YEARLY PLAN 2007
MATHEMATICS FORM 4
NO TOPIC WEEKS LEARNING OBJECRTIVES LEARNING OUTCOME
1 STANDARD FORM 2 Students will be taught to:
(i) understand and use the concept of significant figure;
1 (ii) understand and use the concept of standard form to solve problems Students will be able to:
(ii) round off positive numbers to a given number of significant figures when the numbers are:
a) greater than 1;
b) less than 1;
(iii) perform operations of addition, subtraction, multiplication and division, involving a few numbers and state the answer in specific significant figures;
(iv) solve problems involving significant figures;
(i) state positive numbers in standard form when the numbers are:
a) greater than or equal to 10;
b) less than 1;
(ii) convert numbers in standard form to single numbers;
(iii) perform operations of addition, subtraction, multiplication and division, involving any two numbers and state the answers in standard form;
(iv) solve problems involving numbers in standard form.
2 QUADRATIC EXPRESSIONS AND EQUATION 3 2.1 understand the concept of quadratic expression; Students will be able to:
(i) identify quadratic expressions;
(ii) form quadratic expressions by multiplying any two linear expressions;
(iii) form quadratic expressions based on specific situations;
2.2 factorise quadratic expression; (i) factorise quadratic expressions of the form , where b = 0 or c = 0;
factorise quadratic expressions of the form px2 q, p and q are perfect squares;
(ii) factorise quadratic expressions of the form , where a, b and c not equal to zero;
(iii) factorise quadratic expressions containing coefficients with common factors;
(iv)
2.3 understand the concept of quadratic equation; (i) Identify quadratic equations with one unknown;
(ii) write quadratic equations in general form i.e.
;
(iii) form quadratic equations based on specific situations;
2.4 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;
(ii) determine the solutions for quadratic equations by:
b) trial and error method;
c) factorisation;
(iii) solve problems involving quadratic equations.
3 SETS 3 3.1 Students will be taught to:
understand the concept of set; Students will be able to:
(i) sort given objects into groups;
(ii) define sets by:
a) descriptions;
b) using set notation;
(iv) identify whether a given object is an element of a set and use the symbol or ;
(v) represent sets by using Venn diagrams;
(vi) list the elements and state the number of elements of a set;
(vii) determine whether a set is an empty set;
(viii) determine whether two sets are equal;
3.2 understand and use the concept of subset, universal set and the complement of a set; (i) determine whether a given set is a subset of a specific set and use the symbol or ;
(ii) represent subset using Venn diagram;
(iii) list the subsets for a specific set;
(iv) illustrate the relationship between set and universal set using Venn diagram;
(v) determine the complement of a given set;
(vi) determine the relationship between set, subset, universal set and the complement of a set;
a) 3.3 perform operations on sets:
• the intersection of sets;
the union of sets. (vii) determine the intersection of:
a) two sets;
b) three sets;
and use the symbol ;
(viii) represent the intersection of sets using Venn diagram;
(ix) state the relationship between
a) A B and A ;
b) A B and B ;
(x) determine the complement of the intersection of sets;
(xi) solve problems involving the intersection of sets;
(xii) determine the union of:
a) two sets;
b) three sets;
and use the symbol ;
(xiii) represent the union of sets using Venn diagram;
(xiv) state the relationship between
a) A B and A ;
b) A B and B ;
(xv) determine the complement of the union of sets;
(xvi) solve problems involving the union of sets;
4 MATHEMATICAL REASONING 3 Students will be taught to:
4.1 understand the concept of statement;
Students will be able to:
(i) determine whether a given sentence is a statement;
(ii) determine whether a given statement is true or false;
(iii) construct true or false statement using given numbers and mathematical symbols.
4.2 understand the concept of quantifiers “all” and “some”; (i) construct statements using the quantifier:
all;some;
(ii) determine whether a statement that contains the quantifier “all” is true or false;
(iii) determine whether a statement can be eneralized to cover all cases by using the quantifier “all”;
(iv) construct a true statement using the quantifier “all” or “some”, given an object and a property.
4.3 perform operations involving the words “not” or “no”, “and” and “or” on statements; (i) change the truth value of a given statement by placing the word “not” into the original statement;
(ii) identify two statements from a compound statement that contains the word “and”;
(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” ;
(v) form a compound statement by combining two given statements using the word “or”;
(xvii) determine the truth value of a compound statement which is the combination of two statements with the word “and”;
(xviii) determine the truth value of a compound statement which is the combination of two statements with the word “or”.
4.4 understand the concept of implication; (i) identify the antecedent and consequent of an implication “if p, then q”;
(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;
determine whether the converse of an implication is true or false.
