Bowdoin College Acceptance Rate, SAT/ACT Scores

Bowdoin College is a private liberal arts college with an acceptance rate of 10.3%. Located near the coast in Brunswick, Maine, Bowdoin takes pride in both its beautiful location and its academic excellence.  Eight miles away from the main campus is Bowdoins 118-acre Coastal Studies Center on Orrs Island. Bowdoin was one of the first colleges in the country to move to a financial aid process that allows students to graduate without loan debt.   For its strong programs in the liberal arts and sciences, Bowdoin was awarded a chapter of the prestigious  Phi Beta Kappa  honor society. With its 9-to-1 student/faculty ratio and wide-ranging strengths, Bowdoin made our lists of top New England colleges and  top liberal arts colleges.   Considering applying to this highly selective school? Here are the Bowdoin College admissions statistics you should know. Acceptance Rate During the 2017-18 admissions cycle, Bowdoin College had an acceptance rate of 10.3%. This means that for every 100 students who applied, 10 students were admitted, making Bowdoins admissions process highly competitive. Admissions Statistics (2017-18) Number of Applicants 9,081 Percent Admitted 10.3% Percent Admitted Who Enrolled (Yield) 55% SAT Scores and Requirements Bowdoin has a test-optional standardized testing policy. Applicants to Bowdoin may submit SAT or ACT scores to the school, but they are not required. During the 2017-18 admissions cycle, 60% of admitted students submitted SAT scores. SAT Range (Admitted Students) Section 25th Percentile 75th Percentile ERW 650 740 Math 650 770 ERW=Evidence-Based Reading and Writing This admissions data tells us that of those who submitted test scores during the 2017-18 admissions cycle, most of Bowdoins admitted students fall within the  top 20% nationally  on the SAT. For the evidence-based reading and writing section, 50% of students admitted to Bowdoin scored between 650 and 740, while 25% scored below 650 and 25% scored above 740. On the math section, 50% of admitted students scored between 650 and 770, while 25% scored below 650 and 25% scored above 770. While the SAT is not required, this data tells us that a composite SAT score of 1510 or higher is a competitive score for Bowdoin College. Requirements Bowdoin does not require SAT scores for admission. For students who choose to submit scores, note that Bowdoin participates in the scorechoice program, meaning that the admissions office will consider your highest score from each individual section across all SAT test dates. Home-schooled applicants and those from high schools that dont assign grades will need to submit SAT or ACT test scores, including 2 or more SAT Subject tests. ACT Scores and Requirements Bowdoin College has a test-optional standardized testing policy. Applicants to Bowdoin may submit SAT or ACT scores to the school, but they are not required. During the 2017-18 admissions cycle, 46% of admitted students submitted ACT scores. ACT Scores (Admitted Students) Section 25th Percentile 75th Percentile English 32 35 Math 27 33 Composite 30 34 This admissions data tells us that of those students who submitted ACT scores to Bowdoin College, most fall within the  top 7% nationally  on the ACT. The middle 50% of students admitted to Bowdoin received a composite ACT score between 30 and 34, while 25% scored above 34 and 25% scored below 30. Requirements Bowdoin does not require ACT scores for admission. For students who choose to submit scores, note that Bowdoin participates in the scorechoice program, meaning that the admissions office will consider your highest score from each individual section across all ACT test dates. Home-schooled applicants and those from high schools that dont assign grades will need to submit SAT or ACT test scores, including 2 or more SAT Subject tests.. GPA Bowdoin College does not provide data about admitted students high school GPAs. Self-Reported GPA/SAT/ACT Graph Bowdoin College Applicants Self-Reported GPA/SAT/ACT Graph. Data courtesy of Cappex. The admissions data in the graph is self-reported by applicants to Bowdoin College. GPAs are unweighted. Find out how you compare to accepted students, see the real-time graph, and calculate your chances of getting in with a free Cappex account. Admissions Chances Bowdoin College, which accepts one tenth of applicants,  is a highly selective liberal arts college. Bowdoin uses a  holistic admissions  process which is based on much more than numbers. A strong  application essay  and glowing  letters of recommendation  can strengthen your application, as can participation in meaningful  extracurricular activities  and a  rigorous course schedule which includes AP, IB, Honors, and dual enrollment classes. In the graph above, the blue and green dots represent accepted students. Most had average high school GPAs in the A range (3.7 to 4.0) and combined SAT scores (ERWM) above 1300, but lower scores wont affect your chance of acceptance as the college has a test-optional admissions policy.  Applicants can choose whether to include their scores when they apply to Bowdoin. All admissions data has been sourced from the National Center for Education Statistics and Bowdoin College Undergraduate Admissions Office.

