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Soal-Soal dan Pembahasan SNMPTN Matematika IPA Tahun Pelajaran 2010/2011 Tanggal Ujian: 01 Juni 2011 1. Diketahui vektor u = (a, -2, -1) dan v = (a, a, -1). Jika vektor u tegak lurus pada v , maka nilai a adalah ... A. -1 B. 0 C. 1 D. 2 E. 3 Jawab: Vektor: vektor u tegak lurus pada v maka u . v = 0 u = −2 , v = −1 −2 . −1 −1 (a – 1) (a-1) = 0 maka a = 1 −1 = a2 – 2a + 1 = 0 (a - 1)2 = 0 Jawabannya adalah C 2. Pernyataan berikut yang benar adalah ... A. Jika sin x = sin y maka x = y B. Untuk setiap vektor u , v dan w berlaku u . ( v . w ) = ( u . v ). w C. Jika b f ( x) dx = 0, maka a D. Ada fungsi f sehingga E. 1 – cos 2x = 2 cos2 x f ( x )= 0 Lim f(x) ≠ f(c) untuk suatu c xc www.belajar-matematika.com - 1 Jawab: Trigonometri, vektor, integral, limit A. Ambil nilai dimana sin x = sin y sin α = sin (1800 – α ) ambil nilai α = 600 sin 600 = sin 1200 ; tetapi 600 ≠ 1200 Pernyataan SALAH B. Operasi u . ( v . w ) tak terdefinisi karena v . w = skalar, sedangkan u = vektor vektor . skalar = tak terdefinisi Pernyataan SALAH C. Ambil contoh cari cepat hasil dimana b f ( x) dx = 0 ; a 1 Didapat b = 1 dan a = -1 maka f(x)= x x dx = 0 1 terbukti : f(x) = x bukan f(x) = 0 x2 | Pernyataan SALAH D. Ambil contoh f(x) = Lim xc f(x) = Lim x 1 ( ( = ( ( ) ( )( ) = ) ( ) Lim f(x) ≠ f(c) 2 ≠ 1 xc ) ( )( ) = ) ( ) =2 Pernyataan BENAR E. 1 – cos 2x = 1 – ( 2cos2 x – 1) = 1 + 1 - 2cos2 x = 2 - 2cos2 x = 2 ( 1 – cos2 x) Pernyataan SALAH Jawabannya adalah D www.belajar-matematika.com - 2 = (1 – 1) = 0 3. Luas daerah di bawah y = -x2 +8x dan di atas y = 6x - 24 dan terletak di kuadran I adalah.... a. ∫ (− b. ∫ (− c. ∫ (− +8 ) +8 ) +8 ) d. ∫ (6 − 24) e. ∫ (6 − 24) Jawab: Integral: +∫ ( + ∫ (− + ∫ (− + ∫ (− + ∫ (− − 2 − 24) + 2 + 24) + 2 + 24) +8 ) +8 ) kuadran I titik potong kedua persamaan : y1 = y2 -x2 +8x = 6x-24 -x2 +8x - 6x+24 = 0 -x2 +2x + 24 = 0 x2 -2x - 24 = 0 (x - 6) (x+4)0 x = 6 atau x = -4 karena di kuadran I maka yang berlaku adalah x = 6 y = 6.6 – 24= 12 berada di titik (6,12) www.belajar-matematika.com - 3 L = ∫ (− = ∫ (− +8 ) +8 ) + ∫ ((− + ∫ (− Jawabannya adalah B + 8 ) − (6 − 24)) + 2 + 24) 4. sin 350 cos 400 - cos 35 sin 400 = A. cos 50 B. sin 50 C. cos 950 D. cos 750 E. sin 750 Jawab: Trigonometri: Pakai rumus: sin (A - B) = sin A cos B - cos A Sin B A= 350 ; B = 400 = sin (350 - 400) = sin -50 Cos (90 0 - ) = sin rumus Cos (90 0 - (-50) ) = sin -50 = -50 Cos 950 = sin -50 Jawabannya adalah C 5. Diketahui g(x) = ax2 – bx + a – b habis dibagi x – 1. Jika f(x) adalah suku banyak yang bersisa a ketika dibagi x – 1 dan bersisa 3ax + b2 + 1 ketika dibagi g(x), maka nilai a adalah...... A. -1 B. -2 C. 1 D. 2 Jawab: Suku Banyak: g(x) = ax2 – bx + a – b habis dibagi x – 1 g(1) = 0 g(1) = a . 1 – b .1 + a – b = 0 =a–b+a–b=0 2a – 2b = 0 2a = 2b a = b karena a = b maka: g(x) = ax2 – ax + a – a = ax2 – ax www.belajar-matematika.com - 4 E. 3 f(x) dibagi dengan f(x-1) sisa a f(1) = a f(x) dibagi dengan g(x) sisa 3ax + b2 + 1 f(x) dibagi dengan ax2 – ax sisa 3ax + b2 + 1 f(x) dibagi dengan ax(x – 1) sisa 3ax + b2 + 1 teorema suku banyak: Jika suatu banyak f(x) dibagi oleh (x- k) akan diperoleh hasil bagi H(x) dan sisa pembagian S f(x) = (x- k) H(x) + S f(x) dibagi dengan ax(x – 1) sisa 3ax + b2 + 1 f(x) = ax (x - 1) H(x) + (3ax + b2 + 1) substitusikan nilai nol dari pembagi yaitu x = 0 dan x = 1 dari ax (x - 1) ambil x = 1 untuk x = 1 f(1) = a . 1 (1 – 1) H(0) + 3a.1 + b2 + 1 a = 0 + 3a + b2 + 1 diketahu a = b, masukkan nilai a = b a = 3a + a2 + 1 a2 + 2a + 1 = 0 (a+1)(a+1) = (a+1)2 = 0 a = -1 Jawabannya adalah A 6. Rotasi sebesar 450 terhadap titik asal diikuti dengan pencerminan terhadap y = -x memetakan titik (3,4) ke .... A. √ B. − Jawab: ,√ √ ,√ C. D. √ √ ,−√ ,−√ E. − Transformasi Geometri: cos Rotasi sebesar 450 terhadap titik asal = sin sin cos 0 1 pencerminan terhadap y = -x 1 0 www.belajar-matematika.com - 5 √ ,√