4.5 understand the concept of argument; (i) identify the premise and conclusion of a given simple argument;
(ii) make a conclusion based on two given premises for:
a) Argument Form I;
b) Argument Form II;
c) Argument Form III;
(iii) complete an argument given a premise and the conclusion.
4.6 understand and use the concept of deduction and induction to solve problems. (i) determine whether a conclusion is made through:
a) reasoning by deduction;
b) reasoning by induction;
(ii) make a conclusion for a specific case based on a given general statement, by deduction;
(iv) make a generalization based on the pattern of a numerical sequence, by induction;
(iv) use deduction and induction in problem solving.
5 THE STRAIGHT LINE 3 Students will be taught to:
5.1 understand the concept of gradient of a straight line; (i)determine the vertical and horizontal distances between two given points on a straight line.
(ii) determine the ratio of vertical distance to horizontal distance.
5.2 understand the concept of gradient of a straight line in Cartesian coordinates; (i) derive the formula for the gradient of a straight line;
(ii) calculate the gradient of a straight line passing through two points;
(iii) determine the relationship between the value of the gradient and the:
a) steepness,
b) direction of inclination, of a straight line;
5.3 understand the concept of intercept; (i) determine the x-intercept and the y-intercept of a straight line;
(ii)derive the formula for the gradient of a straight line in terms of the x-intercept and the y-intercept;
(iii) perform calculations involving gradient, x-intercept and y-intercept;
c) 5.4 understand and use equation of a straight line;
(i) draw the graph given an equation of the form
y = mx + c ;
(ii) determine whether a given point lies on a specific straight line;
(iii) write the equation of the straight line given the gradient and y-intercept;
(iv) determine the gradient and y-intercept of the straight line which equation is of the form:
d) y = mx + c;
e) ax + by = c;
(v) find the equation of the straight line which:
a) is parallel to the x-axis;
b) is parallel to the y-axis;
c) passes through a given point and has a specific gradient;
d) passes through two given points;
(vi) find the point of intersection of two straight lines by:
e) drawing the two straight lines;
f) solving simultaneous equations.
5.5 understand and use the concept of parallel lines. (vi) verify that two parallel lines have the same gradient and vice versa;
(vii) determine from the given equations whether two straight lines are parallel;
(viii) find the equation of the straight line which passes through a given point and is parallel to another straight line;
(ix) solve problems involving equations of straight lines.
6 STATISTICS 4 Students will be taught to:
6.1 understand the concept of class interval; (i) complete the class interval for a set of data given one of the class intervals;
(ii) determine:
a) the upper limit and lower limit;
b) the upper boundary and lower boundary
of a class in a grouped data;
(iii) calculate the size of a class interval;
(iv) determine the class interval, given a set of data and the number of classes;
(v) determine a suitable class interval for a given set of data;
(vi) construct a frequency table for a given set of data.
6.2 understand and use the concept of mode and mean of grouped data; (i) determine the modal class from the frequency table of grouped data;
(ii) calculate the midpoint of a class;
(iii) verify the formula for the mean of grouped data;
(iv) calculate the mean from the frequency table of grouped data;
(v) discuss the effect of the size of class interval on the accuracy of the mean for a specific set of grouped data..
6.3 represent and interpret data in histograms with class intervals of the same size to solve problems; (i) draw a histogram based on the frequency table of a grouped data;
(ii) interpret information from a given histogram;
(iii) olve problems involving histograms
6.4 represent and interpret data in frequency polygons to solve problems. (i) draw the frequency polygon based on:
a) a histogram;
b) a frequency table;
(ii) interpret information from a given frequency polygon;
(iii) solve problems involving frequency polygon
6.5 understand the concept of cumulative frequency; (i) construct the cumulative frequency table for:
a) ungrouped data;
b) grouped data;
(ii) draw the ogive for:
a) ungrouped data;
b) grouped data;
6.6 understand and use the concept of measures of dispersion to solve problems. (i) determine the range of a set of data.
(ii) determine:
a) the median;
b) the first quartile;
c) the third quartile;
d) the interquartile range;
from the ogive.
(iii) interpret information from an ogive;
(iv) solve problems involving data representations and measures of dispersion.
7 PROBABILITY 1 2 Students will be taught to:
7.1 understand the concept of sample space; Students will be able to:
(v) determine whether an outcome is a possible outcome of an experiment;
(ii) list all the possible outcomes of an experiment:
a) from activities;
b) by reasoning;
(iii) determine the sample space of an experiment;
(iv) write the sample space by using set notations.
7.2 understand the concept of events. (i) identify the elements of a sample space which satisfy given conditions;
(ii) list all the elements of a sample space which satisfy certain conditions using set notations;
(iii) determine whether an event is possible for a sample space.
