1.2.3 Prefixes

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Prefixes are the preceding factor used to represent very small and very large physical quantities in SI units.

Table below shows the prefixes that you need to know in SPM.

Conversion of prefixes

Prefixes to Normal Number

Example 1:
The frequency of the radio wave is 350M Hz. What is the frequency of the radio wave in Hz?
Answer:

Mega (M) = 1,000,000 or 106

Therefore,
350MHz = 350 x 106Hz


Example 2:
The thickness of a film is 25nm. What is the thickness in unit meter?
Answer:

nano (n) = 0.000000001 or 10-9

Therefore
25nm = 25 x 10-9m

Normal number to Prefixes

Example 3:
0.255 s is equal to how many ms.
Answer:
mili (m) = 0.001 or 10-3

To write a normal number with prefixes, we divide the number with the value of the prefixes
0.0255 s = 0.0255 ÷ 10-3 = 25.5 ms

Example 4:
Convert 265,500,000 W into GW.
Answer:
Gega (G) = 1,000,000,000 or 109
Therefore
265,500,000 W = 265,500,000 ÷ 109 = 0.2655GW

 

Scientific Notation

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  1. Scientific notation (also known as Standard index notation) is a convenient way to write very small or large numbers. 
  2. In this notation, numbers are separated into two parts, a real number with an absolute value between 1 and 10 and an order of magnitude value written as a power of 10.

Significant Figure

  1. In measurement, significant figures relate the certainty of the measurement.
  2. As the number of significant figures increases, the certainty of the measurement increase, which means we are more certain about what we have measured.
Example:
Speed of light in a vacuum = 299 792 458 ms-1 = 3.00 x 108 ms-1 (to 3 significant figures)

Example:
Write the number of significance figure (s.f.) of the following value:
  1. 135 m, (____s.f.) 
  2. 0.013s (____s.f.) 
  3. 0.2000A (____s.f.) 
  4. 25.10 g (____s.f.) 
  5. 3700km (____s.f.) 
  6. 0.003kg (____s.f.) 
  7. 1.54 10-3 (____s.f.) 
  8. 0.001200 (____s.f.)
Answer:
  1. 135 m, ( 3 s.f.) 
  2. 0.013s ( 2 s.f.) 
  3. 0.2000A ( 4 s.f.) 
  4. 25.10 g ( 4 s.f.) 
  5. 3700km ( 4 s.f.) 
  6. 0.003kg ( 1 s.f.) 
  7. 1.54 x 10-3 ( 3 s.f.) 
  8. 0.001200 ( 4 s.f.)


 

 

1.3.1 Scalar Quantities and Vector Quantities

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Scalar Quantity

  1. Scalars are quantities which are fully described by a magnitude alone. 
  2. Magnitude is the numerical value of a quantity. 
  3. Examples of scalar quantities are distance, speed, mass, volume, temperature, density and energy. 

Vector Quantity

  1. Vectors are quantities which are fully described by both a magnitude and a direction. 
  2. Examples of vector quantities are displacement, velocity, acceleration, force, momentum, and magnetic field.

Example:
Categorize each quantity below as being either a vector or a scalar.

Speed, velocity, acceleration, distance, displacement, energy, electrical charge, density, volume, length, momentum, time, temperature, force, mass, power, work, impulse.
Answer:
Scalar Quantities:
  • speed 
  • distance 
  • energy 
  • electrical charge 
  • density 
  • volume 
  • length 
  • time 
  • temperature 
  • mass 
  • power 
  • work
Vector Quantities
  • velocity 
  • acceleration 
  • displacement 
  • momentum 
  • force 
  • impulse

 

1.2.2.2 Unit of Speed, Density and Pressure

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Speed, density and pressure are derived quantities. When converting their units, firstly, we write the units in fraction form, then only do the unit convertion for the numerator and denominator.


Example
1. Complete the following unit conversion of speed.
  1. 90 kmh-1 = __________ ms-1
  2. 110 kmh-1 = __________ ms-1
  3. 1.3 ms-1 = __________ kmh-1
  4. 8.12 ms-1 = __________ kmh-1
Answer:
a.

b.

c.

d.

2. Complete the following unit conversion of density and pressure.
  1. 760 kgm-3 = __________ gcm-3
  2. 12000 kgm-3 = __________ gcm-3
  3. 5.1 gcm-3 = __________ kgm-3
  4. 3600 Nm-2 = __________ Ncm-2
  5. 12x106  Nm-2 = __________ Ncm-2
  6. 1.5x103 Nm-2= __________ Ncm-2
  7. 3.16x10-5 Ncm-2= __________ Nm-2
  8. 7.1x10-3 Ncm-2 = __________ Nm-2

Answer:
a.

b.

c.

d.

e.

f.

g.

h.


