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 correct answer)
a. H6 p qL H2 p rL
them
b. 2 p * 3 q * r
c. 6 pqr
d. 6 pq + 2 pr e. None of
3. Write each of these numbers in scientific notation
- 0.0000327 _______________________
______________________
3724000000
Write in scientific notation the result of each of the following operations (4-7)
4.
I3 * 10-5M I4.2 * 102M I5 * 10-3M
________________________
5.
1.5*10-7
3.0*104
_________________________
6.
-2.5 * 103 + 3.2 * 102
_________________________
I5*106 M I2*103 M I3*10-4 M
7.
I8*10-2 M H5*10L
___________________________
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8. The number I 23 M
a.
2-4
3-4
b.
-8
-12
can be written as (more than one answer is possible)
4
c. I 32 M
d. 2-4 * 34
e. All of them
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FUNDAMENTAL KNOWLEDGE BANK.nb
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8. The number I 23 M
a.
2-4
3-4
b.
-8
-12
can be written as (more than one answer is possible)
4
c. I 32 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 long (in 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 the 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. The volume of a sphere with radius R is V =
4
3
Π R3. Given that the radius of the
earth is 6.3 * 106 meters and its mass, M, is 5.9742 ´ 1024 kilograms. Find the density of the earth in kg ‘ m3 . Give the answer in scientific notation. (The density Ρ is
given by Ρ =
M
)
V
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 the problem, 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 hr
1 mg
1g
1L
1 cm
1000 Ðg 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 aluminum used in making aluminum baseball
bats is 2.70 g ‘ cm3. Which material has more density?
FUNDAMENTAL KNOWLEDGE BANK.nb
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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 aluminum used in making aluminum 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 x108meters 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? in feet?
5. A car travels 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?
PERCENTAGES, RATIO, PROPORTIONS
1. Calculate
1
3
+
3
5
-2
2
3
-
3
2
-2
-1
+3
4
2
7
3¸
2
3
-2
5
¸8
2
-2
5
1 1
+
2 3
2. Calculate
What is 3% of 27?
What is 0.001% of 350?
What percentage of 37 is 25?
5
3
* -2
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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? How about after 7 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. It is estimated that on average 70% of a cubic
feet of water is not contaminated with contaminant X when the treatment begins.
What percentage of a cubic foot of water is expected to be contaminated with contaminant 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 for each of the following lines
2x-3y = 6
-3 x + 2 y =
1
2
-x - 2 y = 0
9. Find the equation (slope-intercept form) of the line passing through
i) H3, -2L and perpendicular to the line y = -8
x+1
5
ii) H-2, 1L and perpendicular to y = x + 5
iii) H3, 0.5L and perpendicular to y = -0.2 x - 50
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9. Find the equation (slope-intercept form) of the line passing through
i) H3, -2L and perpendicular to the line y = -8
x+1
5
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.
4
10
-2
1
2
-2
(2,5)
H-10, -5L
EQUATIONS AND INEQUALITIES
1. x + 3 =
1
2
x, solve for x
2. 5 = 1 - d, solve for d
3.
t
2
=
t+1
4
+ 1 solve for t
5
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FUNDAMENTAL KNOWLEDGE BANK.nb
4.
2
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
10.
1
3
x + 5 b -2, solve for x
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.
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
FUNDAMENTAL KNOWLEDGE BANK.nb
Solve each of the equations below for the specified variable
21. P V = K Solve for V
22. i = p r t Solve for p
1
23. A = HB + bL Solve for B
2
5
24. C = HF - 32L Solve 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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