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

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Tingkatan 4 Matematik

bab 1
bab 2
bab 3

Tingkatan 5 Matematik

bab 2

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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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Tingkatan 1-4 keseluruhan dan bab 1 Ting 5

graphs of functions

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Simple exersice



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Number base

Exercise:

1 Express 23₁₀ as a number in base 2.

Ungkapkan 23₁₀ sebagai satu nombor dalam asas 2.

A 10000₂

B 10011₂

C 10111₂

D 11111₂

2 What is the value of 6, in base ten, in the number 6 145₅?

Apakah nilai digit 6 dalam nombor 6 145₅, dalam asas sepuluh?

A 5

B 125

C 750

D 6 000

3 Which of the following is true?

Antara yang berikut, manakah benar?

A 10₂ +1₂ = 110₂

B 111₂ – 10₂ = 10₂

C 100₂ + 11₂ = 110₂

D 100₂ – 1₂ = 11₂

4 What is the value of 2⁴ + 2 + 2⁵, as a number in base two?

Apakah nilai bagi 2⁴ + 2 + 2⁵, sebagai satu nombor dalam asas dua?

A 110010₂

B 101010₂

C 110000₂

D 101100₂

5 Express 5 × 2² + 2 × 2³ + 2⁵ as a number in base two.

Ungkapkan 5 × 2² + 2 × 2³ + 2⁵ sebagai satu nombor dalam asas dua.

A 1000000₂

B 1000100₂

C 1001000₂

D 1100000₂

6 Express 4⁴ + 8 as a number in base five.

Ungkapkan 4⁴ + 8 sebagai satu nombor asas lima.

A 264₅

B 2020₅

C 2011₅

D 2024₅

7 2(8³) + 8² + 16 =

A 1024₈

B 1104₈

C 2120₈

D 2220₈

8 11111₂ + 111010₂ =

A 1000110

B 1011001

C 1111001

D 1111110

9 Given 64₈ = 2^f + 2^g + 2^h, find the value of f + g + h.

Diberi 64₈ = 2^f + 2^g + 2^h, cari nilai f + g + h.

A 4

B 5

C 9

D 11

10 Given y₂ = 100₅ + 111₂, find the value of y.

Diberi bahawa y₂ = 100₅ + 111₂, cari nilai y.

A 10001₂

B 10010₂

C 11001₂

D 100000₂

11 Given 10111₂ < k <>2, find the value of k as a number in base 8.

Diberi 10111₂ <>2, cari nilai k sebagai satu nombor dalam asas 8.

A 27₈

B 30₈

C 31₈

D 32₈

1 Express 2⁷ + 2(2³) + 2 + 1 as a number in

Ungkapan 2⁷ + 2(2³) + 2 + 1 sebagai satu nombor dalam

(a) base 2,

asas 2,

(b) base 5.

asas 5.

[6 marks / 6 markah]

2 (a) Express 11111110₂ as a number in base 8.

Ungkapkan 1111110₂ sebagai satu nombor dalam asas 8.

(b) Express 4331₅ as a number in base 8.

Ungkapkan 4331₅ sebagai satu nombor dalam asas 8.

[7 marks / 7 markah]

3 (a) Given that 375₈ = m(8²) + 2n + 5(8⁰), what is the value of m and of n?

Diberi 375₈ = m(8²) + 2n + 5(8⁰), apakah nilai m dan n?

(b) Express 3411₅ in expanded notation.

Ungkapan 3411₅ dalam bentuk cerakin.

[3 marks / 3 markah]

4 (a) Given y₂ = 10111₂ + 111₂, what is the value of y?

Diberi y₂ = 10111₂ + 111₂, apakah nilai y?

(b) Given x₂ = 311₅, what is the value of x?

Diberi x₂ = 311₅, apakah nilai x?

[3 marks / 3 markah]

5 Given p – 1100₂ = 10001₂ and p = 101₂ + q, what is the value of p and of q in base 8?

Diberi p – 1100₂ = 10001₂ dan p = 101₂ + q, apakah nilai p dan q dalam asas 8? [4 marks / 4 markah]

answer

1 (a) 10010011₂

(b) 1042₅

2 (a) 772₈

(b) 1117₈

3 (a) m = 3; n = 28

(b) 3 × 5³ + 4 × 5² + 1 × 5 + 1 × 5⁰

4 (a) 11110₂

(b) 1010001

5 p = 35₈; q = 30₈

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