1
Q
What is a good strategy when rounding multiplied values?
A
Round one factor down and the other factor up.
2
Q
What is the benefit of rounding one factor down and one up?
A
The calculation is easier and it’s closer to the actual value.
3
Q
What is 3.5 × 4.5? * Round one up and round one down
A
A. 3.3
B. 15.75
C. 19.95
D. 300.25
4
Q
What is the benefit of cancelling numbers in calculations?
A
Cancelling numbers is faster and more accurate than rounding.
5
Q
What should you do with review questions that are close together?
A
They can be ignored.
6
Q
What is the significance of Review Question 6 Il and 10.9?
A
They are so close together that they can be ignored.
7
Q
Calculate 11 x 32 / 10.9 x 10
A
3.23
8
Q
What is scientific notation?
A
Scientific notation writes any number as a pre-factor (or mantissa) number between 1 and 10 times 10 to the power of an integer exponent.
9
Q
What is the format of scientific notation?
A
mantissa × 10^integer
10
Q
How do you multiply numbers in scientific notation?
A
Multiply the pre-factors and add the exponents.
11
Q
How do you convert 5000 into scientific notation?
A
5000 = 5 × 10^3
12
Q
How do you convert 0.000074 into scientific notation?
A
0.000074 = 7.4 × 10^-5
13
Q
How do you move the decimal point in scientific notation?
A
Move the decimal point to the left by increasing the exponent by one, or to the right by decreasing it by one.
14
Q
What is an example of moving the decimal point for 5000?
A
5000 = 500 × 10^1 = 50 × 10^2 = 5 × 10^3
15
Q
What is an example of moving the decimal point for 0.000074?
A
0.000074 = 0.00074 × 10^-1 = 0.0074 × 10^-2 = 0.074 × 10^-3 = 0.74 × 10^-4 = 7.4 × 10^-3
16
Q
How do you divide numbers in scientific notation?
A
Divide the pre-factors and subtract the exponents.
17
Q
What is an example of multiplying scientific notation?
A
5 × 10^3 × (7.4 × 10^-5) = (5 × 7.4) × 10^(3 + (-5)) = 37 × 10^-2 = 3.7 × 10^-1
18
Q
What is an example of dividing scientific notation?
A
8.4 × 10^6 ÷ 2 × 10^5 = 4.2 × 10^1
19
Q
Remember this
A
<
20
Q
How do you add or subtract in scientific notation?
A
Shift one of the numbers until the exponents match, then add the numbers in front of the exponential term.
Example: 4.3 × 10^4 + 5.8 × 10^3 = 4.3 × 10^4 + 0.58 × 10^4 = 4.3 × 10^4 + 0.6 × 10^4 = 4.9 × 10^4
21
Q
What should you do if one number is much smaller in scientific notation?
A
You can say it’s negligible.
Example: Adding seven to a million is still approximately a million.
22
Q
What is the result of adding 5.2 × 10^0 and 8.7 × 10^5?
A
5.2 × 10^0 + 8.7 × 10^5 = 5.2 × 10^0 + 0.00087 × 10^0 = 5.2 × 10^0.
This number is a large number.
23
Q
When is a smaller number considered negligible?
A
If the difference in the exponents is more than 2, then the smaller number is negligible.
24
Q
What is the metric system?
A
The metric system gives a standard international (SI) set of units.
25
How many base units are there in the metric system?
There are seven base units which can be combined to measure other properties.
26
What are the seven base units in the metric system?
Length: metre, Mass: kilogram, Time: second, Current: ampere, Temperature: kelvin, Substance: mole, Intensity of Light: candela.
27
What is the purpose of prefixes in the metric system?
Prefixes can change the size of a unit.