Silver-Spotted Skipper (Epargyreus clarus)

The silver-spotted skipper, Epargyreus clarus, frequents roadsides, fields, and backyard gardens throughout North America. Skippers dash quickly from flower to flower, as if they are skipping around the meadow. What Do Silver-Spotted Skippers Look Like? Chances are youve seen a silver-spotted skipper. With their brown wings and quick movement, they might not be the first butterflies youd stop to observe. Take a closer look, and youll notice bands of orange on the forewings, and a silvery patch in the center of the hindwings. The silver-spotted skipper is the largest skipper in North America, with a wingspan of 1 3/4 - 2 5/8 inches. Silver-spotted skippers have enormous eyes that appear to bulge out from the head. Epargyreus clarus also has short antennae with clubbed ends. The odd-looking caterpillar has an enlarged head capsule and a pronounced neck collar. With a deep rust or black head and two bright red eyespots in the front, the caterpillar appears quite like a cartoon alien from outer space. The larvas body is yellow-green, with thin dark lines running across its width. By some accounts, the silver-spotted skipper lays her eggs on plants near the host plant, but not on the actual host. This requires the newly hatched larva to crawl and locate its food source. Most experts seem to dispute this theory, and argue the butterfly lays directly on the host plant. How Are Silver-Spotted Skippers Classified? Kingdom - AnimaliaPhylum - ArthropodaClass - InsectaOrder - LepidopteraFamily - HesperiidaeGenus - EpargyreusSpecies - Epagyreus clarus What Do Silver-Spotted Skippers Eat? Larvae feed on legumes, especially woody legumes. Black locust is the favorite host plant. Other host plants include honey locust, false indigo, bush clover, and tick-trefoils. Adult silver-spotted skippers nectar on many flowers, but show a clear preference for blue, red, pink, or purple varieties. They rarely visit yellow flowers. The Silver-Spotted SkippersLife Cycle Like all butterflies, the silver-spotted skipper undergoes four stages during its life cycle, a complete metamorphosis. The generations per year vary by region, with southern populations having the most broods. Egg - Green, dome-shaped eggs are laid singly on upper side of leaves.Larva - The caterpillar has a large brown head, with red eyespots at the front. The body is a yellow-green color.Pupa - These skippers overwinter in the chrysalis, hidden in rolled leaf litter.Adult - Adults emerge in spring. Males perch on tall weeds or branches, watching for females. They also patrol for potential mates. Special Adaptations and Defenses ofSilver-Spotted Skippers At night, or when the daytime weather prohibits flight, silver-spotted skippers hang upside down under leaves. Caterpillars build themselves tiny shelters using carefully cut pieces of leaves. As they grow, they abandon their old homes and build larger ones by joining leaves with silk. Where DoSilver-Spotted Skippers Live? Open parks, fields, gardens, and meadows, and where larval food plants are available. In North America, the silver-spotted skipper is common from Mexico to southern Canada, with the exception of the Great Basin region and western Texas. Worldwide reports include sightings in parts of Europe, Asia, and Australia. Sources: Silver-spotted Skipper, Butterflies and Moths of North AmericaSilver-spotted Skipper, Massachusetts Audubon - Butterfly Atlas

Integration Free Essays

string(665) " com EXERCISE A 1\) 2\) 3\) 4\) 5\) 6\) 7\) 8\) x \? 2 x \? 10 x \? c 3 2 SPM QUESTIONS 1\) y \? x2 \? 2x \? 7 2\) y \? x3 \? 3 x 2 \? 10 3\) p \? 3, y \? x3 \? 2 x 2 \? 4 x4 \? x3 \? 3x \? c 2 4 3 1 x \? 4x \? \? c 3 x 4 2 x x 1 \? \? 3 \? 2x \? c 2 2 x 6 5 \? \? 2 x 2x 2 x 2 \? \?c 4 x 1 2 x3 \? 3 \? c x 2 x \? 2x \? c 2 ASSESSMENT 1\) \(a \) x 4 \? 3 2 x \? 2x \? c 2 2 3 \(b\) 3x \? \? 2 \? c x x 6 x 1 \(c \) \? \?c 9 24 x 4 x3 9 \(d \) \? 6x \? \? c 3 x y \? x4 \? 2 x2 \? 8 p\? 7 8 2 3 3 2 x \? x \? x 3 2 2 3 x \? 2 3 EXERCISE B 1\) y \? 3x 2 \? 2 x \? 1 3 x 2 24 \? 2 \? 2 2 x 2\) 2\) y \? 2 x 2 \? x \? 3 3\) y \? 3\) 4\) y\? 5\) y\? http://mathsmozac\." http://sahatmozac. blogspot. com ADDITIONAL MATHEMATICS FORM 5 MODULE 4 INTEGRATION http://mathsmozac. We will write a custom essay sample on Integration or any similar topic only for you Order Now blogspot. com http://sahatmozac. blogspot. com CHAPTER 3 : INTEGRATION Content Concept Map page 2 3–4 5 6 7 8–9 10 – 11 12 4. 1 Integration of Algebraic Functions Exercise A 4. 