Scheme of Work Mathematics 2013
Form Four
Standard Form
WEEK / LEARNING OBJECTIVES / SUGGESTED TEACHING AND LEARNING ACTIVITIES / LEARNING OUTCOME / POINTS TO NOTE / VOCABULARY
Students will be taught to: / 1 / Students will be able to:
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2.1.13 – 4.1.13 / Orientation week
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07.1.13 – 11.1.13 / a) understand and use the concept of significant figure; / Discuss the significance of zero in a number. / (ii) round off positive numbers to a given number of significant figures when the numbers are:
a) greater than 1;
b) less than 1; / Rounded numbers are only approximates.
Limit to positive numbers only. / significance
significant figure
relevant
round off
accuracy
Discuss the use of significant figures in everyday life and other areas. / (iii) perform operations of addition, subtraction, multiplication and division, involving a few numbers and state the answer in specific significant figures; / Generally, rounding is done on the final answer.
(iv) solve problems involving significant figures;
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14.1. 13 – 18.1. 13 / a) understand and use the concept of standard form to solve problems. / Use everyday life situations such as in health, technology, industry, construction and business involving numbers in standard form.
Use the scientific calculator to explore numbers in standard form. / (v) state positive numbers in standard form when the numbers are:
a) greater than or equal to 10;
b) less than 1; / Another term for standard form is scientific notation. / standard form
single number
scientific notation
(vi) convert numbers in standard form to single numbers;
(vii) perform operations of addition, subtraction, multiplication and division, involving any two numbers and state the answers in standard form; / Include two numbers in standard form.
(viii) solve problems involving numbers in standard form.
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QUADRATIC EXPRESSIONS AND EQUATIONS / Form 4
LEARNING OBJECTIVES / SUGGESTED TEACHING AND LEARNING ACTIVITIES / LEARNING OUTCOME / POINTS TO NOTE / VOCABULARY
Students will be taught to: / 2 / Students will be able to:
4
21.1. 13 – 25.1. 13 / a) understand the concept of quadratic expression; / Discuss the characteristics of quadratic expressions of the form, where a, b and c are constants, a ¹ 0 and x is an unknown. / (i) identify quadratic expressions; / Include the case when b = 0 and/or c=0. / quadratic expression
constant
constant factor
(ii) form quadratic expressions by multiplying any two linear expressions; / Emphasise that for the terms x2 and x, the coefficients are understood to be 1. / unknown
highest power
expand
(iii) form quadratic expressions based on specific situations; / Include everyday life situations. / coefficient
term
a) factorise quadratic expression; / Discuss the various methods to obtain the desired product. / (i) factorise quadratic expressions of the form , where b = 0 or c = 0; / factorise
common factor
(ii) factorise quadratic expressions of the form px2 - q, p and q are perfect squares; / 1 is also a perfect square. / perfect square
Begin with the case a = 1.
Explore the use of graphing calculator to factorise quadratic expressions. / (iii) factorise quadratic expressions of the form , where a, b and c not equal to zero; / Factorisation methods that can be used are:
· cross method;
· inspection. / cross method
inspection
common factor
complete factorisation
(iv) factorise quadratic expressions containing coefficients with common factors;
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28.1. 13 – 29.1.13 / a) understand the concept of quadratic equation; / Discuss the characteristics of quadratic equations. / (v) identify quadratic equations with one unknown; / quadratic equation
general form
(vi) write quadratic equations in general form i.e.
;
(vii) form quadratic equations based on specific situations; / Include everyday life situations.
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30.1.13 – 1.2.13
6
4.2.13 – 8.2.13 / PRA USBF 1
a) understand and use the concept of roots of quadratic equations to solve problems. / (i) determine whether a given value is a root of a specific quadratic equation; / substitute
root
Discuss the number of roots of a quadratic equation. / (ii) determine the solutions for quadratic equations by:
a) trial and error method;
b) factorisation; / There are quadratic equations that cannot be solved by factorisation. / trial and error method
Use everyday life situations. / (iii) solve problems involving quadratic equations. / Check the rationality of the solution. / Solution
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SETS / Form 4
LEARNING OBJECTIVES / SUGGESTED TEACHING AND LEARNING ACTIVITIES / LEARNING OUTCOME / POINTS TO NOTE / VOCABULARY
Students will be taught to: / 3 / Students will be able to:
7
11.2. 13 – 15.2. 13 / a) understand the concept of set; / Use everyday life examples to introduce the concept of set. / (i) sort given objects into groups; / The word set refers to any collection or group of objects. / set
element
(ii) define sets by:
a) descriptions;
b) using set notation; / The notation used for sets is braces, { }.
