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 = ______kgc) 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)3x - 5 = 16

b)-6x + 20 = 11

c)25/x = 7

d)4x – 20 + 3x = -3x +45

e)2x2 +45 = 173

f)5x2 – 10y = 5y + 35

g)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
/
  1. 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 /
  1. a) 4 b) 5 c) 3 d) 3 e) 3 f) 5
/
  1. a)90.0 g
b) 1.68 km
c) 128.6 kg
d) 47.9 s
  1. 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 /
  1. a) 22.2 m
b) 21 m2 /
  1. 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 /
  1. 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 figuresif:

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) / (d) / (e)
  1. a) 0.532
b) 0.998
c) 0.999
d) 1.60
e) 0.643
f) 0.356 /
  1. a) 84.0o
b) 27.0o
c) 35.0̊
d) 36.9̊
e) 49.0̊
f) 12.0̊ /
  1. a) 6.8
b) 2.5
c) 7.6
d) 58.1̊
e) 36.0̊

D> Graphing

12)The following forces were measured as a spring was elongated to the following changes in length.

Force
(N) / Change in Length
(cm)
0.00 / 0.00
10.2 / 0.75
19.5 / 1.50
22.0 / 2.25
41.5 / 3.00
52.0 / 3.75
60.4 / 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)