was:
A) 120
18)
B) 240
C) 360
D) 480
17)________
24 x 3 y  10w 2
in simplest form is equivalent to which of the following?

6w 4
12 x 2 y 4
A)
 10 x
3w 2 y 3
B)
 10 xy
3w 2 y 3
C)
 10 x
3w 2  y 3
D)
 7x
4w 2 y 3
18)________
19) Which ordered pair is a solution of the linear system 6x – 3y = 2 and 2x – 9y = -2?
A) (1 , 4/3)
B) (8 , 2)
C) (10/3 , 6)
D) (1/2 , 1/3)
20) What are the roots of the equation 1.5x2 – 4.5x = – 3?
A) – 2 and 1
B) – 1 and 1
19)________
C) 1 and 2
20) _______
D) 2 and 3
Part II: Answer all questions in this part. Each correct answer will receive 3 points. Clearly
indicate the necessary steps, including appropriate equations, diagrams, etc. For all questions in
this part, a correct numerical answer with no work shown will receive only 1 point. Show all
work in the space provided. Please circle or box in your answer(s).
1) Which number below is rational?
2
3
2
1
256
Explain why the number you chose is rational__________________________________________
__________________________________________________________________________________
2) Factor each of the following polynomials. Circle your final answer.
a) 64 - 225x8
b) x2 - 3xy - 10y2
( 1 pt each)
c) 36ab2c3 - 72a5bc2
3) A seagull flying over a lake drops a fish from a height of 81 feet. After how many seconds does the
fish land in the water? (solve algebraically)
4) Four times the difference of a number and 8 is equal to 4 less than half the number. Write and
solve an equation to find the number.
5) Write a polynomial equation, in standard form, whose roots are 0, -5, and ½.
6) Solve for x:
7 x  5 3x  15

2
8
10
7) A taxicab company charges a flat fee of $1.75 plus an additional 80 cents per mile.
a) Write a formula to find the total cost, C, for each fare.
(1 pt)
b) If Mark is a passenger in a taxi from this company, what is the maximum number of full
miles he can travel in the cab if he only has $17.68 ?
(2 pts)
8)
a) Solve the following inequality
-2 ( 5 + 2x ) < x + 3
b) Sketch a graph using your answer from part (a) on the number line below.
(2 pts)
(1 pt)
9) Find the dimensions of the rectangle shown below if the area is 15 square meters.
(solve algebraically)
(2x – 1) m
(x + 3) m
10) Write the equation of the line passing through the points ( -3 , 5 ) and ( 1 , -11 ) using algebra.
11) Given lines k and m are parallel and transversal t, find the measure of angle R. (Not drawn to scale)
t
k
(6x – 5)°
R
(2x + 11) °
m
12) Subtract the sum of (2x2 - 3x + 1) and (x2 + 5x - 9) from the square of (2x + 3). Express your
answer in standard form.
13) A bank is offering a certificate of deposit at 11% for a one year deposit. How much should be
invested if a person wanted to earn $770 on his money?
14) Graph the system of linear inequalities.
x<3
y>1
y> –x
15) Your scores on the first 3 tests of the year were 87%, 93%, and 94%. What must you score on
your next test, as a percent, to have an average of exactly 93%? (solve algebraically)
16) You are shopping for a jacket and find that your favorite store has jackets 35% off. If the sale
price of the jacket you want is $55.25, what was the original price of the jacket?
Part III: Answer all questions in this part. Each correct answer will receive 4 points. Clearly
indicate all necessary steps, including appropriate equations, diagrams, charts, etc. For all
questions in this part, a correct answer with no work shown will receive only 1 credit. Please
circle or box in your answer(s).
1) You are selling candles and tubs of popcorn to raise money for the ski club. During the first week,
you sold 8 candles and 4 tubs of popcorn for $92. During the second week, you sold 12 candles
and 10 tubs of popcorn for $178. Write and solve a system of equations algebraically to find the
cost of one candle and the cost of one tub of popcorn.
2) At East High School, 355 students take Spanish. This number has been increasing at a rate of about
30 students per year. The number of students taking French is 579 and has been decreasing at a rate
of about 2 students per year.
a) After how many years will the number of students taking French and Spanish be the same?
(2 pts)
b) How many students will be enrolled in each class at this time? (1 pt)
c) How many years will it take for there to be exactly 475 students enrolled in Spanish? (1 pt)
3) Solve the linear system by graphing.
2x – y = 6
4x – 2y = 8