The same elements in a set need not be repeated.
Sets are usually denoted by capital letters.
The definition of sets has to be clear and precise so that the elements can be identified. / description
label
set notation
denote
(iii) identify whether a given object is an element of a set and use the symbol Î or Ï; / The symbol Î (epsilon) is read “is an element of” or “is a member of”.
The symbol Ï is read “is not an element of” or “is not a member of”.
Discuss the difference between the representation of elements and the number of elements in Venn diagrams. / (iv) represent sets by using Venn diagrams; / Venn diagram
empty set
Discuss why { 0 } and { Æ } are not empty sets. / (v) list the elements and state the number of elements of a set; / The notation n(A) denotes the number of elements in set A. / equal sets
(vi) determine whether a set is an empty set; / The symbol Æ (phi) or { } denotes an empty set.
(vii) determine whether two sets are equal; / An empty set is also called a null set.
a) understand and use the concept of subset, universal set and the complement of a set; / Begin with everyday life situations. / (i) determine whether a given set is a subset of a specific set and use the symbol Ì or Ë ; / An empty set is a subset of any set.
Every set is a subset of itself. / Subset
(ii) represent subset using Venn diagram;
(iii) list the subsets for a specific set;
Discuss the relationship between sets and universal sets. / (iv) illustrate the relationship between set and universal set using Venn diagram; / The symbol x denotes a universal set. / universal set
(v) determine the complement of a given set; / The symbol A¢ denotes the complement of set A. / complement of a set
(vi) determine the relationship between set, subset, universal set and the complement of a set; / Include everyday life situations.
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18.2.13 – 22.2.13 / a) perform operations on sets:
· the intersection of sets;
· the union of sets. / (i) determine the intersection of:
a) two sets;
b) three sets;
and use the symbol Ç ; / Include everyday life situations. / intersection
common elements
Discuss cases when:
· A Ç B = Æ
· A Ì B / (ii) represent the intersection of sets using Venn diagram;
(iii) state the relationship between
a) A Ç B and A ;
b) A Ç B and B ;
(iv) determine the complement of the intersection of sets;
(v) solve problems involving the intersection of sets; / Include everyday life situations.
(vi) determine the union of:
a) two sets;
b) three sets;
and use the symbol È ;
(vii) represent the union of sets using Venn diagram;
(viii) state the relationship between
a) A È B and A ;
b) A È B and B ;
(ix) determine the complement of the union of sets;
(x) solve problems involving the union of sets; / Include everyday life situations.
(xi) determine the outcome of combined operations on sets;
(xii) solve problems involving combined operations on sets. / Include everyday life situations.
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MATHEMATICAL REASONING / Form 4
LEARNING OBJECTIVES / SUGGESTED TEACHING AND LEARNING ACTIVITIES / LEARNING OUTCOME / POINTS TO NOTE / VOCABULARY
Students will be taught to: / 4 / Students will be able to:
9 / a) understand the concept of statement; / Introduce this topic using everyday life situations. / (i) determine whether a given sentence is a statement; / Statements consisting of: / statement
25.2.13 – 1.3.13 / Focus on mathematical sentences. / (ii) determine whether a given statement is true or false; / · words only, e.g. “Five is greater than two.”;
· numbers and words, e.g. “5 is greater than 2.”;
· numbers and symbols, e.g. 5 > 2. / true
false
mathematical sentence
mathematical statement
mathematical symbol
Discuss sentences consisting of:
· words only;
· numbers and words;
· numbers and mathematical symbols; / (iii) construct true or false statement using given numbers and mathematical symbols; / The following are not statements:
· “Is the place value of digit 9 in 1928 hundreds?”;
· 4n - 5m + 2s;
· “Add the two numbers.”;
· x + 2 = 8.
a) understand the concept of quantifiers “all” and “some”; / Start with everyday life situations. / (i) construct statements using the quantifier:
a) all;
b) some; / Quantifiers such as “every” and “any” can be introduced based on context. / quantifier
all
every
any
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4.3.13 / (ii) determine whether a statement that contains the quantifier “all” is true or false; / Examples:
· All squares are four sided figures.
· Every square is a four sided figure.
