STEP PROGRAM
FUNDAMENTAL CONCEPTS BANK OF QUESTIONS
MOST OF THESE PROBLEMS CAN BE SOLVED BY HAND USING PROPERTIES OF THE REAL NUMBERS. PROBLEMS THAT REQUIRE TECHNOLOGY ARE INDICATED WITH A (*)
SCIENTIFIC NOTATION
1. The expression 3 x * H2 x + 3L equals to which of the following expressions (there may be more than one answer)
a. 5 x2 + 6 x
b. 6 x2 + 9 x
c. 6 x2 + 3
d. 5 x + 3
e. None of them
2. The expression 2 p * H3 q * rL equals to which of the following expressions (there may be more than one answer correct)
a. H6 p qL H2 p rL
b. 2 p * 3 q * r
c. 6 pqr
3. Write each of these numbers in scientific notation
-0.0000327 _______________________
d. 6 pq + 2 pr e. None of them
3724000000 ______________________
Write in scientific notation the result of each of the following operations
4. I3 * 10-5 M I4.2 * 102 M I5 * 10-3 M
5.
________________________
1.5*10-7
_________________________
3.0*104
6. - 2.5 * 103 + 3.2 * 102
7.
_________________________
I5*106 M I2*103 M I3*10-4 M
___________________________
I8*10-2 M H5*10L
2
-4
8. The number J 3 N
a.
2-4
3-4
b.
-8
-12
can be written as (more than one answer is possible)
3
4
c. I 2 M
d. 2-4 * 34
e. All of them
9. The speed of light is 3 x 108 meters/second. If the sun is 1.5x 1011 meters from earth, how many seconds does it take light to
reach the earth. Express your answer in scientific notation
10. What is the ratio of Milky Way radius to our solar system radius given that, the distance from pluto, the farthest planet from
the sun in the solar system, to sun is 5.9´1012 meters and the Milky Way disk radius is.3.9 x 1020 meters. Round the coefficient to the nearest tenth
11. Using
the following data:The volume of a sphere with radius R is
V=
4
3
Π R3
Radius of the earth 6.3 * 106 meters
Mass of earth 5.9742 ´ 1024 kilograms
Find the density of the earth in kg ‘ m3 (Note: this method will only yield an approximate value for
the density of the earth).
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FUNDAMENTAL KNOWLEDGE BANK.nb
11. Using
the following data:The volume of a sphere with radius R is
V=
4
3
Π R3
Radius of the earth 6.3 * 106 meters
Mass of earth 5.9742 ´ 1024 kilograms
Find the density of the earth in kg ‘ m3 (Note: this method will only yield an approximate value for
the density of the earth).
12. Given that the average density of water is 1000 kg/m3 , what would be the average density of
the earth (closest tenth) in gm/cm3?
DIMENSIONAL ANALYSIS
These are some conversions you can use for these problems. Of course, there are many more. Make sure in each problem you
indicate where you start and all the conversion factors used
2.54 cm
1 ft
1m
16 oz
1000 m
5280 ft
453.6 g
1 in
12 in
100 cm
1 lb
1 km
1 mi
1 lb
3600 s
1 mg
1 hr
1000 Ðg
1g
1L
1 cm
1000 mg 1000 mL 10 mm
1. An Olympic swimming pool is 25 meters long. How long is it in feet?
2. The density of white ash used in making wooden baseball bats is listed as 0.025 lb ‘ inch3 . The density of aluminium
used in making aluminium baseball bats is 2.70 g ‘ cm3 . Which material has more density?
3. A can of certain soda contains 55 milligrams of sodium. If the can of soda contains 300 mL, how many pounds of sodium
would there be in one liter of the same soda?
4. The speed of light is 3.00 x108 meters per second.
a. What is the speed of light in feet per second?
b. What is the speed of light in kilometers per day?
c. One light-year is the distance the the light travels in a year. What is a light year in miles per second?
5. A car travles at 60 miles per hour. How fast does it travel per minute? Give your answer using different distance units as
indicated below.
a. Feet
b. Meters
c. Kilometers
6. You have a great job in which you earn $35 per hour.
* How much do you earn per minute?