2 The Equation of a Curve from Functions of Gradients. Exercise B SPM Question Assessment Answer http://mathsmozac. blogspot. com 1 http://sahatmozac. blogspot. com Indefinite Integral a) o o a x n a dx = ax + c. xn+ 1 + c. n+ 1 b) x n dx = c ) o d x = a o x n d x = a n x + n + 1 1 + c . Integration of Algebraic Functions ) ) The [f (x)  ± g(x) ]dx = o f (x) dx  ± d o Equation of a Curve from Functions of Gradients o g(x)dx y = y = o f ‘( x ) d x c, f (x) + http://mathsmozac. blogspot. com 2 http://sahatmozac. blogspot. com INTEGRATION 1. Integration is the reverse process of differentiation. dy 2. If y is a function of x and = f ‘( x) then o f ‘( x)dx = y + c, c = constant. dx If dy = f ( x ), then dx o f ( x)dx = y 4. 1. Integration of Algebraic Functions Indefinit e Integral a) b) o o a dx = ax + c. n a and c are constants xn+ 1 x dx = + c. n+ 1 n c is constant, n is an integer and n ? – c) o ax dx = a o ax n + 1 x dx = + c. n+ 1 n and c are constants n is an d) o [f ( x )  ± g ( x ) ]dx = o f ( x) dx  ± o g ( x)dx http://mathsmozac. blogspot. com 3 http://sahatmozac. blogspot. com Find the indefinite integral for each of the following. a ) ? 5dx b) ? x 3 dx c) ? 2 x dx 5 d) ? ( x ? 3x 2 )dx Always remember to include ‘+c’ in your answers of indefinite integrals. Solution : a) ? 5dx ? 5x ? c b) 3 ? x dx ? x3? 1 ? c 3 ? 1 x4 = ? c 4 2 c) 5 ? 2 x dx ? 2 x5? 1 ? c 5 ? 1 2 x6 = ? c 6 1 = x6 ? c 3 d) ? ( x ? 3x )dx ? ? xdx ? ? 3x 2 dx = x 2 3 x3 ? ?c 2 3 x2 = ? x3 ? c 2 Find the indefinite integral for each of the following. a) ? ? x ? 3x ? dx 2 x 4 b) ?x ? x 2 4 ? ? ? 3 ? ? dx x ? ? a) Solution : x ? 3Ãâ€"2 ? ? x 4 ?dx ? ? x 3Ãâ€"2 ? ? ? x4 ? x4 ? dx ? ? b) 2 4? ? ? 2 4? ? 3 ? 4 ? dx = ? ? 3x ? 2 ? dx x ? x ? ? ? = ? 3à â€"2 ? 4 x ? 2 dx ? x ? 1 ? 3x 3 = ? 4? c 3 ? ?1 ? 4 = x3 ? ? c x ? ? x? 3 ? 3x? 2 dx ? x? 1 ? x? 2 = ? 3? c ? 2 ? ?1 ? 1 3 =? 2 ? ?c 2x x ? ? ? ? http://mathsmozac. blogspot. com 4 http://sahatmozac. blogspot. com 1. Find ? ? 3x 2 ? 4 x ? 10 dx. ? [3m] 2. Find ? ? x 2 ? 1 ? 2 x ? 3 ? dx. ? [3m] 1? ? 3. Find ? ? 2 x ? ? dx. x? ? 2 [3m] 4. Find ? ? 2x ? ? 3 ?x? 3 ? ? 2 ? dx. 4 x ? [3m] 6x ? 5 5. Integrate with respect to x. x3 [3m] 6. Find ? ?x 5 ? 4Ãâ€"2 2x 4 ? dx [3m] 3 ? ? 7. Find ? x ? 6 ? 6 ? x . x ? ? 2 [3m] 8. Integrate x 2 ? 3x ? 2 with respect to x. x ? 1 [3m] http://mathsmozac. blogspot. com 5 http://sahatmozac. blogspot. com The Equation of a Curve from Functions of Gradients dy ? f ‘( x), then the equation of the curve is dx If the gradient function of the curve is y ? ? f ‘( x ) dx c is constant. y ? f ( x) ? c, Find the equation of the curve that has the gradient function 3x ? 2 and passes through the point (2, ? 3). Solution The gradient function is 3x ? 2. dy ? 3x ? 2 dx y ? ? (3x ? 2)dx y? 3Ãâ€"2 ? 2x ? c 2 The curve passes through the point (2, ? 3). Thus, x = 2, y = ? 3. 3(2) 2 ? 3 ? ? 2x ? c 2 ? 3 ? 6 ? 4 ? c c ? 5 Hence, the equation of curve is y? 3x 2 ? 2x ? 5 2 http://mathsmozac. blogspot. com 6 http://sahatmozac. blogspot. com 1. Given that dy ? 6 x ? 2 , express y in terms of x if y = 9 when x = 2. dx 2. Given the gradient function of a curve is 4x ? 1. Find the equation of the curve if it passes through the point (? 1, 6). 3. The gradient function of a curve is given by dy 48 ? kx ? 3 , where k is a constant. dx x Given that the tangent to the curve at the point (-2, 14) is parallel to the x-axis, find the equation of the curve. http://mathsmozac. blogspot. com 7 http://sahatmozac. blogspot. com SPM 2003- Paper 2 :Question 3 (a) Given that y ? 2 x ? 2 and y = 6 when x = ? 1, find y in terms of x. dx [3 marks] SPM 2004- Paper 2 :Question 5(a) The gradient function of a curve which passes through A(1, ? 12) is 3 x 2 ? 6 x. Find the equation of the curve. [3 marks] http://mathsmozac. blogspot. com 8 http://sahatmozac. blogspot. com SPM 2005- Paper 2 :Question 2 A curve has a gradient function px 2 ? 4 x , where p is a constant. The tangent to the curve at the point (1, 3) is parallel to the straight line y + x ? 5 =0. Find (a) the value of p, [3 marks] (b) the equation of the curve. [3 marks] http://mathsmozac. blogspot. com 9 http://sahatmozac. blogspot. com 1. Find the indefinite integral for each of the following. (a) ? ? 4x 3 ? 3 x ? 2 dx ? (b) 3? x ? ? 2 2 ? 6? ? dx x3 ? 1 ? 2 ( c) (c) ? ? x 5 + 5 6x ? 3 ? ? dx ? ? x2 ? 3 (d) ? ? ? x2 ? ? ? 2 ? ? dx ? ? 2. If dy ? 4 x3 ? 4 x, and y = 0 when x = 2, find y in terms of x. dx http://mathsmozac. blogspot. com 10 http://sahatmozac. blogspot. com 3. If dp v3 ? 2v ? , and p = 0 when v = 0, find the value of p when v = 1. dv 2 4. Find the equation of the curve with gradient 2 x 2 ? 