THE MALAY COLLEGE KUALA KANGSAR
EVALUATION FORM TO CHECK MASTERY OF SYLLABUS
SUBJECT:
MATHEMATICS
FORM: 4 Science ................
NAME : ___________________________________________
1. KNOW
2. HAS NOT MASTERED
3. MASTERED
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STANDARD FORM
1. Round off positive numbers to a given number of significant
figures when the numbers are :
a) greater than 1, b) less than 1
2.
Perform operations of addition, subtraction, multiplication
and division, involving a few numbers and state the answer in
specific significant figures;
3.
Solve problems involving significant figures.
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4.
are:
State positive numbers in standard form when the numbers
a) greater than or equal to 10;
b) less than 1;
5.
Convert numbers in standard form to
Single numbers;
6.
Perform operation of addition, subtraction, multiplication and
division, involving any two numbers and state the answers in
standard form;
7.
Solve problems involving numbers in standard form.
QUADRATIC EXPRESSIONS AND EQUATIONS
1.
2
Identify quadratic expressions
2.
Form quadratic expressions by multiplying any two linear
expressions
3.
Form quadratic expressions based on specific situations.
4.
Factorise quadratic expressions of the
where b = 0 or c = 0;
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form ax ² + bx + c,
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5.
Factorise quadratic expressions of the form px ² - q, p and q
are perfect squares;
6.
Factorise quadratic expressions of the form ax ² + bx + c,
where a, b and c not equal to zero;
7.
Factorise quadratic expressions containing coefficients with
common factors;
8.
Identify quadratic equations with one unknown;
9.
10.
Write quadratic equations in general form i.e ax ² + bx + c = 0
Form quadratic equations based on specific situations;
11.
Determine whether a given value is a root of a specific
quadratic equations;
12.
Determine the solutions for quadratic equations by:
a)
trial and error method;
b)
factorization;
13.
Solve problems involving quadratic equations.
SETS
1.
Sort given objects into groups;
2.
Define sets by:
a)descriptions;
b)using set notation
3.
Identify whether a given object is an element of a set and use
the symbol
or ;
4.
Represent sets by using Venn diagrams
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5.
List the elements and state the number of elements of a set;
6.
Determine whether a set is an empty set;
7.
Determine whether two sets are equal;
8.
Determine whether a given set is a subset of a specific set and
use the symbol or ;
9.
Represent subset using Venn diagram;
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10.
List the subsets for a specific set;
11. Illustrate the relationship between set and universal set using
Venn diagram;
12. Determine the complement of a given set;
13. Determine the relationship between set, subset, universal set and
the complement of a set:
14.
Determine the intersection of:
a) two sets
b) three sets;
and use the symbol
15.
Represent the intersection of sets using Venn diagram;
16. State the relationship between
a) A ∩ B and A; b) A ∩ B and B
17. Determine the complement of intersection of sets;
18.
Solve problems involving the intersection of sets;
19. Determine the union of: a) two sets;
b) three sets; and use the symbol U;
20. Represent the union of sets using Venn diagram;
21. State the relationship between
a) A U B and A; b) A U B and B
22. Determine the complement of the union of sets;
23.
Solve problems involving the union of sets;
24.
Determine the outcome of combined operations on sets;
25.
Solve problems involving combined operations on sets.
MATHEMATICAL REASONING
4
1.
Determine whether a given sentence is a statement;
2.
Determine whether a given statement is true or false;
3.
Construct true or false statement using given numbers and
mathematical symbols;
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4.
Construct statements using the quantifier:
a) all; b) some;
5.
Determine whether a statement that contains the quantifier
“all” is true or false;
6.
Determine whether a statement can be generalized to cover
all cases by using the quantifier “all”;
7.
Construct a true statement using quantifier “all” or “some”,
given an object and a property.
8.
Change the truth value of a given statement by placing the
word “not” into the original statement;
9.
Identify two statements from a compound statement that
contains the word “and”
10.
Form a compound statement by combining two given
statements using the word “and”
11.
Identify two statement from a compound statement that
contains the word “or”;
12.
Form a compound statement by combining two given
statements using the word “or”;
13.