Historic Sites Locations #1 Victorian Village Memphis, TN 38103 (901) 526-1469 In the area of Adams Avenue in Memphis, a number of landmark 19th century homes have been saved from destruction by interested citizens. The Boyd-Massey-Maydwell house likely is the oldest of those pictured below. A neo-classic cottage at 664 Adams, it is owned by the City of Memphis and used by the City Beautiful Commission. The Harsson-Goyer-Lee house at 690 Adams originally was a small four-square cottage built by William Harsson, a lath mill operator. It was expanded in 1855 by his son-in-law, Charles Wesley Goyer, who added the present threestory front in 1871. The house was sold in 1890 to steamboat empire owner James Lee Jr. whose Mallory-Neely house, 1854-1883 Mollie Fontaine Taylor house, 1886 Elias Lowenstein house, 1890 Harsson-Goyer-Lee house, 1848-1873 Woodruff-Fontaine house, 1870 529 State of Tennessee daughter later began the James Lee Memorial Academy of Art which flourished there until the City of Memphis relocated the school to Overton Park. Currently owned by the City of Memphis, the Mallory-Neely house at 652 Adams, a Tuscan villa, first was owned by Isaac Kirtland and later by Benjamin Babb who added the second story and sold to James Columbus Neely in 1883. The French Victorian Woodruff-Fontaine house at 680 Adams Boyd-Massey-Maydwell house, 1817-1849 was build by architects Edward Culliott Jones, of Charleston, and Mathias Baldwin, of Memphis, for Amos Woodruff who, in 1883, sold to Noland Tennessee Blue Book Historic Sites Fontaine, the third-wealthiest cotton factor in the country. The house later was part of the James Lee Academy of Art and currently is open to the public for tours. The Victorian Mollie Fontaine Taylor house was built by Noland Fontaine as a wedding gift for his daughter at 679 Adams (directly across the street from the Woodruff-Fontaine). The Elias Lowenstein house is located at Jefferson and Manassas Streets. #2 Hunt/Phelan House 533 Beale Street Memphis, TN 38103 (901) 525-8225 This 16-room reddish-brick house in the Federal style was built in two stages, the first in 1830 by George H. Wyatt. The second stage, circa 1851, added a two-story kitchen and service wing and a two-story porch. In the early months of the Civil War, the house served as headquarters for Confederate General Leonidas Polk. After the Battle of Shiloh, Union General Ulysses S. Grant used the house, planning the siege of Vicksburg in the parlor. The mansion also served as a Union hospital from 1863-1865. Although unlikely, it has been rumored that a The Hunt/Phelan House, once “a treasure trove” of 19th century tunnel under the house was part of the undermagnificence ground railroad through which slaves escaped and boarded boats for Illinois. At one time a schoolhouse was located behind the mansion for the Phelan children and the family’s slave children and was the first school known to have educated blacks in Memphis. In later years the house was occupied by northern teachers sent to the South to educate newly freed slaves. #3 Graceland 3734 Elvis Presley Boulevard Memphis, TN 38186-0508 (901) 332-3322 (800) 238-2000 www.elvis.com/graceland/ Home of world-famous singer and movie star Elvis Presley, Graceland was built circa 1940 by the former Ruth Fraser Brown and her husband, Dr. Thomas David Moore. The 20-room mansion was named Graceland after Mrs. Moore’s aunt, Grace Toof, whose family had built a cottage on the site earlier. Elvis bought the house in 1957, 10 years after he moved to Memphis. During the 1950s the “King” became a national and international hero of young people Graceland, home of Elvis Presley 530 Locations Tennessee Blue Book as rock ‘n’ roll’s biggest star. Eventually, he sold more than 500 million records and had more gold records (28) than anyone before him, and also made 33 movies. Guided tours of the home, featuring the trophy room, Hall of Gold, automobile collection, touring bus, and Conair jet (the “Lisa Marie”), also include the Meditation Garden where Elvis and his parents are buried. Elvis Presley died in 1977 but his fame lives after him as thousands visit his home each year. #4 Chucalissa Prehistoric Indian Village 1987 Indian Village Drive T. O. Fuller State Park Memphis, TN 38109 (901) 785-3160 Hundreds of years before Europeans came to America, Indians flourished along the eastern shore of the Mississippi River. These ancient peoples hunted; made tools of bone, stone, and wood; were capable farmers; and lived in thatch-roofed homes. They built earthworks and worshipped the sun. Chucalissa is a working reconstruction of a 1,000-yearold Indian village that flourished here, with grass thatched huts, a temple, and a ceremonial burial ground. A museum at the site helps visitors understand its history. The name means “house abandoned” or “deserted town” and was chosen for the site by its rebuilders. The original peoples were encountered by DeSoto in 1541, but had deserted the town by 1673 when the French arrived. Today Choctaw Indians live on the site and demonstrate Indian crafts. The rebuilt village is operated by the University of Memphis. Thatch-roofed structure at Chucalissa Prehistoric Indian Village...