Physics 1
Mathematical Toolkit
Problem Set 1 – Mathematics Refresher
A> Measurement
1) Express the following masses in scientific notation.
a) 810 000 g
_______________
b) 0.000634 g _______________
c) 60 000 000 g
_______________
d) 0.0000010 g
_______________
2) Solve the following problems. Express your answers in scientific notation
with proper units.
a) 6.2 x 10-4 m + 5.7 x 10-3 m = _______________
b) 8.7 x 108 km - 3.4 x 107 km = _______________
c) (9.21 x 10-5 cm) (1.83 x 108 cm) = _______________
d) (2.63 x 10-6 m) / (4.08 x 106 s) = _______________
3) State the number of significant digits in the following measurements.
a) 3218 kg
_____
b) 60.080 mm
_____
c) 801 cm
_____
d) 0.000534 s
_____
e) 5.60 x 108 m
_____
f) 3.0005 x 10-6 km
_____
4) Add or subtract as indicated using significant figures correctly. Also provide
the correct units.
a) 85.26 g + 4.7 g = __________
b) 1.07 km + 0.608 km = __________
c) 186.4 kg - 57.83 kg = __________
d) 60.08 s – 12.2 s = __________
5) Multiply or divide as indicated using significant figures correctly. Also
provide the correct units.
a) (5 x 108 m) (4.2 x 107 m) = __________ b) (0.0167 km) (8.5 x 10-6 km) = __________
c) (2.60 x 104 kg) / (9400 m3) = __________
d) (0.63 m) / (380 s) = __________
6) A rectangular room is 8.7 m by 2.41 m. (Use significant figures correctly)
a) What length of baseboard molding must be purchased to go around the perimeter
of the floor?
b) What area must be covered if floor tiles are laid?
7) Complete each of the following conversions. (Use significant figures
correctly)
a) 58 ms = ________ s
b) 870 g = ________ kg
c) 485 N = ________ lbs
d) 925 s = ________ h
e) 12.3 nm = ________ km f) 38 km/h = ________ m/s
B> Algebraic Expressions
8) Solve for x in each equation below. Round numeric answers to the nearest
tenth.
a)
b)
c)
d)
e)
f)
g)
3x - 5 = 16
-6x + 20 = 11
25/x = 7
4x – 20 + 3x = -3x +45
2x2 +45 = 173
5x2 – 10y = 5y + 35
3x2 – 19x = 14
1. a) 8.1 x 105 g
b) 6.34 x 10-4 g
c) 6 x 107 g
d) 1.0 x 10-6 g
5. a) 2 x 1016 m2
b) 1.4 x 10-7 km2
c) 2.8 kg/m3
d) 1.7 x 10-3 m/s
2. a) 6.32 x 10-3 m
b) 8.36 x 108 km
c)1.69 x 104 cm2
d) 6.45 x 10-13 m/s
6. a) 22.2 m
b) 21 m2
3. a) 4 b) 5 c) 3
d) 3 e) 3 f) 5
7. a) 0.058 s
b) 0.870 kg
c) 109 lbs
d) 0.257 h
e) 1.23 x 10-11km
f) 11 m/s
4. a) 90.0 g
b) 1.68 km
c) 128.6 kg
d) 47.9 s
8. a) x = 7.0
b) x = 1.5
c) x = 3.6
d) x = 6.5
e) x = 8.0
f) x = √(3y + 7)
g) x = 7.0 or
-0.7
C>Trigonometry
9) To three significant figures, find the value of:
a) tan 28 __________
b) sin 86
__________
c) cos 2
__________
d) tan 58 __________
e) sin 40
__________
f) cos 71
__________
10) Find  rounded to three significant figures if:
a) tan  = 9.5143 __________
b) sin  = 0.4540
__________
c) cos  = 0.8192 __________
d) tan  = 3/4
__________
e) sin  = 0.7547 __________
f) cos  = 0.9781
__________
11) Determine x to the nearest tenth for the following right triangles.
(a)
(b)
(c)
x
x
6.2
(d)
25
4.0
58
x
9. a) 0.532
b) 0.998
c) 0.999
d) 1.60
e) 0.643
f) 0.356
12.1
(e)
5.1
x
8.2
39
10. a) 84.0o
b) 27.0o
c) 35.0̊
d) 36.9̊
e) 49.0̊
f) 12.0̊
11.9
7.0
11. a) 6.8
b) 2.5
c) 7.6
d) 58.1̊
e) 36.0̊
x
D> Graphing
12) The following forces were measured as a spring was elongated to the following
changes in length.
Force
(N)
0.00
10.2
19.5
22.0
41.5
52.0
60.4
Change in Length
(cm)
0.00
0.75
1.50
2.25
3.00
3.75
4.50
a) Plot Force vs. Change in Length from the values given and draw the line/curve that best
fits all the data points.
b) Describe the graph.
c) What is the slope of this graph?
d) Write an equation relating force (F) and change in length (∆x).
b) Linear; Direct
c) approx. 15.0 N/cm
d) F = 15.0 N/cm (∆x)