Determine the truth value of a compound statement which is
the combination of two statements with the word “and”;
14.
Determine the truth value of a compound statement which is
the combination of two statements with the word “or”.
15.
Identify the antecedent and consequent of an implication “if
p, then q”;
16.
Write two implications from a compound statements
containing “if and only if”;
17.
Construct mathematical statements in the form of
implication:
a)
If p, then q;
b)
P if and only if q;
18.
Determine the converse of a given implication;
19.
Determine whether the converse of an implication is true or
false.
20. Identify the premise and conclusion of a given simple
argument
21.
Make a conclusion based on two given premises for:
a)
Argument Form I;
b)
Argument Form II;
c)
Argument Form III;
22.
Complete an argument given a premise and the conclusion.
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23.
Determine whether a conclusion is made through:
a) reasoning by deduction;
b) reasoning by induction.
24.
Make a conclusion for a specific case based on a given
general statement, by deduction;
25.
Make a generalization based on the pattern of a numerical
sequence, by induction;
26.
Use deduction and induction in problem solving
THE STRAIGHT LINE
1.
Determine the vertical and horizontal distances between two
given points on a straight line.
2.
Determine the ratio of vertical distance to horizontal distance.
3.
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Derive the formula for the gradient of a straight line;
4.
Calculate the gradient of a straight line passing through two
points;
5.
Determine the relationship between the value of the gradient
and the:
a)
steepness; b) direction of inclination, of a straight line;
6.
Determine the x-intercept and the y-intercept of a straight
line;
7.
Derive the formula for the gradient of a straight line in terms
of the x-intercept and the y-intercept;
8.
Perform calculations involving gradient, x-intercept and yintercept;
9.
Draw the graph given an equation of the form y = mx + c ;
10.
Determine whether a given point lies on a specific straight
line;
11.
Write the equation of the straight line given the gradient and
y-intercept;
12.
Determine the gradient and y-intercept of the straight line
which equation is of the form:
a)
y = mx + c;
b)
ax + by = c;
13.
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
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a)
b)
15.
versa;
Find the point of intersection of two straight line by:
drawing the two straight lines;
solving simultaneous equations.
Verify that two parallel lines have the same gradient and vice
16.
Determine from the given equations whether two straight
lines are parallel;
17.
Find the equation of the straight line which passes through a
given point and is parallel to another straight line;
18.
Solve problems involving equations of
Straight lines.
STATISTICS
1. Complete the class interval for a set of data given one of the
class intervals;
2.
Determine:
a)
the upper limit and lower limit;
b)
the upper boundry and lower boundry of a class in a group of
data;
3.
Calculate the size of a class interval;
4.
Determine the class interval, given a set of data and the
number of classes;
5.
Determine a suitable class interval for a given set of data;
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6.
Construct a frequency table for a given set of data.
7.
Determine the modal class from the frequency table of
grouped data;
8.
Calculate the midpoint of a class;
9.
Verify the formula for the mean of grouped data;
10.
Calculate the mean from the frequency table of grouped data;
11.
Discuss the effect of the size of class interval on the accuracy
of the mean for a specific set of grouped data.
12.
Draw a histogram based on the frequency table of a grouped
data;
13.
Interpret information from a given histogram;
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14.
Solve problems involving histograms.
15.
16.
Draw the frequency polygon based on:
a) a histogram b) a frequency table;
Interpret information from a given frequency polygon;
17.
Solve problems involving frequency polygon.
18.
Construct the cumulative frequency table for:
a) ungrouped data; b) grouped data;
19.
a)
20.
Draw the ogive for:
ungrouped data; b) grouped data;
Determine the range of a set of data;
21.
a)
c)
22.
Determine:
the median;
b) the first quartile;
the third quartile; d) the interquartile range; from the ogive.
Interpret information from an ogive;
23.
Solve problems involving data representations and measures
of dispersion.
PROBABILITY I
1.
Determine whether an outcome is a possible outcome of an
experiment
2.
List all the possible outcomes of an experiment;
a)
from activities;
b)
by reasoning;
3.
Determine the sample space of an experiment;
4.
Write the sample space by using set Notations.
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5.
