REVISION CHAPTER 1 (from Mid-Semester Exam Sem. II 09/10) 1 2 Given the function : y 2 sin 2x 3 a) Find the i) amplitude ii) period iii) phase shift. . b) Sketch the graph of the function over one period. [6] 2 Find the exact value of the expressions below. Rationalize the denominator where appropriate: a) cot 70 tan 650 csc( 250 ) sec( 110 ) 5 19 tan cos 6 6 4 23 cot sin 3 6 [5] b)
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Part 1. Describe the order of operations and explain how it is used to simplify expressions. Explain specifically the order in which mathematical operations must be performed to correctly simplify an expression. The order of operations is a rule that always applies to mathematical problems. It includes addition‚ subtraction‚ multiplication and division as well as grouping of numbers (such as in parentheses and powers). It gives a definite order of how to do a problem involving multiple operations
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cognitive development‚ one discovered by Jean Piaget and the other by Lev Vygotsky. However‚ Vygotsky had more of a significance on social interactions in children’s cognitive development‚ than Piaget‚ and their specific r theories were informed by their own cultural influences. Cognitive development theory describes how humans acquire and make sense of themselves and their planet. The theory of cognitive development was first proposed by Jean Piaget. Piaget approached the subject from a biological and
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2012-The Year of Mathematics P.Bhattacharyya [pic] [pic] (GH Hardy ‚ Ramanujan and Littlewood) The great Indian mathematician Srinivasa Ramanujan was born on the 22nd of December 1887 in Erode‚ Tamilnadu. In a function held in the Centenary Hall of Madras University on the 26th of December 2011 marking the 125th birth anniversary of Srinivasa Ramanujan‚ the Prime Minister of India Dr. Manmohan Singh proclaimed: “Our
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Mathematics is the Sphere of Life All is Numbers‚ is still echoing from the walls of the White City‚ when once the great Pythagoras said it on an early sunny morning to his disciples. No great discoveries in history every made‚ without the intervention of this mystical ray we call Mathematics. Einstein in his general relativity theory‚ to prove that the path of a ray of light‚ in the presence of a gravitational field‚ is curved and never straight used intensely the non-Euclidean geometry
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Explain the importance of teaching Math and Science in early education.Use theory or theorist applicable. The importance in teaching mathematics and science is of great concern to all levels of education especially in early education. Because early experiences affect later educational outcomes‚ providing young children with research-based mathematics and science learning opportunities is more likely to pay off with increased achievement‚ literacy‚ and work skills in these critical areas
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Decline of the Greek Mathematics Historically‚ the Greek Mathematics had reached a high level in Greece and its colonies during the Hellenic era‚ beginning in the sixth century B.C.E. and ending in 476 C.E. when the barbarians invaded Rome. Although there were achievements made during the Roman Empire‚ the Greeks have had their best productive times before the Roman Empire – the end of third century B.C.E. Although there might be many reasons why the Greek mathematics decline‚ I think that the
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When comparing Piaget and Vygotsky‚ many critics argue that both have many similarities as well as many differences. Meece and Daniels talk about how both Vygotsky and Piaget agreed that knowledge must be learned mentally by the child‚ yet Vygotsky was the one who emphasized that social interactions were a key role in helping the child achieve this knowledge. Another idea that Vygotsky emphasized more than Piaget was the idea that culture was detrimental in molding a child’s cognitive development
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DISCRETE MATHEMATICS Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly"‚ the objects studied in discrete mathematics – such as integers‚ graphs‚ and statements in logic – do not vary smoothly in this way‚ but have distinct‚ separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects
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When comparing the work of Piaget and Vygotsky‚ thought is given about the profound impact their theories have made on child development and learning. It is interesting how they both approached this topic from different perspectives and emphasized different methodologies. Educators‚ scholars‚ and parents have used their philosophies to understand how children learn and to create strategies to teach them. While their theories do share some similarities‚ there are some differences. Piaget’s theory
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