7.3 understand and use the concept of probability of an event to solve problems (i) find the ratio of the number of times an event occurs to the number of trials;
(ii) find the probability of an event from a big enough number of trials;
(iii) calculate the expected number of times an event will occur, given the probability of the event and number of trials;
(iv) solve problems involving probability;
(v) predict the occurrence of an outcome and make a decision based on known information.
8 CIRCLE III 2 Students will be taught to:
8.1 understand and use the concept of tangents to a circle. Students will be able to:
(i) identify tangents to a circle;
(ii) make inference that the tangent to a circle is a straight line perpendicular to the radius that passes through the contact point;
(iii) construct the tangent to a circle passing through a point:
a) on the circumference of the circle;
b) outside the circle;
(iv) determine the properties related to two tangents to a circle from a given point outside the circle;
(v) solve problems involving tangents to a circle
8.2 understand and use the properties of angle between tangent and chord to solve problems. (i) identify the angle in the alternate segment which is subtended by the chord through the contact point of the tangent;
(ii) verify the relationship between the angle formed by the tangent and the chord with the angle in the alternate segment which is subtended by the chord;
(iii) perform calculations involving the angle in alternate segment;
solve problems involving tangent to a circle and angle in alternate segment.
8.3 understand and use the properties of common tangents to solve problems. (i) determine the number of common tangents which can be drawn to two circles which:
a) intersect at two points;
b) intersect only at one point;
c) do not intersect;
(ii) determine the properties related to the common tangent to two circles which:
d) intersect at two points;
e) intersect only at one point;
f) do not intersect;
(iv) solve problems involving common tangents to two circles;
(v) solve problems involving tangents and common tangents.
9 TRIGONOMETRY II 3 Students will be taught to:
9.1 understand and use the concept of the values of sin , cos and tan (0 360) to solve problems. Students will be able to:
(i) identify the quadrants and angles in the unit circle;
(ii) determine:
(iii) the value of y-coordinate;
a) the value of x-coordinate;
b) the ratio of y-coordinate to x-coordinate;
of several points on the circumference of the unit circle;
(iii) verify that, for an angle in quadrant I of the unit circle :
a) sin = y-coordinate ;
b) cos = x-coordinate;
c) ;
(iv) determine the values of
a) sine;
b) cosine;
c) tangent;
of an angle in quadrant I of the unit circle;
(v) determine the values of
a) sin ;
b) cos ;
c) tan ;
for 90 360;
(vi) determine whether the values of:
a) sine;
b) cosine;
c) tangent,
of an angle in a specific quadrant is positive or negative;
(vii) determine the values of sine, cosine and tangent for special angles;
(viii) determine the values of the angles in quadrant I which correspond to the values of the angles in other quadrants;
(ix) state the relationships between the values of:
a) sine;
b) cosine; and
c) tangent;
of angles in quadrant II, III and IV with their respective values of the corresponding angle in quadrant I;
(x) find the values of sine, cosine and tangent of the angles between 90 and 360;
(xi) find the angles between 0 and 360, given the values of sine, cosine or tangent;
(xii) solve problems involving sine, cosine and tangent.
9.2 draw and use the graphs of sine, cosine and tangent. (i) draw the graphs of sine, cosine and tangent for angles between 0 and 360;
(ii) compare the graphs of sine, cosine and tangent for angles between 0 and 360;
(xiii) solve problems involving graphs of sine, cosine and tangent.
10 ANGLE OF ELEVATION AND DEPRESSION 2 Students will be taught to:
10.1 understand and use the concept of angle of elevation and angle of depression to solve problems. Students will be able to:
(i) identify:
a) the horizontal line;
b) the angle of elevation;
c) the angle of depression,
for a particular situation;
(ii) Represent a particular situation involving:
d) the angle of elevation;
e) the angle of depression, using diagrams;
(iii) Solve problems involving the angle of elevation and the angle of depression.
11 LINES AND PLANES IN
3-DIMENSIONS 3 11.1 Understand and use the concept of angle between lines and planes to solve Students will be able to:
(i) identify planes;
(ii) identify horizontal planes, vertical planes and inclined planes;
(iii) sketch a three dimensional shape and identify the specific planes;
(iv) identify:
a) lines that lies on a plane;
b) lines that intersect with a plane;
(v) identify normals to a given plane;
(vi) determine the orthogonal projection of a line on a plane;
(vii) draw and name the orthogonal projection of a line on a plane;
(viii) determine the angle between a line and a plane;
(ix) solve problems involving the angle between a line and a plane.
11.2 understand and use the concept of angle between two planes to solve problems. (i) identify the line of intersection between two planes;
(ii) draw a line on each plane which is perpendicular to the line of intersection of the two planes at a point on the line of intersection;
(iii) determine the angle between two planes on a model and a given diagram;
(iv) solve problems involving lines and planes in 3-dimensional shapes.
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