| CONTENT |
Relations, mapping and functions; graphical representation of numerical and statistical data; graphs of simple linear and non-linear functions
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SPECIFIC OBJECTIVES:
The student should be able to:
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| 1. |
Recognize a relation
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| 2. |
Describe a relation as a set of ordered pairs
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| 3. |
Use arrow diagrams to show relations
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| 4. |
Define a function as a many-to-one or one-to-one relation
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| 5. |
Distinguish between the graph of a relation and the graph of a function
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| 6. |
Use the functional notations, for example, f : x → x 2; or f(x) = x2; as well as y = f(x) for given domains
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| 7. |
Represent numerical and statistical data by bar chart, pie chart, line graph, histogram, frequency polygon, as well as on the rectangular cartesian plane
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| 8. |
Interpret data presented in any of the graphical or pictorial forms named in objective 7
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| 9. |
Draw, read and interpret graphs of:
(a) the functions {(x,y): y = a + bx +cx²} where a, b, and c are integers;
(b) simple non-linear functions given a table of values;
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| 10. |
Recognize the gradient of a line as the ratio of the vertical rise to the horizontal shift
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| 11. |
Find by drawing and or calculation, the gradients and intercepts of graphs of linear functions
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| 12. |
Determine the equation of a line given:
(a) the graph of the line
(b) the co-ordinates of two points on the line
(c) the gradient and one point on the line
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| 13. |
Represent the solution of linear inequalities in one unknown using:
(a) set notation
(b) The number line
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| 14. |
Recognize simple functions that have inverses
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| 15. |
Distinguish between functions defined for different domains by the same formula;
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| 16. |
Interpret and make use of functional notations for example, f(x), g(x), f -1 (x), and their compositions
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| *17. |
Draw and use the graphs of the functions of the form y = ax³, y = ax-1 and y =ax-2 for specific domains
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| 18. |
Recognize simple everyday expressions of exponential growth
(for example, population growth, multiplication of bacteria, compound interest)
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| 19. |
Draw and use graphs of a given quadratic function to determine;
(a) the elements of the domain that have a given image or vice versa
(b) the intervals of a domain for which the elements of the range maybe
positive or negative
(c) the interval of the domain for which the elements of the range may be
greater than or less than a given value.
(d) the roots of the given function
(e) the maximum and minimum values of the function over a given interval
of the domain.
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| 20. |
Draw and sketch graphs to represent cases of variation such as y varies as xn where n has the values 1, 2 or -1, -2
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| *21. |
Determine maximum and minimum values of quadratic functions by the method of completing the square
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| 22. |
Use graphs of functions to solve simple problems
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| *23. |
Draw and use distance-time-graphs and speed-time-graphs
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| 24. |
Use the gradient of the graph of a linear function to determine the rate of change of one variable with respect to the other
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| 25. |
Recognize the relation between the tangent of a certain angle and the gradient of a curve
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| 26. |
Estimate the value of the gradient of a curve by constructing a tangent to the curve at a given point
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| *27. |
Apply the ideas of gradient of a curve and area under a curve to problems in the physical, biological and social sciences
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| *28. |
Use linear programming techniques to solve problems involving two variables.
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*optional objectives which may be tested in section II of the general proficiency exam.
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Math
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