Home › View all posts by user › Page 66

Author: user

1.2.2.2 Unit of Speed, Density and Pressure

Posted on by

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

Posted on by

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

Posted on by
  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

Posted on by

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

Posted on by

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

Posted on by

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

Posted on by

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:


8.2.2 Coordinates, PT3 Focus Practice

Posted on by

Question 6:
The point M (x, 4), is the midpoint of the line joining straight line Q (-2, -3) and R (14, y).
The value of x and y are

Solution:

x= −2+14 2 x= 12 2 x=6 4= −3+y 2 8=−3+y y=11


Question 7:
In diagram below, PQR is a right-angled triangle. The sides QR and PQ are parallel to the y-axis and the x-axis respectively. The length of QR = 6 units.

Given that M is the midpoint of PR, then the coordinates of M are

Solution:
x-coordinate of R = 3
y-coordinate of R = 1 + 6 = 7
R = (3, 7)

P( 1,1 ),R( 3,7 ) Coordinates of M =( 1+3 2 , 1+7 2 ) =( 2,4 )


Question 8:
Given points P (–2, 8) and Q (10, 8), find the length of PQ.

Solution:
Length of PQ = [ 10−( −2 ) ] 2 + ( 8−8 ) 2 = ( 14 ) 2 +0 =14 units


Question 9:
In diagram below, ABC is an isosceles triangle.

Find
(a) the value of k,
(b) the length of BC.

Solution:
( a ) For an isosceles triangle,  y−coordinate of C is the midpoint of straight line AB. 2+k 2 =−3 2+k=−6   k=−8 ( b ) B=( −2,−8 ) BC= [ 10−( −2 ) ] 2 + [ −3−( −8 ) ] 2  = 12 2 + 5 2  =13 units


Question 10:
Diagram below shows a rhombus PQRS drawn on a Cartesian plane. PS is parallel to x-axis.

Given the perimeter of PQRS is 40 units, find the coordinates of point R.

Solution:
All sides of rhombus have the same length, therefore length of each side= 40 4 =10 units PQ=10 ( 9− x 1 ) 2 + ( 7−( −1 ) ) 2 = 10 2 81−18 x 1 + x 1 2 +64=100 x 1 2 −18 x 1 +45=0 ( x 1 −3 )( x 1 −15 )=0 x 1 =3,15 x 1 =3 Q=( 3,−1 ),R=( x 2 ,−1 ) QR=10 ( x 2 −3 ) 2 + [ −1−( −1 ) ] 2 = 10 2 x 2 2 −6 x 2 +9+0=100 x 2 2 −6 x 2 −91=0 ( x 2 +7 )( x 2 −13 )=0 x 2 =−7,13 x 2 =13 ∴R=( 13,−1 )



4.2.2 Linear Equations I, PT3 Practice

Posted on by

Question 6:
Solve each of the following equations:
(a)  5 a − 16 = a (b)  6 + 2 3 ( − 9 p + 12 ) = p


Solution:
(a)
5 a − 16 = a 5 a − a = 16 4 a = 16 a = 4

(b)
6 + 2 3 ( − 9 p + 12 ) = p 6 − 6 p + 8 = p − 6 p − p = − 8 − 6 − 7 p = − 14 p = 2


Question 7::
Solve each of the following equations:
(a)  a − 2 = a 5 (b)  b − 3 4 = 2 + b 5

Solution:
(a)
a − 2 = a 5 5 a − 2 = a 4 a = 2 a = 2

(b)
b − 3 4 = 2 + b 5 5 b − 15 = 8 + 4 b 5 b − 4 b = 8 + 15 b = 23

</div
Question 8:
Solve each of the following equations:
(a)  x = − 24 − x (b)  y + 5 4 ( 4 − 2 y ) = − 4

Solution:
(a)
x = − 24 − x 2 x = − 24 x = − 12

(b)
y + 5 4 ( 4 − 2 y ) = − 4 4 y + 20 − 10 y = − 16    ( × 4 ) − 6 y = − 16 − 20 − 6 y = − 36 y = 6


Question 9:
Solve each of the following equations:
(a)  5 p = 8 p − 9 (b)  3 q = 20 − 13 q 4

Solution:
(a)
5 p = 8 p − 9 5 p − 8 p = − 9 − 3 p = − 9 p = 3

(b)
3 q = 20 − 13 q 4 12 q = 20 − 13 q 12 q + 13 q = 20 25 q = 20 q = 4 5

2.2.2 Number Patterns and Sequences, PT3 Practice

Posted on by

Question 6:
How many prime numbers are there between 10 and 40?

Solution:
Prime numbers between 10 and 40
= 11, 13, 17, 19, 23, 29, 31, 37
There are 8 prime numbers between 10 and 40.


Question 7:
Diagram below shows a sequence of prime numbers.
13, 17, x, y, 29 Find the value of x + y.

Solution:
Value of x + y
= 19 + 23
= 42


Question 8:
The following data shows a sequence of prime numbers in ascending order.
 5, 7, x, 13, 17, 19, 23, 29, y, z  Find the value of x, y and of z.

Solution:
x = 11, y = 31, z = 37


Question 9:
The following data shows a sequence of prime numbers in ascending order.
  p, 61, 67, q, 73, r, 83  Find the value of p, q and of r.

Solution:
p = 59, q = 71, r = 79



Question 10:
Diagram below shows several number cards.
    49     39     29         87     97     77          5      15     25     List three prime numbers from the diagram.

Solution:
Prime number card from the diagram = 5, 29 and 97.