3 x ? 1, which passes through the origin. 5. d2y dy dy Given that ? 4 x, and that ? 0, y = 2 when x = 0. Find and y in terms 2 dx dx dx of x. http://mathsmozac. blogspot. om 11 http://sahatmozac. blogspot. com EXERCISE A 1) 2) 3) 4) 5) 6) 7) 8) x ? 2 x ? 10 x ? c 3 2 SPM QUESTIONS 1) y ? x2 ? 2x ? 7 2) y ? x3 ? 3 x 2 ? 10 3) p ? 3, y ? x3 ? 2 x 2 ? 4 x4 ? x3 ? 3x ? c 2 4 3 1 x ? 4x ? ? c 3 x 4 2 x x 1 ? ? 3 ? 2x ? c 2 2 x 6 5 ? ? 2 x 2x 2 x 2 ? ?c 4 x 1 2 x3 ? 3 ? c x 2 x ? 2x ? c 2 ASSESSMENT 1) (a ) x 4 ? 3 2 x ? 2 x ? c 2 2 3 (b) 3x ? ? 2 ? c x x 6 x 1 (c ) ? ?c 9 24 x 4 x3 9 (d ) ? 6x ? ? c 3 x y ? x4 ? 2 x2 ? 8 p? 7 8 2 3 3 2 x ? x ? x 3 2 2 3 x ? 2 3 EXERCISE B 1) y ? 3x 2 ? 2 x ? 1 3 x 2 24 ? 2 ? 2 2 x 2) 2) y ? 2 x 2 ? x ? 3 3) y ? 3) 4) y? 5) y? http://mathsmozac. You read "Integration" in category "Essay examples" blogspot. com 12 http://sahatmozac. logspot. com ADDITIONAL MATHEMATICS FORM 5 MODULE 5 INTEGRATION http://mathsmozac. blogspot. com 13 http://sahatmozac. blogspot. com CONTENT CONCEPT MAP INTEGRATION BY SUBSTITUTION DEFINITE INTEGRALS EXERCISE A EXERCISE B ASSESSMENT SPM QUESTIOS ANSWERS 2 3 5 6 7 8 9 10 http://mathsmozac. blogspot. com 14 http://sahatmozac. blogspot. com CONCEPT MAP INTEGRATION BY SUBSTITUTION un ? ax ? b ? dx ? ? du ? a n DEFINITE INTEGRALS If b d g(x) ? f (x) then dx b where u = ax + b, a and b are constants, n is an integer and n ? -1 OR (a) ? f (x)dx g(x)? ? g(b) ? g(a) a a (b) ? f (x)dx f (x)dx a a b b (c) ? f (x)dx f (x)dx ? ? f (x)dx a b a b c ? a x ? b ? ? ? ax ? b ? dx ? a ? n ? 1? n n ? 1 ? c, where a, b, and c are constants, n is integer and n ? -1 http://mathsmozac. blogspot. com 15 http://sahatmozac. blogspot. com INTEGRATION BY SUBSTITUTION un ? ? ax ? b ? dx ? ? a du n where u = ax + b, a and b are constants, n is an integer and n ? -1 O R ? ax ? b ? ? ? ax ? b ? dx ? a ? n ? 1? n n ? 1 ? c, where a, b, and c are constants, n is integer and n ? -1 Find the indefinite integral for each of the following. (a) ? ? 2 x ? 1? dx 3 (b) ? 4(3 x ? 5)7 dx 2 (c) ? dx (5 x ? 3)3 SOLUTION (a) ? ? 2 x ? 1? dx 3 Let u = 2x +1 du du ? 2 ? dx ? dx 2 3 3 ? du ? ? (2 x ? 1) dx ? ? u ? ? ? ? u3 = ? du 2 u 3 ? 1 = ? c 2(3 ? 1) u4 +c 8 (2 x ? 1) = +c 8 = Substitute 2x+1 and substitute dx with du dx = 2 OR (2 x ? 1) 4 ? c ? (2 x ? 1) dx ? 2(4) 3 = ? 2 x ? 1? 8 4 ?c Substitute u = 2x +1 http://mathsmozac. blogspot. com 16 http://sahatmozac. blogspot. com (b) ? 4(3 x ? 5) dx 7 (c) Let u ? 3 x ? 5 du du ? 3 ? dx ? dx 3 7 4u 7 du ? 4(3 x ? 5) dx ? ? 3 4u 8 = ? c 3(8) u8 ? c 6 (3u ? 5)8 = ? c 6 = 2 dx ? ? 2(5 x ? 3) ? 3 dx (5 x ? 3)3 Let u ? 5 x ? 3 du du ? 5 ? dx ? dx 5 ? 3 2u ? 3 du ? 2(5 x ? 3) dx ? ? 5 2u ? 3 = ? c 5(? 2) ? OR 4(3 x ? 5)8 ? c ? 4(3 x ? 5) dx ? 3(8) 7 u ? 2 ? c ? 5 1 = ? 2 5u 1 =? ?c 5(5 x ? 3)2 = = (3x ? 5)8 ? 6 DEFINITE INTEGRALS If d g ( x) ? f ( x) then dx b (a) (b) ? b a b f ( x)dx ? ? g ( x) ? ? g (b) ? g (a) a ? (c ) ? a b f ( x)dx ? ? ? f ( x)dx a b a f ( x)dx ? ? f ( x)dx ? ? f ( x)dx b a c c http://mathsmozac. blogspot. com 17 http://sahatmozac. blogspot. com Evaluate each of the following ( x ? 3)( x ? 3) (a) ? 12 dx x4 1 1 (b) ? 0 dx (2 x ? 1) 2 SOLUTION (a) x2 ? 9 2 ( x ? 3)( x ? 3) ? c ? ?12 4 dx ? 1 x4 x 2 9 ? 2? x = ? 1 ? 4 ? 4 ? dx x ? ?x = ? 12 ( x ? 2 ? 9 x ? 4 )dx ? x ? 1 ? x ? 3 ? ? =? ? 9? ? ? 3 ? ?1 ? ?1 2 2 (b) ?0 1 1 1 dx ? ?0 (2 x ? 1)? 2 dx 2 (2 x ? 1) 1 = ? 0 (2 x ? 1) ? 2 dx ? (2 x ? 1) ? 1 ? =? ? ? ?1(2) ? 0 ? 1 = ? ? 2(2 x ? 1) ? 0 =? ? ? 1 1 ? 2[2(1) ? 1] ? 2[2(0) ? 1] ? 1 1 ? 1 3? = ? 3 ? ? x x ? 1 ? 1 3 ? ? 1 3? = ? 3 ? ? 3 ? ? 2 2 ? ? 1 1 ? 1 3 = ? ? ? (? 1 ? 3) 2 8 1 =? ?2 8 1 =? 2 8 1 ? 1? = ? ? 6 ? 2? 1 = 3 http://mathsmozac. blogspot. com 18 Distributed:18. 1. 09 Return:20. 1. 09 INTEGRATE THE FOLLOWING USING SUBSTITUTION METHOD. (1) ? ( x ? 1)3dx (2) ? ?4 ? 3 x ? 5 ? dx ? 5 (3) ? 1 ? 5 x ? 3? dx 4 1 ? ? (4) ? ? 5 ? x ? dx 2 ? ? ?3 1 ? ? (5) ? 5 ? 4 ? y ? dy 2 ? ? 4 3? 2 ? (6) ? ? 5 ? u ? du 2? 3 ? 5 19 http://sahatmozac. blogspot. com EXERCISE B 8 1. Evaluate ? 3 ( x3 ? 4)dx Answer : 1023. 75 2. Evaluate Answer: 3 ? ?3 1 2 x( x ? x ? 5)dx 8 83 96 ?2 ? 3. Integrate ? x ? 5 ? with respect to x ? 3 ? 4 4. Evaluate ? 1 3 1 ? ? ? 2 ? 3x ? 4 ? dx ? 1 x ? ? 1 Answer: 3 ? 2 ? ? x ? 5? ? c 10 ? 3 ? 5 Answer : 3 5. Evaluate ? 3 1 ? 2 x ? 1 2 x ? 1? dx 4 x2 6. Given that of 2 5 ? 5 2 f ( x)dx ? 10 , find the value 5 Answer: 1 6 ? ? 1 ? 2 f ( x)? dx Answer :17 http://mathsmozac. blogspot. com 20 http://sahatmozac. blogspot. com ASSESSMENT ?6 and 2. (a) ? 5(2 ? 3v) dv 4 (b) ? dx 5 3 ? 