 

1.2.2.1 Derived Units

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SI unit

  1. The International System of Units (abbreviated SI from the French language name Système International d'Unités) is the modern form of the metric system. 
  2. It is the world's most widely used system of units, both in everyday commerce and in science.

Derived Unit

  1. The derived unit is a combination of base units through multiplying and/or dividing them.
  2. For instance,  Speed is defined as the rate of distance change, and can be written in the mathematic form

Example:
Find the derived unit of density.

Answer:

Unit of Density = kg/m3

 

1.2.2 Derived Quantities

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  1. A derived quantity is a Physics quantity that is not a base quantity. It is the quantities which derived from the base quantities through multiplying and/or dividing them.
  2. For example, speed is define as rate of change of distance, Mathematically, we write this as Speed = Distance/Time. Both distance and time are base quantities, whereas speed is a derived quantity as it is derived from distance and time through division.
    Example

    (Speed is derived from dividing distance by time.)
  3. Belows are the derived quantities that you need to know in SPM. You need to know the equation of all the quantities, so that you can derive their unit from the equation.
  4. If you find it difficult to memorise all these equation, you can skip it now because you are going to learn all of them in the other chapter. 

 

1.2.1 Base Quantities

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Physical Quantity

  1. A physical quantity is a quantity that can be measured.
  2. A physical quantity can be divided into base quantity and derived quantity.

Base Quantities

  1. Base quantities are the quantities that cannot be defined in term of other physical quantity.
  2. The base quantities and its units are as in the table below:

TIPS: In SPM, you MUST remember all 5 base quatities and its SI unit.  

1.1.1 Understanding Physics

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1.1.1 Understanding Physics

Physics is a branch of science that study the

  1. natural phenomena
  2. properties of matter
  3. energy

Field of study in Physcis

The field of studys in Physics including

  1. Motion
  2. Pressure
  3. Heat
  4. Light
  5. Waves
  6. Electricity'
  7. Magnetism and electromagnetism
  8. Electronics
  9. Nuclear Physics

1.2.2 Angles and Lines II, PT3 Practice

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Question 6:
In Diagram below, PQRST is a straight line. Find the value of x.

Solution:
Interior angle of  R = ( 180 o − 76 o ) ÷ 2 = 52 o ∠ x = exterior angle of  R   ( corresponding angles ) Hence,  x = 76 o + 52 o = 128 o


Question 7:
In Diagram below, find the value of y.



Solution:


∠ A B C = ∠ B C D    = 108 o  (alternate angle) y o + 130 o + 108 o = 360 o   y o = 360 o − 238 o   y o = 122 o


Question 8:
In Diagram below, PSR and QST are straight lines.
Find the value of x.

Solution:
∠UST+∠STV= 180 o ∠UST= 180 o − 116 o = 64 o ∠PST=∠QSR x o +∠UST= 135 o x o +∠UST= 135 o x o = 71 o x=71


Question 9:
In Diagram below, PWV is a straight line.

(a) Which line is perpendicular to line PWV?
(b) State the value of  ∠ RWU.

Solution:
(a) SW

(b) ∠ RWU = 13o + 29o + 20o = 62o

 


Question 10:
In Diagram below, UVW is a straight line.


(a) Which line is parallel to line TU?
(b) State the value of  ∠ QVS.

Solution:
(a) QV

(b) ∠ QVS = 8o + 18o = 26o

 

12.2.2 Solid Geometry (II), PT3 Focus Practice

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12.2.2 Solid Geometry (II), PT3 Focus Practice

Question 5:
Sphere below has a surface area of 221.76 cm2.


Calculate its radius.
( π = 22 7 )

Solution:
Surface area of sphere = 4πr2
4 π r 2 = 221.76 4 × 22 7 × r 2 = 221.76 r 2 = 221.76 × 7 4 × 22 r 2 = 17.64 r = 17.64 r = 4.2 cm


Question 6:
Diagram below shows a right pyramid with a square base.

Given the height of the pyramid is 4 cm.
Calculate the total surface area, in cm2, of the right pyramid.

Solution:
h2 = 32 + 42
= 9 + 16
= 25
h = √25   = 5 cm2

Total surface area of the right pyramid
= Base area + 4 (Area of triangle)
= (6 × 6) + 4 × 4 (½ × 6 × 5)
= 36 + 60
= 96 cm2


Question 7:
Diagram below shows a prism.

Draw to full scale, the net of the prism on the grid in the answer space. The grid has equal squares with sides of 1 unit.

Solution: