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Unknown Important Concept ‘An unknown is a quantity whose value has not been determined’
4.1.1Example Exercise
1. Azmi bought some durians
Solution:
The unknown is the number of durian.
1.
2.
3.
4.
5.
There were a lot of people in the fun fair.Solution:
Mr.Tan lost a large amount of money when he dropped his walletSolution:
A number of students are studying in the library.Solution:
My father bought a few kilograms of rambutans yesterday.Solution:
Ketty gained a few kilograms of weight during the holidaysSolution:
Algebraic term identifying algebraic terms with one unknown.
Important concept: ‘An algebraic term with one unknown is the product of a number and an unknown’
4.1.2EXAMPLE EXERCISE
is the multiplication of the number 6 with the unknown
1.
2.
Determine the algebraic term with one unknown for each of the following.3eSolution:
-5tSolution:
Algebraic Expressions 1
CHAPTER 4 4.1 ALGEBRAIC EXPRESSION I, II, III
EXERCISE EXERCISE
3. 0.8tSolution:
4. 80wSolution
Identify Coefficients in given algebraic term Important concept: ‘ the number is known as the coefficient of the unknown’
4.1.3EXAMPLE EXERCISE
1.
2.
3.
: 6 is the coefficient of
: -3 is the coefficient of
: is the coefficient of
because
: is the coefficient of
1.
2.
3.
4.
5.
Solution:
Solution:
Solution:
Solution:
Solution:
Identify Like Algebraic Term and Unlike algebraic Term. Important concept: Like term : are term have that same unknowns Unlike term : are term that have different unknowns
4.1.4EXAMPLE EXERCISE
Like Term:
and same
and unknowns
and
Unlike Term :
1.
2.
3.
4.
Determine the term in each of the following pairs of term given below like terms or unlike terms.
Solution:
Solution:
Solution:
Algebraic Expressions 2
and different
and unknowns
and
5.
Solution:
Solution:
Algebraic ExpressionsImportant concept: group all the like terms together add/subtract the coefficient of the terms leave the terms as your answer
4.1.5EXAMPLE EXERCISE
1.
2.
3.
4.
1.
2.
3.
4.
Simplify the following algebraic expressions.
EXERCISE EXERCISE
5. 6.
An algebraic term in two or more unknowns is a product of two or more
unknowns and a number.4.1.6
Algebraic Expressions 3
EXAMPLE EXERCISE
1.
= The coefficient of is 5 = The coefficient of is = The coefficient of is
1.
2.
3.
4.
Write the unknowns in the following algebraic terms.
Solution:
Solution :
Solution:
5tSolution:
Finding the product of two algebraic terms.4.1.7
EXAMPLE EXERCISE
1.
2.
1.
2.
3.
4.
Solution:
Solution:
Solution:
Solution:
Algebraic Expressions 4
3.
4.
5.
6.
Solution:
Solution:
EXERCISE EXERCISE
7.
9.
Solution:
Solution:
8.
10.
Solution:
Solution:
Expanding single brackets and two brackets.4.1.8
EXAMPLE EXERCISE
Algebraic Expressions 5
1.
2.
3.
4.
Expanding single brackets 1.
2.
3.
4.
EXERCISE EXERCISE5.
7.
6
8.
EXAMPLE EXERCISE
Algebraic Expressions 6
1.
2.
Expanding two brackets; 9.
10.
11.
12.
EXERCISE EXERCISE13.
15.
14.
16.
EXAMPLE EXERCISE
3.17.
Algebraic Expressions 7
4.18.
19.
20.
:
)6( 2
Solution
qp
Factorising Algebraic Expressions.4.1.9
EXAMPLE EXERCISE
Algebraic Expressions 8
1.
2.
3.
4.
5.
6.
1.
2.
3.
4.
5.
6.
EXAMPLE EXERCISE
Algebraic Expressions 9
7.
8.
7.
8.
9.
Questions based on examination format
Algebraic Expressions 10
4. Factorize
Algebraic Expressions 11
15. The length of a football field (4h-3) m and its width is (3h +2) m. The perimeter of the field, in m, is
16.If and , find the value of
17.Find the value of when and
18.Tickets to a circus for child is RM and for an adult is RM . The total price of tickets for 10 children and 2 adults, in RM, is
19.The value of when and
is
Algebraic Expressions 12
PAST YEAR SPM QUESTIONS.
November 20031.
A. C. B. D.
November 20042.
A. C. B. D.
November 2005
3. A. C. B. D.
Jun 2006
4. (y + x)(2y - x) =A. 2y2 - xy + x2 C. 2y2 + xy - x2
B. 2y2 - xy - x2 D. 2y2 + xy - x2
November 20065. 3x2 - x(1 - x) =
A. 2x2 - 1 C. 4x2 - 1B. 2x2 - x D. 4x2 - x
Jun 2007
6. (x – y) (5x + 3y) – x(x – y) = A. 4x2 –xy -3y2 C. 4x2 –xy + 3y2
B. 4x2 -3xy – 3y2 D. 4x2 -3xy + 3y2
November 2007
7. (2x –y)2 – x ( x – y) =
Algebraic Expressions 13
A.3x2 - 3xy + y2 C. 3x2 + xy –y2
B. 3x2 - 5xy + y2 D. 3x2 - 5xy –y2
November 2008
8. 5pq – 2( 1 – pq) =A. 3pq - 2 C. 6pq - 2B. 4pq - 2 D. 7pq - 2
ANSWERS
Chapter 4 Algebraic Expressions
Algebraic Expressions 14
4.1.1 1. ‘a lot of people’ 2. ‘a large amount of money’ 3. ‘a number of students’ 4. ‘a few kilograms of rambutans 5. ‘a few kilograms’4.1.2 1.e 2.t 3.t 4.w 4.1.3 1. 8 2. 0.65 3.-13
4.
5. -1
4.1.4 1.unlike terms 2.like terms 3.unlike terms 4.like terms 5. like terms
4.1.5 1.-3y 2. -7n 3. -4w-9x 4. -4k-3 5. 10v-d 6. -3u-15
4.1.6 1.a and b 2. p and q 3. x, y and z 4. t4.1.7 1. 2. 3. 4. 5. 6. 7. 8.
Algebraic Expressions 15
9.
10.
4.1.8
4.19
Algebraic Expressions 16
Examination Format Questions1. C 11. C2. B 12. C3. D 13 D4. A 14. B5. D 15 D6. C 16 A7. D 17 D8. A 18 B9. A 19 C10. C 20 B
SPM Past year questions. 1. A 2. B 3. B 4. C 5. D 6. A 7. A 8. D
Algebraic Expressions 17
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