28
What is the power of ten for the prefix 'femto'?
femto: 10^-15
29
What is the power of ten for the prefix 'pico'?
pico: 10^-12
30
What is the power of ten for the prefix 'nano'?
nano: 10^-9
31
What is the power of ten for the prefix 'micro'?
micro: 10^-6
32
What is the power of ten for the prefix 'milli'?
milli: 10^-3
33
What is the power of ten for the prefix 'centi'?
centi: 10^-2
34
What is the power of ten for the prefix 'deci'?
deci: 10^-1
35
What is the power of ten for the prefix 'kilo'?
kilo: 10^3
36
What is the power of ten for the prefix 'mega'?
mega: 10^6
37
What is the power of ten for the prefix 'giga'?
giga: 10^9
38
What is the power of ten for the prefix 'tera'?
tera: 10^12
39
What is the power of ten for the prefix 'peta'?
peta: 10^15
40
What are the standard units for velocity and area?
Velocity: m/s, Area: m².
41
What is the standard unit of mass?
The unit of mass is the kilogram (kg).
42
How do you convert 5 cm to meters?
5 cm = 5 × 10^-2 m = 0.05 m.
43
Can you use other units in ratios?
Yes, in ratios, you can use other units as the units cancel out.
44
What is the conversion for 1 millimetre?
1 mm = 10^-3 m = 0.001 metre.
45
What is the conversion for 1 centimetre?
1 cm = 10^-2 m = 0.01 metre.
46
What is the conversion for 1 kilometre?
1 km = 10^3 m = 1000 metre.
47
What is the method called for adding or subtracting by the opposite bottom term?
This is called 'cross-multiplying'.
48
What is the square of 1?
1
49
What is the square of 6?
36
50
What is the square of 11?
121
51
What is the square of 2?
4
52
What is the square of 7?
49
53
What is the square of 12?
144
54
What is the square of 3?
9
55
What is the square of 8?
64
56
What is the square of 13?
169
57
What must you memorize regarding square roots?
You must memorize the square roots of 2 and 3.
58
What is the square root of 2?
√2 = 1.4
59
What is the square of 4?
16
60
What is the square of 9?
81
61
What is the square of 14?
196
62
What is the square root of 3?
√3 = 1.7
63
What is the square of 5?
25
64
What is the square of 10?
100
65
What is the square of 15?
225
66
What happens to the square root of a number smaller than 1?
The square root of a number smaller than 1 is larger than the number.
67
How do we square decimals?
(0.6)² = (6 × 10¹)² = 36 × 10-2 = 0.36
68
What is the cube root of x?
The cube root of x is a number which to the power of 3 becomes x.
69
What is the cube root of 8?
The cube root of 8 is 2 because 2³ = 8.
70
What is the cube root of 27?
The cube root of 27 is 3 because 3³ = 27.
71
What is the logarithmic function used for in chemistry?
The logarithmic function is used in pH calculations.
72
Can logarithmic calculations be done in our head?
No, we can't do logarithmic calculations in our head, but we can get approximate values.
73
What does the logarithm tell you?
The logarithm tells you what power of 10 gives you the value.
74
What is log(100)?
log(100) = 2
## Footnote
Because 10^2 = 100
75
What is log(1,000)?
log(1,000) = 3
## Footnote
Because 10^3 = 1,000
76
What is log(0.001)?
log(0.001) = -3
## Footnote
Because 10^-3 = 0.001
77
What is log(0.0001)?
log(0.0001) = -4
## Footnote
Because 10^4 = 0.0001
78
What is the exact integer logarithm of a power of 10?
A power of 10 has an exact integer logarithm.
79
How can logarithms for other numbers be found?
Any other number can be found between the logarithms of powers of 10.
80
What is log(700)?
log(700) is closer to 3.
81
What is log(100,000)?
log(100,000) = 5
## Footnote
Because 10^5 = 100,000
82
What is log(946,000)?
log(946,000) = 5.9.
83
What happens to a logarithm when a number is increased by a factor of 10?
It increases by 1.
84
What happens to a logarithm when a number is decreased by a factor of 10?
It decreases by 1.
85
If log(700) = 2.84, what is log(7000)?
log(7000) = 2.84 + 1 = 3.84.
86
If log(700) = 2.84, what is log(1400)?
log(1400) is between log(700) and log(1000).
87
What is log(1000)?
log(1000) = 3.
88
What is log(10000)?
log(10000) = 4.
