Download Skills Check #1 ESM 1

Skills Check #1
ESM 1
I. Perform the operations; simplify completely.
a) 40  5  2  10
d)
4  1 3
2(1  5) 2
g) 2.16  7(0.3) 2
II. Simplify:
b) 8  2 32  4 4
c) 32  ( 2)3  14
e) 2  3 13  65
f)   6    40 
 5  9 
h) 5.93  4.3  7.1
i) (3  1.8)2  3.065
( 3)  ( 3) 2  4(9)( 2)
2(9)
III. Write as a simplified fraction or integer.
i)
2
3
0.02
ii)
0.06
4.2
Skills Check #2
ESM 1
I. Perform the operation – simplify completely.
a) ( 0.4)3  2.16  5.409
b)
4
7

82 82
c) (2 23 )2  ( 48)
II. Divide - use long division to write each fraction as a decimal.
a) Round to hundredths.
2.15
0.6
b) *decimal terminates*
4 203
c) Write with repeat bar.
7
18
III. Write each decimal as a % and as a simplified fraction.
a) 0.014
b) 8.6
IV. a) Write the fraction as a %.
11
40
b) Write each % as a simplified fraction.
i) 175%
V. Find the perimeter and area of the rectangle. Use correct units.
0.92 cm 0.6 ii) 4.2%
Skills Check #3
ESM 1
I. On a wintry night in Big Bear, it was 5 C at 10 PM. By 3 AM, the temperature had decreased by 12 C .
a) Find the temperature at 3 AM.
b) If the temperature was 6 C at 11 AM, find the difference between the 3 AM and 11 AM temps.
II. In a room of 60 voters, two-fifths are registered Democrats, while one-third is registered Republican. The
remaining voters are listed as “decline to state”; 55% of the voters are women.
a) How many registered Republicans are present? b) How many voters are women?
c) Find the % registered as Democrats.
III. Evaluate each formula at the given value(s).
1  an
a) S 
; a  4, n  3
1 a
IV. a) Evaluate f ( x)  x  1.7  7 x 2 at:
x  0.2
d) Find the simplified fraction of “decline to state” voters.
b) C  95 ( F  32); F  31
b) Evaluate g (a )  2a 2  a  4 at:
a   34
Skills Check #4
ESM 1
I. Solve and simplify. Use the Quadratic Formula.
3x 2  5 x  2  0
II. Determine if the value is a solution. Show!
(a  2) 2  a 3  2; a  3
III. The triangles are similar. Find a .
cm 9
5 cm
IV. Simplify the expressions; solve the equations.
a) (2 x  10)  2[(5  x )4  3 x]
d) (1 13 w  119 )  4 12 w  169
b) (2 x  10)  2[(5  x )4  3 x]
e) 0.3a 3  5a  a (0.09a 2  2.2)
c) 0.28 y  1.5  0.6
f)  12 x  53  101  83 x
Skills Check #5
I. Solve:
ESM 1
II. A car can traveled 91 miles on 3 12 gallons of gas.
How far can the car travel on 5 gallons of gas?
Write an equation; solve.
2
4