Identify the elements of a sample space which satisfy given
conditions;
6.
List all the elements of a sample space which satisfy certain
conditions using set notations;
7.
Determine whether an event is possible for a sample space.
8.
Find the ratio of the number of times an event occurs to the
number of trials;
9.
Find the probability of an event from a big enough number of
trials;
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10.
Calculate the expected number of times an event will occur,
given the probality of the event and number of trials;
11.
Solve problems involving probability;
12.
Predict the occurrence of an outcome and make a decision
based on known information.
CIRCLES III
1.
Identify tangents to a circle;
2.
Make inference that the tangent to a circle is a straight line
perpendicular to the radius that passes through the contact point;
3.
Construct the tangent to a circle passing through a point:
a)
on the circumference of the circle;
b)
Outside the circle;
4.
Determine the properties related to two tangents to a circle
from a given point outside the circle;
5.
Solve problems involving tangents to a circle.
6.
Identify the angle in the alternate segment which is subtended
by the chord through the contact point of the tangent;
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7.
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;
8.
Perform calculations involving the angle in alternate
segment;
9.
Solve problems involving tangent to a circle and angle in
alternate segment.
10.
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;
11.
Determine the properties related to the common tangent to
two circles which:
a)
intersect at two points;
b)
intersect only at one point;
c)
do not intersect;
12.
Solve problems involving common tangents to two circles;
13.
Solve problems involving tangents and common tangents
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TRIGONOMETRY II
1.
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Identify the quadrants and angles in the unit circle
2.
Determine :
a)
the value of y-coordinate;
b)
the value of x-coordinate;
c)
the ratio of y-coordinate to x-coordinate; of several points on
the circumference of the unit circle;
3.
Verify that, for an angle in quadrant 1 of the unit circle:
a)
sin Ө = y-coordinate;
b)
cos Ө = x-coordinate;
c)
tan Ө = y-coordinate/ x-coordinate
4.
determine the values of
a) sine; b) cosine; c) tangent; of an angle in quadrant I of the unit
circle;
5.
Determine the values of
a)sin Ө; b) cosine Ө; c) tan Ө, for 90° ≤ θ ≤ 360 ° ;
6.
Determine whether the values of;
a) sine; b) cosine; c) tangent, of an angle in a specific quadrant is
positive or negative;
7.
Determine the values of sine, cosine and tangent for special
angles;
8.
Determine the values of the angles in quadrant I which
correspond to the values of the angles in other quadrants;
9.
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;
10.
Find the values of sine, cosine and tangent of the angles
between 90° and 360°;
11.
Find the angles between 0° and 360°, given the values of
sine, cosine or tangent;
12.
Solve problems involving sine, cosine and tangent.
13.
Draw the graphs of sine, cosine and tangent for angles
between 0° and 360°;
14.
Compare the graphs of sine, cosine and tangent for angles
between 0° and 360°;
15.
Solve problems involving graphs of sine, cosine and
tangent.
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ANGLES OF ELEVATION AND DEPRESSION
1.
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Identify:
a) the horizontal line;
b) the angle of elevation;
c) the angle of depression,
for a particular situation;
2.
Represent a particular situation involving:
a.
the angle of elevation;
b.
the angle of depression, using diagrams;
3.
Solve problems involving the angle of elevation and the angle
of depression.
LINES AND PLANES IN 3-DIMENSIONS
1.
Identify planes;
2.
Identify horizontal planes, vertical planes and inclined planes;
3.
sketch a three dimensional shape and identify the specific
planes;
4.
Identify:
a)
lines that lies on a plane;
b)
lines that intersect with a plane;
5.
Identify normals to a given plane;
6.
Determine the orthogonal projection of a line on a plane;
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7.
Draw and name the orthogonal projection of a line on a
plane;
8.
Determine the angle between a line and a plane;
9.
Solve problems involving the angle between a line and a
plane.
10.
Identify the line of intersection between two planes;
11.
Draw a line on each plane which is perpendicular to the line
of intersection of two planes at a point on the line of intersection;
12.
Determine the angle between two planes on a model and a
given diagram;
13.
Solve problems involving lines and planes in 3-dimensional
shapes.
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