· Any square is a four sided figure. / some
several
one of
part of
(iii) determine whether a statement can be generalised to cover all cases by using the quantifier “all”; / Other quantifiers such as “several”, “one of” and “part of” can be used based on context.
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5.3.13 – 7.3.13 / USBF 1 / (iv) construct a true statement using the quantifier “all” or “some”, given an object and a property. / Example:
Object: Trapezium.
Property: Two sides are parallel to each other.
Statement: All trapeziums have two parallel sides.
Object: Even numbers.
Property: Divisible by 4.
Statement: Some even numbers are divisible by 4. / negate
contrary
object
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11.3.13 – 15.3.13 / a) perform operations involving the words “not” or “no”, “and” and “or” on statements; / Begin with everyday life situations. / (i) change the truth value of a given statement by placing the word “not” into the original statement; / The negation “no” can be used where appropriate.
The symbol “~” (tilde) denotes negation.
“~p” denotes negation of p which means “not p” or “no p”.
The truth table for p and ~p are as follows:
p / ~p
True
False / False
True
/ negation
not p
no p
truth table
truth value
(ii) identify two statements from a compound statement that contains the word “and”; / The truth values for “p and q” are as follows:
p / q / p and q
True / True / True
True / False / False
False / True / False
False / False / False
/ and
compound statement
(iii) form a compound statement by combining two given statements using the word “and”;
(iv) identify two statement from a compound statement that contains the word “or” ; / The truth values for “p or q” are as follows: / Or
(v) form a compound statement by combining two given statements using the word “or”; / p / q / p or q
True / True / True
True / False / True
False / True / True
False / False / False
(vi) determine the truth value of a compound statement which is the combination of two statements with the word “and”;
(vii) determine the truth value of a compound statement which is the combination of two statements with the word “or”.
a) understand the concept of implication; / Start with everyday life situations. / (i) identify the antecedent and consequent of an implication “if p, then q”; / Implication “if p, then q” can be written as p Þ q, and “p if and only if q” can be written as p Û q, which means p Þ q and q Þ p. / implication
antecedent
consequent
(ii) write two implications from a compound statement containing “if and only if”;
(iii) construct mathematical statements in the form of implication:
a) If p, then q;
b) p if and only if q;
(iv) determine the converse of a given implication; / The converse of an implication is not necessarily true. / Converse
(v) determine whether the converse of an implication is true or false. / Example 1:
If x < 3, then
x < 5 (true).
Conversely:
If x < 5, then
x < 3 (false).
Example 2:
If PQR is a triangle, then the sum of the interior angles of PQR is 180°.
(true)
Conversely:
If the sum of the interior angles of PQR is 180°, then PQR is a triangle.
(true)
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18.3.13 – 22.3.13 / a) understand the concept of argument; / Start with everyday life situations. / (i) identify the premise and conclusion of a given simple argument; / Limit to arguments with true premises. / argument
premise
conclusion
(ii) make a conclusion based on two given premises for:
a) Argument Form I;
b) Argument Form II;
c) Argument Form III; / Names for argument forms, i.e. syllogism (Form I), modus ponens (Form II) and modus tollens (Form III), need not be introduced.
Encourage students to produce arguments based on previous knowledge. / (iii) complete an argument given a premise and the conclusion. / Specify that these three forms of arguments are deductions based on two premises only.
Argument Form I
Premise 1: All A are B.Premise 2: C is A.
Conclusion: C is B.
Argument Form II:
Premise 1: If p, then q.
Premise 2: p is true.
Conclusion: q is true.
Argument Form III:
Premise 1: If p, then q.
Premise 2: Not q is true.
Conclusion: Not p is true.
a) understand and use the concept of deduction and induction to solve problems. / Use specific examples/activities to introduce the concept. / (i) determine whether a conclusion is made through:
a) reasoning by deduction;
b) reasoning by induction; / reasoning
deduction
induction
pattern
(ii) make a conclusion for a specific case based on a given general statement, by deduction; / special conclusion
general statement
general conclusion
(iii) make a generalization based on the pattern of a numerical sequence, by induction; / Limit to cases where formulae can be induced. / specific case
numerical sequence
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23.3.13 – 31.3.13 / CUTI PERTENGAHAN PENGGAL 1 / (iv) use deduction and induction in problem solving. / Specify that:
· making conclusion by deduction is definite;
· making conclusion by induction is not necessarily definite.
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