89
What is the logarithm of 10?
log10 = 1
90
What is the formula for pH?
pH = -log[Hydrogen ion concentration]
91
What is the pH when the hydrogen ion concentration is (2.2 × 10^-4)?
pH = 4 - 0.2 = 3.0
## Footnote
The calculation shows that pH = -log(2.2 × 10^-4) = 3.0.
92
What is the pH when the hydrogen ion concentration is (9.0 × 10^-9)?
pH = 5.1
## Footnote
The calculation shows that pH = -log(9.0 × 10^-9) = 5.1.
93
What is the formula for calculating a new ratio when comparing functions?
new ratio = old ratio
94
Why is using a ratio useful when comparing functions?
Dividing like this cancels out many unknown values and factors.
95
What is the formula for kinetic energy of a particle?
KE = ½mv²
96
If a box moving at 3 m/s has a kinetic energy of 90 J, what is its kinetic energy at 7 m/s?
The kinetic energy at 7 m/s is 490 J.
97
What are the axes of a graph?
Most graphs have an x axis (the independent variable) and a y axis (the dependent variable).
## Footnote
For example, a volume control is an independent variable, and the loudness of the speaker is the dependent variable.
98
What does the slope of a graph represent?
The slope of a graph is how much y changes in response to x.
## Footnote
You can find the average slope between two points using the formula: slope m = (Y2 - Y1) / (X2 - X1).
99
How can you find the instantaneous slope at a point on a graph?
You can find the instantaneous slope at a point by drawing a tangent to the line at that point.
100
What does a positive slope indicate?
If the line is going up, the slope is positive.
101
What does a negative slope indicate?
If the line is going down, the slope is negative.
102
What does a zero slope indicate?
If the line is horizontal, the slope is zero.
103
What does a constant slope indicate?
If the line is a straight line, the slope is constant.
104
What does a changing slope indicate?
If the line is a curve, the slope is changing.
105
What are the units of slope?
Units of slope are the units of the y-axis divided by the units of the x-axis.
106
What does the graph of displacement versus time represent?
The graph shows the position of a particle over time.
107
What is a linear function?
A linear function depends directly on a value and appears as a straight line on a graph.
108
What does it mean if a linear function goes through zero?
If the line goes through zero, we say they are directly proportional.
109
What is the equation for pressure due to a depth of fluid?
P = pgy, where p is the density of fluid, g is the acceleration due to gravity (g = 10 m/s²), and y is the depth of fluid.
110
How does pressure relate to depth in a fluid?
Pressure is directly proportional to the depth; if depth y is zero, pressure is zero. If depth increases, pressure increases.
111
What happens to pressure if depth doubles?
If depth doubles, the pressure due to that fluid will double.
112
What is the equation for total pressure at a depth that does not go through zero?
P = surface + pgy.
113
How does pressure change with depth in the equation P = surface + pgy?
Pressure increases with depth, but is not zero when depth is zero.
114
What is the equation for kinetic energy?
KE = 1/2 mv², where m is the mass of the object and v is the velocity of the object.
115
How does kinetic energy relate to velocity?
Kinetic energy depends on the velocity squared.
116
What happens to kinetic energy if velocity is doubled?
If we double the velocity, we quadruple the kinetic energy.
117
What happens to kinetic energy if velocity is reduced to one-third?
If we reduce the velocity to one-third, we would reduce the kinetic energy to one-ninth.
118
What is a cubic function?
A cubic function curves like a square but even faster.
119
What is a scalar?
A scalar is just a number, like temperature, mass, or time.
120
What is a vector?
A vector has both magnitude and direction.
121
What is an example of a vector?
"10 km/h North" is a vector.
122
What is an example of a non-vector?
"30 m/s wiggling around" is not a vector.
123
What is the difference between speed and velocity?
Speed is a scalar, while velocity is a vector (velocity is speed with a direction).
124
What is the magnitude of a vector?
The magnitude of a vector is just its size, reducing it to a scalar.
125
How is the magnitude of a vector written?
The magnitude of a vector F is written |F|.
126
How do you add vectors?
Use the tip-to-tail method to find the resultant.
127
How do you subtract vectors?
To subtract vectors: A - B = A + (-B), where -B is a vector pointing in the opposite direction to B.
