Problem Set: Mathematics Refresher

Problem Set: Mathematics Refresher

1)  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 _____

2)  Add or subtract as indicated. Express your answer using 4 significant digits. Also provide the correct units.

a) 85.261 g + 4.73 g = ______b) 1.0736 m + 0.608 m = ______

c) 186.4 kg - 57.83 kg = ______d) 1228 s – 108 s = ______

3)  Multiply or divide as indicated. Express your answer using 4 significant digits. Also provide the correct units.

a) (5.11 x 108 m) (4.2 x 107 m) = ______b) (0.0167 km) (0.00845 km) = ______

c) (2.60 x 104 kg) / (9400 m3) = ______d) (0.63 m) / (380 s) = ______

4)  Complete each of the following conversions. Express your answer using 4 significant digits.

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

5)  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

6)  To 4 significant digits, find the value of:

a) tan 28° ______b) sin 86° ______c) cos 2° ______

7)  Find q rounded to 4 significant digits if:

a) tan q = 6.5143 ______b) sin q = 0.4540 ______

c) cos q = 0.8188 ______d) tan q = 3/4 ______

8)  Determine x to the nearest tenth for the following right triangles.

(a) / (b) / (c) / (d) / (e)

9)  Calculate the area of following. Express your answer using 4 significant digits.

a)  A circle with a diameter of 10 cm.

b)  The triangle shown below.

1.  a) 4 b) 5 c) 3 d) 3 e) 3 f) 5 / 2.  a) 89.99g b) 1.682m
c)128.6kg d) 1.120x103s / 3.  a) 2.146x1016m2
b)1.411x10-4km2
c) 2.766 kg/m3
d) 0.001658 m/s / 4.  a) 0.05800
b) 0.8700
c) 109.0
d) 0.2569
e) 1.230 x 10-11
f) 10.56
5.  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 / 6.  a) 0.5317 b) 0.9976
c) 0.9994 / 7. a) 81.27˚
b) 27.00˚
c) 35.04˚
d) 36.87˚ / 8. a) 6.8 b) 2.5 c) 7.6
d) 31.9˚ e) 36.0˚
9.  a) 78.50 cm2
b)  1.000x103 cm2

10)  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)