1 ? 5 x ? 1. Given that ? 2 2 1 f ( x)dx ? 3 ? 2 3 f ( x)dx ? ?7 . Find (a) the value of k if (b) ? ? kx ? f ( x)? dx ? 8 1 ? ? 5 f ( x) ? 1? dx 3 1 Answer : (a) k = (b) 48 22 3 3. Show that d ? x 2 ? 2 x 2 ? 6 x 4. . ? dx ? 3 ? 2 x ? ? 3 ? 2 x ? 2 4 Given that ? 4 0 f ( x)dx ? 3 and Hence, find the value of Answer : 1 10 ? ? 3 ? 2x ? 0 1 x ? x ? 3? ? 0 g ( x)dx ? 5 . Find 4 0 2 dx . ? f ( x)dx ? ? g ( x)dx (b) ? ?3 f ( x) ? g ( x)? dx (a) 0 4 0 4 Answer: (a) – 15 (b) 4 http://mathsmozac. blogspot. com 21 http://sahatmozac. blogspot. com SPM QUESTIONS SPM 2003 – PAPER 1, QUESTION 17 1. Given that ? SPM 2004 – PAPER 1, QUESTION 22 k n dx ? k ? 1 ? x ? ? c , 2. Given that 1 ? 2 x ? 3? dx ? 6 , where k ; -1 , find the value of k. [4 marks] ? 1 ? x ? find the value of k and n [3 marks] Answer: k = 5 5 Answer: k = ? =-3 3 5 4 SPM 2005 – PAPER 1, QUESTION 21 6 6 3. Given that ? 2 f ( x)dx ? 7 and ? 2 (2 f ( x) ? kx)dx ? 10 , find the value of k. Answer: k = 1 4 http://mathsmozac. blogspot. com 22 http://sahatmozac. blogspot. com ANSWERS EXERCISE A 1. 3 ( x + 1)4 + c 2. 60 (3 x +5) – 4 + c 3. ?20 EXERCISE B 1. 1023. 75 ? 5 x ? 3? 3 ?c 2. 3 83 96 5 4. 3? 1 ? ?5 ? x? ? c 2? 2 ? ? y? ?c ? 6 4 ?2 3 ? 2 ? 3. ? x ? 5? ? c 10 ? 3 ? 1 3 5 5. 1 6 6. 17 1 ? 5. ?10 ? 4 ? 2 ? 6. 4. 3 2 ? ? ? 5 ? 5 ? u ? ? c 3 ? ? ASSESSMENT 22 1. (a) k = 3 (b) 48 2. (a) 90(2 – 3v) +c ? 100 (b) (1 ? 5 x) ? 4 ? c 3 3. 1 10 -5 SPM QUESTIONS 1. k = ? 2. k = 5 3. = 1 4 5 3 n=-3 4. (a) – 15 (b) 4 http://mathsmozac. blogspot. com 23 http://sahatmozac. blogspot. com ADDITIONAL MATHEMATICS MODULE 6 INTEGRATION http://mathsmozac. blogspot. com 24 http://sahatmozac. blogspot. com CHAPTER 3 : INTEGRATION Content Concept Map 9. 1 Integration as Summation of Areas page 2 3 4–6 7–8 9 – 11 12 – 14 15 Exercise A 9. 2 Integration as Summation of Volumes Exercise B SPM Question Answer http://mathsmozac. blogspot. com 25 http://sahatmozac. blogspot. com a) The area under a curve which enclosed by x-axis, x = a and x = b is a) The volume generated when a curve is rotated through 360? bout the x-axis is ? ? b a y dx b ) The area under a curve which enclosed by y-axis, y = a and y = b is b a Vx ? ? ? y 2 dx a b x dy b) The volume generated when a curve is rotated through 360? about the y-axis is c) The area enclosed by a curve and a straight line ? ? f ( x) ? g ( x)? dx b a Vy ? ? ? x 2 dy a b http://mathsmozac. blogspot. com 26 http://sahatmozac. blogspot. com 3. INTEGRATION 3. 1 Integration as Summation of Area y y = f(x) b a a b 0 The area under a curve which enclosed by x = a and x = b is x 0 x y = f(x) ? b a ydx The area under a curve which is enclosed by y = a and y = b is Note : The area is preceded by a negative sign if the region lies below the x – axis. ? b a xdy Note : The area is preceded by a negative sign if the region is to the left of the y – axis. The area enclosed by a curve and a straight line y y = g (x) y = f (x) a The area of the shaded region = = b b x ? ? ? f ( x) ? g ( x)? dx a b a a b f ( x)dx ? ? g ( x) http://mathsmozac. blogspot. com 27 http://sahatmozac. blogspot. com 1. Find the area of the shaded region in the diagram. y y = x2 – 2x 2. Find the area of the shaded region in the diagram. y y = -x2 + 3x+ 4 x -1 0 4 0 x http://mathsmozac. blogspot. com 28 http://sahatmozac. logspot. com 3. Find the area of the shaded region y y=2 4. Find the area of the shaded region in the diagram. y y = x2 + 4x + 4 0 x = y2 x -2 -1 0 2 x http://mathsmozac. blogspot. com 29 http://sahatmozac. blogspot. com 5. Find the area of the shaded region in the diagram y 1 x = y3 – y x 6. y y = ( x – 1)2 0 0 x x=k -1 Given that the area of the shaded region in 28 the diagram above is units2. Find the 3 value of k. http://mathsmozac. blogspot. com 30 http://sahatmozac. blogspot. com 3. 2 Integration as Summation of Volumes y y=f(x) The volume generated when a curve is rotated through 360? about the x-axis is 0 a b x Vx ? ? ? y 2 dx a b y y=f(x) The volume generated when a curve is rotated through 360? about the y-axis is b a 0 x Vy ? ? ? x 2 dy a b http://mathsmozac. blogspot. com 31 http://sahatmozac. blogspot. com y y=x(x+1) Find the volume generated when the shaded region is rotated through 360? about the x-axis. x 0 Answer : x=2 ? ? ? y 2 dx 0 2 Volume generated ? ? ? x 2 ? x ? 1? dx 2 2 0 ? ? ? ( x 4 ? 2 x3 ? x 2 )dx 0 2 ? x 5 2 x 4 x3 ? ? ? ? ? 4 3 ? 0 ? 5 2 25 2(2)4 23 ? ? ? ? ? ? ? ? 0? 5 4 3? ? 256 1 ? ? @ 17 ? units 3 . 15 15 y y ? 