0.3 y  1 0.5 y  0.7
III. The perimeter is 64 inches.
a) Find x .
b) Find the area of rectangle.
IV. The angles are complementary.
a) Find n (in degrees).
b) Find the measure of each angle.
V. Janelle scored 85, 71 and 93, respectively, on her first three physics exams.
a) Find her average score.
b) If she scores 87 on her fourth exam, find her new average.
VI. A16-gram necklace is 18 carat gold, which means it is 75% gold. It also contains 2.4 grams of silver.
a) How many grams of gold are there in the necklace?
b) What percent of the necklace is silver?
Skills Check #6
ESM 1
I. The label on a 48-ounce bottle of fruit drink states that it contains 12% fruit juice. Each 8-ounce serving
contains 105 calories and 28 grams of sugar. There are 3.6 ounces of orange juice in the drink.
a) How many ounces of pure fruit juice are in the bottle? b) How much sugar is in 10 ounces of the drink?
c) Find the number of calories in 12 ounces of the drink.
d) What % of the drink consists of orange juice?
II. Translate each sentence fragment into an algebraic expression. Simplify if possible.
a) the difference of a number and 15 less
b) the total of four-ninths a number and
than three times the number
five-sixths the number
c) 8% of a squared number (use decimal)
d) the ratio of twice a number and the number increased by 11
III. Translate each sentence to an equation; solve.
a) One-fourth the sum of a 12 and a number is 8.
b) Forty percent of some number is the number
reduced by 42.
Skills Check #7
ESM 1
I. Translate.
a) the quotient of eight less than a number
and three times the number
b) the quotient of a number and eight less
than three times the number
II. Translate and simplify.
a) the difference of nine more than four times a
number and 12 less than the number
b) the total of five eighths a number cubed and
three tenths the number cubed
III. Translate and solve.
a) Nine twenty-fifths of n is 27.
b) Twenty reduced by 8% is what number?
c) Three-fifths the sum of seven and twice a
number is 15.
d) Thirty percent of some number decreased by
18% of that number is 3.6.
IV. A piggy bank contains pennies and quarters. The number of quarters is eight less than one-half the number
of pennies. There are 40 coins in the bank.
a) Describe in terms of x : # pennies = ___________ # quarters = ___________
b) Write an equation; solve.
c) Find the value of the coins in dollars and cents.
Skills Check #8
ESM 1
I. The smaller of two complementary angles is 20% the measure of the larger angle.
a) Describe in terms of x : smaller angle = ___________ larger angle = ___________
b) Write an equation; solve.
c) Find the measure of each angle.
II. The larger of two supplementary angles is 40 degrees less than three times measure of the smaller angle.
a) Describe in terms of x : smaller angle = ___________ larger angle = ___________
b) Write an equation; solve.
c) Find the measure of each angle.
III. Simplify with exponent laws – express answers with positive exponents.
a) 915 (95 )9
b) 8a 4b 3 (4ab7 )
d) (4 p 8 r 3 ) 3
e)
7m 5
m
c) (  65 x 4 y 2 )2
f)
35a 4b6
28a 4b 2
Skills Check #9
ESM 1
I. Simplify with exponent laws – express answers with positive exponents.
3 0
a) ( a b c)
5
(85 ) 4
d)
812
3 0
b) ( a b c)
6 m 5
e)
4m 3
6
 3n 2 
c) 
4 
 6n 
4
 x 2 w 3 
f)  4 
 x w 
4
II. Simplify completely – NO decimal answers.
a) 52  3  50  51
b)
(23 )4
29
c) (9  2  6) 3
d) 5  6 1  32
9
e)   
10


2
f)
3  2 1
4
Skills Check #10
ESM 1
I. Simplify completely – NO decimal answers.
a) ( 5) 2 100  2 3
b) 31 (33  32 )0
c) (31  2 1 ) 2
II. True or False
a) x 3  x 3  0
b)
52  32  5  3
III. Write each number in Scientific Notation, rounded to the nearest hundredth:
a) 0.00004716
b) 805,368
IV. Convert to standard form.
a) 4.71 106
c) ( r 3  r 3 ) 2  r12
.  10
b) 8.2  10 3
V. Perform the operations. Write answers in Scientific Notation, rounded to nearest hundredth.
a) (0.012) 2
b) (8.62  10 5 )  (4.75  10 5 )
c) (8.62  107 )  (4.75  107 )
Skills Check #11
ESM 1
I. Perform the operations. Write answers in Scientific Notation, rounded to nearest hundredth.
7.62  108
2.5  10 5
a) (0.6  10 9 )3
b)
c)
3  10 4
0.8  10 2
II. i) Translate each statement to an inequality.
Statement
ii) Graph the inequality. Label 3+ numbers.
Inequality
Graph
1) Bill has at most $15 in his wallet.
2) There are more than 200 students enrolled.
3) At least 12 people arrived, but fewer than 20.
III. Solve and graph the inequalities. Label 3+ numbers.
a)
b)
200  w
d)
x  2.5  4.8
11
20
e)
2  3w  2  10
c)
10  3( c  6)  4c  c  2
y   225
Skills Check #12
ESM 1
I. i) Translate each statement to an inequality.
ii) Graph the inequality. Label 3+ numbers.
Statement
Inequality
Graph
1) Between 300 and 400 people attended the concert.
2) Sid weighs more than 150 lbs., but at most 170.
3) My cat weighs less than 3.2 kilograms.
II. Solve and graph the inequalities. Label 3+ numbers.
a)
b)
6 23 w  100
d)
c)
a  0.8a  1.4
p  83 p  250
e)
2  14 x  3  3
0.5  0.6 y  1  2
III. The relationship between Fahrenheit and Celsius temperatures is modeled by C  95 ( F  32) .
On a winter day, the temperature in the Alps ranged from -10 to 5 degrees Celsius. Solve the inequality
10  95 ( F  32)  5 in order to find the corresponding range of Fahrenheit temperatures that day.