Download Science Skills

Physics Math
pre-test
You will have a test on these – NO CALCULATOR.
Algebra Skills
1. Solve an equation for any variable. Here are some examples, make sure you can solve them
for x. See answers on last page.
a) v + w = x2yz
c)
2 1 1
 
x 3 2
b)
d)
a y

b x
2 1 y
 
x 3 2
2. Be able to reduce fractions containing powers of ten, for example:
102
104
a)
3
10
103
b)
106
3. Be able to take a multiplicative expression to a power, for example:

a) 2  x
 x2 
b)  3 
y 

3 2
PP means Practice
Problem, the solutions
to odd ones are in the
back of the book.
2
Science Skills
4. Convert a number into scientific notation in standard form, and from scientific notation. This
includes both large numbers (> 1,000) and small numbers (< 0.01). Try these examples (answers
at end):
a) 12,345
b) 15000000
c) 1/100
d) 2/10,000
5. Unit pre-fixes: Find Table 1-2 on p. 6. Memorize the multipliers for the following: nano,
micro, milli, centi, kilo, mega, giga. You do not need to memorize other prefixes. Try this: 2,000
mockingbirds = 2 ___________. 1 x 106 phones = ______ Invent others.
6. Significant figures. Know how to find the number of sig figs in a value. PP 9, 11. Try these
(answers at end):
a) 123
b) 1.23 c) 12,300
d) 0.0123
e) 1.230 x 10-4
7. Unit conversion: Be able to use the factor-label method. A conversion factor is a multiplier
that is equal to one. For example, 1 foot = 12 inches, so 
1 foot
 1 . If we want to convert
12inches
113.2 inches to feet, we multiply by the conversion factor:
113.2inches 
1 foot
113.2 inches
1 foot
113.2 feet



 9.433 feet
12inches
1
12
12 inches
a) 13.4 inches to feet
b) 4.31 feet to inches
8. Arithmetic operations in scientific notation. For addition and subtraction, the operands must
all be expressed in the same powers of ten. For multiplication and division, the exponents are
also involved in the operation. Appendix A, p. 842, PP #13.
a) 435 + 2.7x102
b) 4.35 + 2.7 x 10-1
c) 4.35 x 2.7x10-2
d)
540
2.7 102
Geometry and right-angle Trigonometry
9. Know sin, cos, tan (memorize SOH CAH TOA) and how to apply them to find the side of a
right triangle. Appendix A. a) Find sin, cos, and tan of θ. b) Suppose θ = 50°, sin 50 = 0.766,
cos 50 = 0.643, & c = 9. Find a & b.
a
Sin-1 (0.5) can be read as “the angle whose
sin is 0.5”.
c
Similarly for tan-1 and cos-1
θ
b
10. Know sin-1, cos-1, tan-1 and how to apply them to find the angle in a right triangle Appendix A
p. 856. Find the value of θ in the triangle above if a = 57.3 and c = 100.
Know the Pythagorean theorem, be able to use it to find the third side of a right triangle when the
other two sides are given.
Do not apply any of the three laws stated above to triangles that are not right triangles.
11. Understanding Ratios. The ratio or fraction
465
signifies the number of times 23 is
23
contained in 465 – the number of successive subtractions of 23 from 465. The result of the
division tells us how much of the numerator is associated with one of the denominator. a) How
much will one pound cost if we paid $5.00 for 3 pounds? b) If the ratio of girls to boys is 5 to 3,
how many girls are there if there are 9 boys? c) If the ratio of length to width is 1.33, what will
be the width if the length is 7?
----------------------------------------------------------------------------
See Ch 1 in your book for problems and solutions related to scientific
notation and significant figures.
1. a) x 
d)
2. a)
vw
yz
 12 
b) x   
 5
c) x 
2 1 y 2  3y
x
6
12
  
 
x
x 3 2
6
2 2  3y
2  3y
102
104  109
3
10
b)
103
 103
6
10
y b
a
3. a)  2  x

2
3 2
 4 x
 x2 
x4
b)  3   6
y
y 
6
4. a) 12,345 = 1.2345 x 104
c) 1/100 = 0.01 or 1 x 10-2
b) 15000000 = 1.5 x 107
d) 2/10,000 = 2 x 10-4
6. a), b) & c) 3 sig figs; d) 4 sig figs
7. a) 40 in 
1 ft
 3.33 ft
12 in
8. a) 435 + 270 = 705
9. a) & b) sin  
tan  
b) 4.31 4.3 ft 
b) 4.35 + 0.27 = 4.62
12in
 51.6in
ft
c) 4.35 x 0.027 = 4.377
opp a
a
   0.766  a  6.89
hyp c
9
cos  
d)
540
2
270
adj b b
   0.643  b  5.79
hyp c 9
opp a

adj b
 57.3 
10.   sin 1 
  35 Questions 9 & 10 are not numerically consistent with one another.
 100 
11. . a)
c) 5.26
cost
5
cost
  1.67 
pound 3
one pound
b)
girls 5
girls
= =1.67=
 girls = 1.67 × boys=15.0
boys 3
boys