6 ? x2 The figure shows the shaded region that is enclosed by the curve y ? ? x 2 , the x-axis and the y-axis. Calculate the volume generated when the shaded region is revolved through 360? about y-axis. 0 Answer : Given y ? 6 ? x 2 substitute x ? 0 into y ? 6 ? x Then, y ? 6? 0 y? 6 2 x Volume generated ? ? ? x 2 dy 0 6 ? ? ? ? 6 ? y ? dx 6 0 ? y2 ? ? ? ?6 y ? ? 2 ? 0 ? 62 ? ? 6(6) ? 2 ? 18? units 3 . ? ? ? ? 0? ? ? 6 http://mathsmozac. blogspot. com 32 http://sahatmozac. blogspot. com 1. y y = x (2 – x) 0 x The above figure shows the shaded region that is enclosed by the curve y = x (2 – x) and x-axis. Calculate the volume generated when the shaded region is revolved through 360? bout the y-axis. [4 marks] http://mathsmozac. blogspot. com 33 http://sahatmozac. blogspot. com 2. y R (0, 4) Q (3, 4) P (0, 2) y? = 4 (x + 1) 0 x=3 x The figure shows the curve y ? ( x ? 2) 2 . Calculate the volume generated when the shaded region is revolved through 360? about the x-axis. http://mathsmozac. blogspot. com 34 http://sahatmozac. blogspot. com 3. y R (0, 4) x y ? ? 3? x 0 x=k The above figure shows part of the curve y ? ? 3 ? x and the straight line x = k. If the volume generated when the shaded region is revolved through 1 360? about the x-axis is 12 ? units3 , find the value of k. 2 http://mathsmozac. logspot. com 35 http://sahatmozac. blogspot. com SPM 2003- Paper 2 :Question 9 (b) Diagram 3 shows a curve x ? y 2 ? 1 wh ich intersects the straight line 3 y ? 2 x at point A. y 3 y ? 2x 3y ? 2x x ? y2 ? 1 ?1 0 x Diagram 3 Calculate the volume generated when the shaded region is involved 360? about the y-axis. [6 marks] http://mathsmozac. blogspot. com 36 http://sahatmozac. blogspot. com SPM 2004- Paper 2 :Question 10 Diagram 5 shows part of the curve y ? y 3 ? 2 x ? 1? 2 which passes through A(1, 3). A(1,3) y? 0 a) b) Diagram 5 3 ? 2 x ? 1? 2 x Find the equation of the tangent to the curve at the point A. [4 marks] A egion is bounded by the curve, the x-axis and the straight lines x=2 and x= 3. i) Find the area of the region. ii) The region is revolved through 360? about the x-axis. Find the volume generated, in terms of ? . [6 marks] http://mathsmozac. blogspot. com 37 http://sahatmozac. blogspot. com SPM 2005- Paper 2 :Question 10 In Diagram 4, the straight line PQ is normal to the curve y ? straight line AR is parallel to the y-axis. y x2 ? 1 at A(2, 3). The 2 y? x2 ? 1 2 A(2, 3) 0 R Diagram 4 Fin d (a) (b) (c) Q(k, 0) x the value of k, [3 marks] the area of the shaded region, [4 marks] the volume generated, in terms of ? when the region bounded by the curve, the y-axis and the straight line y = 3 is revolved through 360? about y-axis. [3 marks] http://mathsmozac. blogspot. com 38 http://sahatmozac. blogspot. com EXERCISE A EXERCISE B 1. 1 1 ? unit 2 15 1. 1 1 units 2 3 5 units 2 6 2. 2. 20 3 6 ? unit 3 5 k ? ?2 3. 3. 2 2 units 2 3 2 units 2 3 SPM QUESTIONS SPM 2003 Volume Generated ? 52 ? units3 15 4. 24 SPM 2004 i) Area ? 1 units 2 5 49 ? units3 1125 5. 1 units 2 2 k? 4 ii) Volume Generated ? 6. SPM 2005 a) k ? 8 1 b) Area ? 12 units2 3 c) Volume Generated ? 4? units? http://mathsmozac. blogspot. com 39 How to cite Integration, Essay examples

Chinese Sports and the Values of Taoism and Confucianism free essay sample

This paper reviews the book Training the Body for China by Brownell, which presents the practices, objects and activities of Chinese sports and material arts. This paper discusses that, unlike Western sports, Chinese sports and martial art are developed based on religious beliefs; in China, sports are based on two native religions, Taoism and Confucianism. The author reviews Susan Brownells Training the Body for China in which she shares her studies of Chinese Olympic sports and martial arts. For example, the author point out that, in sport, Chinese culture employs self-disciplinary actions to deal with misbehavior to sustain order, a value of Confucianism. One of the beliefs Confucianism values is the importance of family; this notion is also the linkage between Confucianism and the practices Chinese sports. One of ethical lessons Confucianism teaches is Hsiao, which signifies love within family; this notion is also apparent in Chinese sports. According to Brownell, there has been a phenomenon of developing family-funded sports clubs and village-based associations among Chinese. We will write a custom essay sample on Chinese Sports and the Values of Taoism and Confucianism or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Having family-funded sport clubs consisting family members as players clearly indicates how Confucianism value has become a part of Chinese life and sports.