128
What is a right triangle?
A right triangle is a triangle where one angle is 90°.
129
What is the hypotenuse?
The side opposite the 90° angle in a right triangle.
130
What is the adjacent side?
The non-hypotenuse side beside the angle in a right triangle.
131
What is the opposite side?
The side opposite the angle in a right triangle.
132
What does SOH-CAH-TOA stand for?
SOH: sin = opposite/hypotenuse, CAH: cos = adjacent/hypotenuse, TOA: tan = opposite/adjacent.
133
What are the sine values for key angles?
0° = 0, 30° = 0.5, 45° = √2/2, 60° = √3/2, 90° = 1.
134
What are the cosine values for key angles?
0° = 1, 30° = √3/2, 45° = √2/2, 60° = 0.5, 90° = 0.
135
What is a useful mnemonic for remembering sine and cosine values?
'SOO what?' helps remember that 'Sin of 0 is 0' and the values increase from 0 to 1.
136
What is the Pythagorean Theorem?
In a right-angle triangle, the equation is a² + b² = c², where c is the hypotenuse.
137
What is a common example of a right-angle triangle?
The 3-4-5 triangle, where the sides are 3 and 4, and the hypotenuse is 5.
## Footnote
This is verified as 3² + 4² = 9 + 16 = 25 = 5².
138
When is the Pythagorean Theorem rarely applicable?
It is rare when all three sides of a right-angle triangle have whole numbers.
139
What are the x and y components of a vector?
Vectors are broken down into x and y components, with x being horizontal and y being vertical.
140
How are the x and y axes oriented?
The x-axis is horizontal (right is positive, left is negative) and the y-axis is vertical (up is positive, down is negative).
141
What is the formula for the x component of a vector at an angle e?
Vx = v cos(e)
142
What is the formula for the y component of a vector at an angle e?
Vy = v sin(e)
143
What is the total horizontal force acting on the object in the example?
The total horizontal force is 30 N to the right.
## Footnote
Calculation: Fx = 100 Cos 45° - 80 Cos 60° = 100(0.707) - 80(0.5) = 70 - 40 = 30 N.
144
What is the value of 100 Cos 45°?
100 Cos 45° = 100 × 0.707 = 70.7
145
What is the value of 80 Cos 60°?
80 Cos 60° = 80 × 0.5 = 40
146
What are the x and y components of a vector?
Vectors are broken down into x and y components, with x being horizontal and y being vertical.
147
How are the x and y axes oriented?
The x-axis is horizontal (right is positive, left is negative) and the y-axis is vertical (up is positive, down is negative).
148
What is the formula for the x component of a vector at an angle e?
Vx = v cos(e)
149
What is the formula for the y component of a vector at an angle e?
Vy = v sin(e)
150
What is the total horizontal force acting on the object in the example?
The total horizontal force is 30 N to the right.
## Footnote
Calculation: Fx = 100 Cos 45° - 80 Cos 60° = 100(0.707) - 80(0.5) = 70 - 40 = 30 N.
151
What is the value of 100 Cos 45°?
100 Cos 45° = 100 × 0.707 = 70.7
152
What is the value of 80 Cos 60°?
80 Cos 60° = 80 × 0.5 = 40
153
What is the perimeter formula for a rectangle?
Perimeter = 2(x + y)
154
What is the circumference formula for a circle?
Circumference = 2πr
## Footnote
Estimate π as 3.
155
What is the area formula for a square?
Area = x²
156
What is the area formula for a rectangle?
Area = xy
157
What is the area formula for a triangle?
Area = (base x height) / 2
158
What is the area formula for a circle?
Area = πr²
## Footnote
We often approximate π as 3 and remember the actual area is a bit bigger.
159
What is the surface area formula for a sphere?
Surface Area = 4πr²
160
What is the formula for the volume of a cube?
Volume = x³
161
What is the formula for the volume of a rectangular prism?
Volume = xyz
162
What is the formula for the volume of a cylinder?
Volume = top × height
## Footnote
Here, Volume = mr
163
What is the formula for the volume of a sphere?
Volume = (4/3)πr³
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