* How much do you earn per week? (1 week=40 hours)
7. You are in Paris and want to buy some peaches for lunch. The sign on the fruit indicates that peaches are 11.5
euros per kilogram. On that day the euro was 1.35 dollars. How much does a pound of peaches cost in dollars ?
FUNDAMENTAL KNOWLEDGE BANK.nb
PERCENTAGES, RATIO, PROPORTIONS
1. Calculate
-1
1
3
+
3
5
4
-2
+3
2
-2
5
5
3
¸8
* -2
7
2
2
3
-
3
2
-2
3¸
2
3
5
1
2
-2
+
1
3
2. Calculate
What is 3% of 27?
What is 0.001% of 350?
What percentage of 37 is 25?
3. Write as percent
0.25 ________
2.01 ________
0.27 _________
4. A population of animals increases at 3.5% every two years. If the initial population is 120, how many animals will there be
after 6 years?
5. A river is treated due to contamination. The amount of contaminant X in the river is decreasing by 0.25% every 6 hours. If it
is estimated that on average 70% of a cubic feet of water is not contaminated with contaminat X, , what percentage of a cubic
foot is expected to be contaminated with contaminat X after 1 day of treatment?
6. In a farm there are goats, cows, and horses. The horses represent 25% of the animals. The total number of goats and cows is
120 , and the ratio of goats to cows is 2/3.
* What is the ratio of horses with respect to the other animals in the farm?
* How many horses are there?
* How many animals of each type are there?
7. A population is bacteria is growing at 30% per hour. If we start with 800 bacterias, how many are there after 4 hours?
8. Find the slope of the line whose equation is 2 x - 3 y = 6
-3 x + 2 y =
1
2
-x - 2 y = 0
9. Find the equation (slope-intercept form) of the line through
i) H3, - 2L and perpendicular to the line y =
-8
5
x+1
ii) H- 2, 1L and perpendicular to y = x + 5
iii) H3, 0.5L and perpendicular to y = - 0.2 x - 50
10. Find k so that the line through
i) (-3,2) and (k,4) is parallel to 3y-2x=7
ii) H- 3, 2L and H4, kL is parallel to x + y = 2
iii) H4, 0L and Hk, 1L is parallel to 2 y = x - 10
11. Find an equation of the line with graph below.
10
-2
4
3
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FUNDAMENTAL KNOWLEDGE BANK.nb
11. Find an equation of the line with graph below.
4
10
-2
1
2
-2
(2,5)
H-10, -5L
EQUATIONS AND INEQUALITIES
1
1. x + 3 =
x, solve for x
2
2. 5 = 1 - d, solve for d
t
t+1
3.
+ 1 solve for t
=
2
4
2
4.
H6 - 2 aL = a + 2, solve for a
3
5. 0.8 m + 10 = 3 + 0.25 Hm - 2L, solve for m
6. 3 - t = 2, solve for t
7. 2 A + 3 -5 = -1, solve for A
8. -2 Hx + 1L = 3, solve for x
9. x - 3 > 2 x + 5, solve for x
1
10.
x + 5 b -2, solve for x
3
11. 7 - 2 x r 8.5 x + 8, solve for x
12. 4.5 - x £ 2, solve for x
13. -2 + 3 Hx - 0.5L > 3.5, solve for x
14. Represent the interval H-2, 8.5L using
a. A double inequality
b. An inequality with absolute value.
FUNDAMENTAL KNOWLEDGE BANK.nb
15. x2 - 2 x = 1, solve for x
16. How many distinct solutions does x2 = 4 x - 4 have ?
17. The solution to the inequality x2 + 3 x ³ 2 is ___ ___ ___ ___ __
18. zH2 z + 7L = 4 solve for z
19. ´ 16 x2 - 16 x = 0 solve for x
20. r2 = 3 r + 5 solve for r
Solve each of the equations below for the specified variable
21. P V = K for V
22. i = p r t for p
1
23. A = HB + bL for B
2
5
24. C = HF - 32L for F
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This material is based upon work supported by the National Science Foundation under Grant # DUE-0622530. Copyright 2007
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