Time And The Tempest Essay Research Paper free essay sample

Time And The Tempest Essay, Research Paper The Tempest, penned by dramatist William Shakespeare, as one of his last plants circa 1612 is a narrative about many things: love, retaliation, greed, political relations, thaumaturgy, and enigma. Even the impression of clip plays a major function, and it is this facet we shall be discoursing in the undermentioned pages. Time plays a reasonably big function in many of the thoughts put frontward in this instead pensive narrative of one adult male s ( Prospero ) treachery at the custodies of his brother and his initial efforts at retaliation. Basically The Tempest terminals with the antique moral that clip heals all lesions as he eventually finds it in his bosom to forgive his brother and convey the narrative to a peaceable declaration. It is non merely here nevertheless, that we find clip to be a utile secret plan device. One should besides pay attending to the assorted departures on within the drama such as Pospero s remarks on the brevity of life # 8211 ; every bit good as the rubr ic of the drama itself. We will write a custom essay sample on Time And The Tempest Essay Research Paper or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page To get down with we shall look at the rubric The Tempest which serves to keep a dual significance. Whilst the word Tempest of class can be seen to mention to the great storm that is used by Prospero to incarcerate his prisoners on the isle, every bit good as the storm of emotion invoked in the characters an the instability of power amongst them caused by the state of affairs, there is another ground why The Tempest is such an disposed name. Indeed, why did Shakespeare non call it The Storm or some other such equivalent words? I believe this stems from its sound. The word s foremost half is temp stemming from the Latin tempestas, average clip, and can besides be seen in it s passage to English in pacing, which means clip, in relation to rush or degree of motion in action. This serves as a farther note to the spectator on the importance of clip, both in the drama s class every bit good as in it s implicit in subjects. The subject of clip in relation to its brevity besides appears as a running subject throughout The Tempest. Although it is merely genuinely noticeable when it comes to a caput with Prospero s address to Miranda and Ferdinand, in which he tells them non to worry about his attempted blackwash: be cheerful, sir: our revels are now ended: these histrions were all liquors, and are melted into thin air: And, like the groundless cloth of this vision Yea, which it inherit, shall fade out, And, like this unsubstantial pageant faded, Leave non a rack behind: we are such material As dreams are made on, and our small life, Is rounded with a slumber. It is here that we see Prospero s plaint on his age and ailing wellness, take a firm standing the young persons non worry about his public assistance, as he is old and that life is excessively short for concerns and declinations. It is possible to see here that possibly Shakespeare has created Prospero as a contemplation of himself, and that these ar e similar ideas to his as he wrote the drama ; sing his age ( early 50s ) at the clip of composing The Tempest and the fact that its release coincided approximately with the clip of his retirement. This could in fact be the beginning of the drama s inspiration as many of its concurrent subjects stem rather closely to this Carpe Diem political orientation. In fact it s whole gay nature seems to stem from this thought of life being excessively abruptly for concern, sorrow, animus, and other such negative emotions. Music, which besides seems to play a instead major function in The Tempest, seems to function as a reminder of this besides. Siting on a bank Crying once more the male monarch my male parent s wreck, This music crept by me upon the Waterss ; Stilling both their rage and my passion. Here we see Ferdinand s liquors roused by the sound of Ariel s music, reminding him the futility of keening what is past and to look towards the beauty of the present. In the declaration of The Tempest we can see Shakespeare s commentary on forgiveness through the transition of clip. Whilst many critics view this as the drama s primary weak point, believing its signifier simply to be a instead weak effort at weaving it up with a peaceable stoping in order to follow with authoritative amusing signifier ( this depends on whether 1 was to really category this as a comedy ) , I believe that given the instead deep content involved every bit good as it s embracing of so many genres ( ie love affair, play, phantasy every bit good as comedy ) , such accusals are badly founded. As Prospero s program are eventually coming into fruition, he eventually realises after a conversation with Ariel that Yet with my nobler ground, gainst my rage Do I take portion: the rarer action is In virtuousness than in retribution: they being penitent, The exclusive impetus of my purpose doth extend Not a frown further. Here he convinces himself that retaliation is non necessary . He shall admit his offender s repentance and forgive their workss in order to travel on ( albeit with some recompense ) , and non go on the short balance of his life in malice. It is here besides in the shutting scene that we see Prospero/Shakespeare keening that he hopes to see the nuptial Of these our dear-beloved solemniz vitamin D ; And thence retire me to my Milan, where Every tierce thought shall be of my grave. Another distinctive feature of this drama is besides the baffled nature of clip s ain transition throughout. Each character seems to hold their ain typical feeling of the narrative s length. Ariel for illustration, spends the full drama numbering the proceedingss til his eventual release which he knows will merely come at the decision of these events. Prospero, on the other manus, passes the clip rapidly ; we see how he has been fixing twelve old ages for this event, and he know he has much to make in the three or so short hours that ensue: the really infinitesimal commands the ope thine ear is another good indicant of his realization that this timing is short and important as his life s works reach their zenith. Of class there is besides Caliban, Trinculo, and Stephano who, whilst being together on the island, all seem to hold wholly different dockets and therefore different impressions of the passing of clip: Caliban becomes excited by the impression of happening a new God and like Ariel herb of graces every minute he has to wait before the hr of Prospero s repose when Stephano has promised to assassinate him, whilst Stephano and Trinculo appear more than happy to roll around in a bibulous daze with really small respect to where or when they should be. This of class discontents Caliban and motivate his reminder I will hold none on T: we shall lose our clip And all be turned to cirripeds, or to apes With brows villanous low. On the other manus, nevertheless, the full island is seen to be encapsulated in thaumaturgy and enigma. Within the charming circle Prospero has created to pin down his prisoners existent clip ( as opposed to the sensed transition of clip single to each character ) seems to take on a slow, phantasmagoric quality that weighs everybody down and makes the events appear to happen in a sleepy, surreal manner. Such deformation helps farther impart a sense of mysticism and enigma to The Tempest. So every bit should by now be seen, clip plays a major, non wholly unsubversive function in Shakespeare s concluding farewell to theatre. Despite it s slightly deficient in deepness of content there is still a universe of beauty and elaborateness here to be seen. Through the usage of linguistic communication and characters, Shakespeare has managed to get the hang the usage and the impression of clip and its assorted signifiers of use, to enrich this moony comedy/romance/drama in ways perchance no other adult male could.

