fakta Matematik

FAKTA PENTING!

90% pelajar Tidak Didedah dengan soalan bertaraf Peperiksaan sejak di peringkat awal lagi.

90% Pelajar Cemerlang Matematik mengatakan mereka mengulangkaji dengan membuat latih tubi Soalan Peperiksaan tahun lepas secara BERULANG KALI

90% pelajar gagal Matematik kerana tidak mengetahui format Soalan dengan baik.Rata-rata tidak tahu perbezaan bentuk soalan di kertas 1 dan kertas 2 dengan baik.

Kebanyakan pelajar langsung tak tahu nama tajuk soalan ,menyebabkan mereka tak tahu formula dan operasi yang sesuai digunakan.

Kebanyakan pelajar tidak tahu soalan mana perlu didahulukan dan Soalan mana perlu dikemudiankan untuk dijadikan medan latihan.

Kebanyakan pelajar tidak mengetahui bahawa Soalan Peperiksaan sebenar hanya dipusing - pusing sedikit sahaja dari sebelumnya

Kebanyakan Pelajar Cemerlang Matematik akan membuat Persediaan Khusus mengikut jenis peperiksaan yang akan dihadapinya berbeza dengan pelajar gagal yang hanya belajar..mengikut topik by topik semata-mata.

Kekurangan pengetahuan dan pendedahan tentang teknik menjawab soalan sejak dari awal lagi juga merupakan salah satu punca pelajar gagal

Bearing

Bearings

A directional compass is shown below. It is used to find a direction or bearing . The four main directions of a compass are known as cardinal points. They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. The above compass shows degree measurements from 0° to 360° in 10° intervals with: north representing 0° or 360° east representing 90° south representing 180° west representing 270° When using a directional compass, hold the compass so that the point marked north points directly away from you. Note that the magnetic needle always points to the north. Bearing The true bearing to a point is the angle measured in degrees in a clockwise direction from the north line. We will refer to the true bearing simply as the bearing. For example, the bearing of point P is 065º which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass at O with the point P (i.e. OP). The bearing of point Q is 300º which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass at O with the point Q (i.e.OQ). Note: The bearing of a point is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass with the point. A bearing is used to represent the direction of one point relative to another point. For example, the bearing of A from B is 065º. The bearing of B from A is 245º. Note: Three figures are used to give bearings. All bearings are measured in a horizontal plane. Example 10 State the bearing of the point P in each of the following diagrams: Solution: a. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P. The bearing of point P is 048°. b. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P. The cardinal point S corresponds to 180°. It is clear from the diagram that the required angle is 60° larger than 180°. So, the angle measured in a clockwise direction from the north line to the line joining the centre of the compass to point P is 180° + 60° = 240°. So, the bearing of point P is 240°. c. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P. The cardinal point S corresponds to 180°. It is clear from the diagram that the required angle is 40° less than 180°. So, the angle measured in a clockwise direction from the north line to the line joining the centre of the compass to point P is 180° – 40° = 140°. So, the bearing of point P is 140°. d. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P. The cardinal point W corresponds to 270°. It is clear from the diagram that the required angle is 20° larger than 270°. So, the angle measured in a clockwise direction from the north line to the line joining the centre of the compass to point P is 270° + 20° = 290°. So, the bearing of point P is 290°. Direction The conventional bearing of a point is stated as the number of degrees east or west of the north-south line. We will refer to the conventional bearing simply as the direction. To state the direction of a point, write: N or S which is determined by the angle being measured the angle between the north or south line and the point, measured in degrees E or W which is determined by the location of the point relative to the north-south line E.g. In the above diagram, the direction of: A from O is N30ºE. B from O is N60ºW. C from O is S70ºE. D from O is S80ºW. Note: N30ºE means the direction is 30º east of north. Example 11 Describe each of the following bearings as directions. a. 076° b. 150° c. 225° d. 290° Solution: a. The position of a point P on a bearing of 076° is shown in the following diagram. The position of the point P is 76° east of north. So, the direction is N76°E. b. The position of a point P on a bearing of 150° is shown in the following diagram. The position of the point P is 180° – 150° = 30° east of south. So, the direction is S30°E. c. The position of a point P on a bearing of 225° is shown in the following diagram. The position of the point P is 225° – 180° = 45° west of south. So, the direction is S45°W. d. The position of a point P on a bearing of 290° is shown in the following diagram. The position of the point P is 360° – 290° = 70° west of north. So, the direction is N70°W.

PEPERIKSAAN PERTENGAHAN TAHUN

PANITIA MATEMATIK ASIS MENGUCAPKAN SELAMAT MENJAWAB PEPERIKSAAN KEPADA PARA PELAJAR ASIS TINGKATAN 5 DAN 4 YANG AKAN MENGAMBIL PEPERIKSAAN PERTENGAHAN TAHUN 2011

latihan Cuti Sekolah

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Tingkatan 4 Matematik

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Tingkatan 5 Matematik

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SET ( F4)

Definition of Sets

A set is a collection of objects, things or symbols which are clearly defined.

The individual objects in a set are called the members or elements of the set.

A set must be properly defined so that we can find out whether an object is a member of the set.

There are two ways of doing this.

1. Listing the elements

The set can be defined by listing all its elements, separated by commas and enclosed within braces.

Example:
B = {2, 4, 6, 8, 10}
X = {a, b, c, d, e}

However, in some instances, it is impossible to list all the elements of a set. In such cases, we define the set by method 2.

2. Describing the elements

The set can be defined, where possible, by describing the elements.

Example:
C = {x : x is an integer, x > – 3 }
This is read as: “C is the set of elements x such that x is an integer greater than –3.”

D= {x: x is a river in a river}

We should describe a certain property which all the elements x, in a set, have in common so that we can know whether a particular thing belongs to the set.

We relate a member and a set using the symbol ∈. If an object x is an element of set A, we write x ∈ A. If an object z is not an element of set A, we write z ∉ A.

∈ denotes “is an element of’ or “is a member of” or “belongs to”

∉ denotes “is not an element of” or “is not a member of” or “does not belong to”

Example:
If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A

Transformations III

Translations - Each Point is Moved the Same Way

The most basic transformation is the translation. The formal definition of a translation is "every point of the pre-image is moved the same distance in the same direction to form the image." Take a look at the picture below for some clarification.

Each translation follows a rule. In this case, the rule is "5 to the right and 3 up." You can also translate a pre-image to the left, down, or any combination of two of the four directions.

More advanced transformation geometry is done on the coordinate plane. The transformation for this example would be T(x, y) = (x+5, y+3).

Reflections - Like Looking in a Mirror

A reflection is a "flip" of an object over a line. Let's look at two very common reflections: a horizontal reflection and a vertical reflection.

Notice the colored vertices for each of the triangles. The line of reflection is equidistant from both red points, blue points, and green points. In other words, the line of reflection is directly in the middle of both points.

Examples of transformation geometry in the coordinate plane...

• Reflection over x-axis: T(x, y) = (x, -y)

• Reflection over y-axis: T(x, y) = (-x, y)

• Reflection over line y = x: T(x, y) = (y, x)

Rotations - Turning Around a Circle

A rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation. You can rotate your object at any degree measure, but 90° and 180° are two of the most common. Also, rotations are done counterclockwise!

The figure shown at the right is a rotation of 90° rotated around the center of rotation. Notice that all of the colored lines are the same distance from the center or rotation than than are from the point. Also all the colored lines form 90° angles. That's what makes the rotation a rotation of 90°.

More transformation geometry in the coordinate plane...

• Rotation 180° around the origin: T(x, y) = (-x, -y)

Chapter 3 Questions

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