Here are some 2012 trial SPM papers from Pinang, Perak for you to challenge your mathematics skill.
SPM Perak
SPM Pulau Pinang
Sunday, March 31, 2013
Thursday, March 21, 2013
Wednesday, March 20, 2013
Tuesday, March 19, 2013
Form 1 Chapter 4, 5 and 6
Form 1
Chapter 4: Decimals
The decimal numeral system (also called base ten or occasionally denary) has ten as its base. It is the numerical base most widely used by modern civilizations.
Decimal notation often refers to a base-10 positional notation such as the Hindu-Arabic numeral system; however, it can also be used more generally to refer to non-positional systems such as Roman or Chinese numerals which are also based on powers of ten.
Decimals also refer to decimal fractions, either separately or in contrast to vulgar fractions. In this context, a decimal is a tenth part, and decimals become a series of nested tenths. There was a notation in use like 'tenth-metre', meaning the tenth decimal of the metre, currently an Angstrom. The contrast here is between decimals and vulgar fractions, and decimal divisions and other divisions of measures, like the inch. It is possible to follow a decimal expansion with a vulgar fraction; this is done with the recent divisions of the troy ounce, which has three places of decimals, followed by a trinary place.
GUYS!! INCASE YOU'RE WONDERING, HERE'S AN EXAMPLE OF
WHAT A DECIMAL IS......
Chapter 5:Percentage
In mathematics, a percentage is a number or ratio as a fraction of 100. It is often denoted using the percent sign, “%”, or the abbreviation “pct.”
For example, 45% (read as “forty-five percent”) is equal to 45/100, or 0.45. A related system which expresses a number as a fraction of 1000 uses the terms "per mil" and "millage". Percentages are used to express how large/small one quantity is, relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity, which should be greater than zero. For example, an increase of $ 0.15 on a price of $ 2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is therefore a 6% increase. The word 'percent' means 'out of 100' or 'per 100'.
Although percentages are usually used to express numbers between zero and one, any ratio can be expressed as a percentage. For instance, 111% is 1.11 and −0.35% is −0.0035. Although this is technically inaccurate as per the definition of percent, an alternative wording in terms of a change in an observed value is “an increase/decrease by a factor of...””
Here's the symbol of percentage
Chapter 6: Integers
An integer is a number that can be written without a fractional or decimal component. For example, 21, 4, and −2048 are integers; 9.75, 5½, and √2 are not integers. The set of integers is a subset of the real numbers, and consists of the natural numbers (0, 1, 2, 3, ...) and the negatives of the non-zero natural numbers (−1, −2, −3, ...).
The name derives from the Latin integer (meaning literally "untouched," hence "whole": the word entire comes from the same origin, but via French[1]). The set of all integers is often denoted by a boldface Z (or blackboard bold
, Unicode U+2124 ℤ), which stands for Zahlen (German for numbers, pronounced [ˈtsaːlən]).[2]The integers (with addition as operation) form the smallest group containing the additive monoid of the natural numbers. Like the natural numbers, the integers form acountably infinite set. In algebraic number theory, these commonly understood integers, embedded in the field of rational numbers, are referred to as rational integers to distinguish them from the more broadly defined algebraic integers.
Symbol often used to denote a set of integers is....
-Anna G
Form 4 Chapter 4
Form 4 Notes
Chapter 4 : Mathematical Reasoning
1) A statement is a sentence that is either true or false but not both.
2) Quantifier denotes the number of objects or cases involved in statement.
3) 'All' refers to each and every object or cases.
4) 'Some' refers to several and not every object and cases.
5) A statement in the form 'if p, then q' is known as an implication. p is the antecedent and q is the consequent.
6) An argument is a process of making a conclusion based on given statements. The given statements are called premises.
7) Deduction is a process of making a specific conclusion from a general statement.
8) Induction is a process of making a general conclusion from specific cases.
For more on Mathematical Reasoning, watch this interesting video by clicking the link below.
http://www.youtube.com/watch?v=NXzGjH2x1gQ
Done by. Suraya Azhar
Chapter 4 : Mathematical Reasoning
1) A statement is a sentence that is either true or false but not both.
2) Quantifier denotes the number of objects or cases involved in statement.
3) 'All' refers to each and every object or cases.
4) 'Some' refers to several and not every object and cases.
5) A statement in the form 'if p, then q' is known as an implication. p is the antecedent and q is the consequent.
6) An argument is a process of making a conclusion based on given statements. The given statements are called premises.
7) Deduction is a process of making a specific conclusion from a general statement.
8) Induction is a process of making a general conclusion from specific cases.
For more on Mathematical Reasoning, watch this interesting video by clicking the link below.
http://www.youtube.com/watch?v=NXzGjH2x1gQ
Done by. Suraya Azhar
Form 4 Chapter 2
Form 4 Notes
Chapter 2 Quadratic Expression and Equations
1) A quadratic expression is an expression of the form ax2 + bx + c = 0 where a, b and c are constants, a does not qual to 0 and x is an unknown.
2) A quadratic expression has only one unknown and the highest power of the unknown in the expression is 2.
3) Multiplying two linear expressions having the same unknown will form a quadratic expression.
Example; (x+5)(x-4)
= x2- 4x + 5x - 20
= x2 + x - 20
4) The process of writing a quadratic expression as a product of two linear expressions is known as factorisation.
For more on Quadratic Expression and Equations, click the link below.
http://www.youtube.com/watch?v=O6uoregIrX0
Done by, Suraya Azhar
Chapter 2 Quadratic Expression and Equations
1) A quadratic expression is an expression of the form ax2 + bx + c = 0 where a, b and c are constants, a does not qual to 0 and x is an unknown.
2) A quadratic expression has only one unknown and the highest power of the unknown in the expression is 2.
3) Multiplying two linear expressions having the same unknown will form a quadratic expression.
Example; (x+5)(x-4)
= x2- 4x + 5x - 20
= x2 + x - 20
4) The process of writing a quadratic expression as a product of two linear expressions is known as factorisation.
For more on Quadratic Expression and Equations, click the link below.
http://www.youtube.com/watch?v=O6uoregIrX0
Done by, Suraya Azhar
CHAPTER 11
Lines and planes in 3-dimensions
POINT-no dimension
LINE-one dimension
PLANES-flat surface,two dimension
SOLID-three dimension
.jpg)
.jpg)
done by:aishu
POINT-no dimension
LINE-one dimension
PLANES-flat surface,two dimension
SOLID-three dimension
done by:aishu
chapter 9
We obtain the following integral formulas by reversing the formulas for differentiation of trigonometric functionsthat we met earlier:
∫sin u du=−cos u+K
∫cos u du=sin u+K
∫sec2u du=tan u+K
∫csc2u du=−cot u+K
Integral of sec x, csc x
These are obtained by simply reversing the differentiation process.
Example 3: Integrate:∫sec u tan u du=sec u+K∫csc u cot u du=−csc u+K ∫csc 2x cot 2x dx
Integral of tan x, cot x
Now, if we want to find∫tanx dx , we note that
∫tanx dx=∫sinxcosxdx
Letu=cosx , thendu=−sinx dx . done by:aishu
∫tanx dx=∫sinxcosxdx=−∫duu=−ln|u|+K=−ln|cosx|+
Subscribe to:
Posts (Atom)