Free Essays on The Little Drummer Girl

Moral Ambiguity of Charlie in The Little Drummer Girl In George J. Lennard’s, â€Å"John le Carre† critical assessment of the ending of Little Drummer Girl, he claims that â€Å"Charlie can not continue to act in the theater of the real...she can no longer return to the romantic fluff of Western middle class society.† Charlie’s last line in the novel, the theater of the real, are â€Å"I am dead† (pp.659), which confirms Lennard’s statement. Charlie, an actress, by nature and craft is a coerced into a scheme to infiltrate a terrorist ring, against her convictions. By playing upon Charlie’s insecurities and her need for acceptance, this scheme forms a kind of moral ambiguity and uncertainness inside Charlie. When it ends, her world is shattered, and she becomes â€Å"dead† in a figurative sense. The theater of the real forces Charlie to give a performance of a lifetime as her own life is at stake. In the beginning Charlie, willing and naive, accepts the script given to her by Joseph. Joseph himself, trains Charlie how to act in this scheme, much like an acting coach trains an inexperienced theatrical student. Along the way, Joseph gives her important pieces of advice such as â€Å"stay with the logic of the fiction...weaken and you will ruin the operation...we’ll repair [any] damage (pp. 468), advice which Charlie does not closely follow. In a world that will be turn upside down for Charlie, Joseph is her one remaining constant. The people Charlie comes in contact with can be best described as characters or actors in fiction as well. The characters names change almost as frequently as Charlie’s views of her situation. The changing names give way to the belief that the characters, under disguise, can not really be held responsible for their actions as they are in costume. As the novel progresses, Charlie also changes costumes much like a chameleon changes with its environment. When Charlie’s character is ... Free Essays on The Little Drummer Girl Free Essays on The Little Drummer Girl Moral Ambiguity of Charlie in The Little Drummer Girl In George J. Lennard’s, â€Å"John le Carre† critical assessment of the ending of Little Drummer Girl, he claims that â€Å"Charlie can not continue to act in the theater of the real...she can no longer return to the romantic fluff of Western middle class society.† Charlie’s last line in the novel, the theater of the real, are â€Å"I am dead† (pp.659), which confirms Lennard’s statement. Charlie, an actress, by nature and craft is a coerced into a scheme to infiltrate a terrorist ring, against her convictions. By playing upon Charlie’s insecurities and her need for acceptance, this scheme forms a kind of moral ambiguity and uncertainness inside Charlie. When it ends, her world is shattered, and she becomes â€Å"dead† in a figurative sense. The theater of the real forces Charlie to give a performance of a lifetime as her own life is at stake. In the beginning Charlie, willing and naive, accepts the script given to her by Joseph. Joseph himself, trains Charlie how to act in this scheme, much like an acting coach trains an inexperienced theatrical student. Along the way, Joseph gives her important pieces of advice such as â€Å"stay with the logic of the fiction...weaken and you will ruin the operation...we’ll repair [any] damage (pp. 468), advice which Charlie does not closely follow. In a world that will be turn upside down for Charlie, Joseph is her one remaining constant. The people Charlie comes in contact with can be best described as characters or actors in fiction as well. The characters names change almost as frequently as Charlie’s views of her situation. The changing names give way to the belief that the characters, under disguise, can not really be held responsible for their actions as they are in costume. As the novel progresses, Charlie also changes costumes much like a chameleon changes with its environment. When Charlie’s character is ...

Apples directional strategy Essay Example | Topics and Well Written Essays - 250 words

Apples directional strategy - Essay Example In advancing through future markets it’s clear that these aspects will constitute the backbone of Apple’s directional strategy. Within this context of understanding, it’s further necessary for the company to implement leverage as a means of retaining their competitive advantage. Sales of the Apple Macintosh as well as iPod and iTunes technology are such that the company is given access to many new segments of the population. In these regards, it’s necessary for the company to implement their consumer access as permitted in this software as a means of promoting innovative software design and industry leading brand. The following years will be a telling period for Apple in terms of whether they are able to continue this innovate product development after the death of company CEO Jobs, but with the corporation’s significant leverage and brand identity there exists plentiful opportunity for the continuation of the success the company has enjoyed in the previous