PEMBAHASAN TRYOUT NASIONAL
MASUK PERGURUAN TINGGI NEGERI
TAHUN 2015
MATEMATIKA DASAR
BAHASA INDONESIA
BAHASA INGGRIS
KEMAMPUAN VERBAL
KEMAMPUAN NUMERAL
KEMAMPUAN FIGURAL
KODE
18
TES KEMAMPUAN DAN
POTENSI AKADEMIK
PEMBAHASAN MATEMATIKA DASAR 18
1. JAWAB: A Pembahasan :
Karena a dan b merupakan akar persamaan kuadrat, maka: a2 + a + 1 = 0
maka 1 = - a2 - a
a2 = - a - 1 kalikan dengan a a3 = - a2 - a
a3=1
berlaku juga untuk b,
b2 + b +1 = 0 maka 1 = - b2 - b
b2 = - b - 1 , kalikan dengan b b3 = - b2 - b
b3 = 1
Maka a6045 + b6045 = a(3(2015)) + b(3(2015)) = 1 + 1 =2 2. JAWAB: D
Pembahasan:
Dari persamaan satu,maka didapatkan jumlah kedua akarnya adalah A+B=-b/a=-2 Dan hasil kali kedua akarnya adalah AB=c/a=-1/2
Persamaan dua, missal akarnya adalah p dan q, maka jumah kedua akarnya adalah p+q=-b/a = 10, dan hasil kali kedua akarnya pq=c/a=√6 .
Maka yang memenuhi adalah (d). (2𝐴2+ 3) +(2𝐵2− 3) = 2(𝐴2+ 𝐵2)
= 2[(𝐴 + 𝐵)2− 2𝐴𝐵] = 10 (2𝐴2+ 3) × (2𝐵2− 3) = 4(𝐴𝐵)2− 6(𝐴2− 𝐵2) − 9
= 4 (14) − 6(𝐴 + 𝐵)(𝐴 − 𝐵) − 9 , (A-B= akarD / a) = 4 (14) − 6(−2)(√6) − 9
= 12(√6) − 8
3. JAWAB: E Pembahasan:
Dari definisi harga mutlak, |𝑥| = 𝑥 untuk ≥ 0 , dan |𝑥| = −𝑥 untuk 𝑥 < 0.
Sedangkan |2-x|=2-x untuk 2-x ≥ 0 atau untuk x ≤ 2,dan |2-x|= - 2 + x untuk 2-x < 0 atau x > 2.
Gabungkan semua syarat diatas didapatkan
x<-1/2
Untuk 0 ≤ x ≤ 2 x+2-x-3 > 0
-1 > 0, jadi untuk interval 0 ≤x ≤ 2 tidak ada yang memenuhi Untuk x > 2
x-2+x -3 > 0 2x > 5 x > 5/2
maka solusi pertidaksamaan adalah x < -1/2 atau x > 5/2.
4. JAWAB: E Pembahasan :
Dengan menggunakan uji salah satu titik pada daerah yang diarsir didapat opsi yang memenuhi x≥0;
y≥0; 2x+3y≤12; -x+y≤2;
5. JAWAB: C Pembahasan :
log(4𝑎 − 14) = log 10 4a-14 = 10 a = 6
log(𝑏 − 4) = log 𝑎 b-4 = 6 b = 10
log𝑥𝑎 = log 𝑏 log𝑥6 = log10 x = 6
6. JAWAB: C Pembahasan :
Diketahui ada 3 nilai dan nilai terendahnya adalah 80 Misal siswa tersebut memiliki nilai 80, 𝑝, 𝑞
Untuk mencari nilai maksimum yang dapat dicapai terlebih dahulu dicari interval nilai siswa tersebut.
Nilai minimum siswa tersebut adalah saat 𝑝 = 𝑞, sehingga nilainya 80, 𝑝, 𝑝. Nilai 𝑝 adalah 80 + 2𝑝
3 = 85
Nilai maksimum siswa tersebut adalah saat 𝑝 = 80, sehingga nilainya 80, 80, 𝑝. Nilai 𝑝 adalah Dengan menggunakan rumus deret tak hingga didapat
Untuk 𝑥 = 270, nilai tan 3𝑥 + cot 3𝑥 = tan(3.270) + cot(3.270) = ∞ Untuk 𝑥 = 315, nilai tan 3𝑥 + cot 3𝑥 = tan(3.315) + cot(3.315) = −2
10. JAWAB: D Pembahasan :
U2.U4 =4
ar.ar3 =4
ar2 =2
2 3 4 5
1 U U U U
U a5r10 =25 =32
11. JAWAB: A
Pembahasan :
Gradien garis singgung sebuah kurva diperoleh dengan mensubstitusi absis titik singgung pada
turunan pertama suatu kurva.
(𝑥)= 𝑦 = 4𝑥− 𝑥2⇒𝑓′(𝑥)= 4−2𝑥
Jadi, gradien garis singgung parabola 𝑦 = 4𝑥 − 𝑥2 di titik (1, 3) adalah : 𝑚 = 𝑓′(1) ⇒𝑚 = 4−2(1) = 4−2 = 2
Sehingga, persamaan garis singgung parabola 𝑦 = 4𝑥− 𝑥2 dengan gradien 𝑚 = 2 di titik A(1, 3) dapat ditentukan dengan :
𝑦−𝑦1= 𝑚(𝑥−𝑥1) ⇒ −3=2(𝑥−1) ⇔𝑦−3=2𝑥−2 ⇔ 𝑦=2𝑥−2+3 ⇔ 𝑦=2𝑥+1
Diketahui bahwa garis singgung parabola 𝑦 = 4𝑥− 𝑥2juga menyinggung parabola 𝑦=𝑥2−6𝑥+𝑘, maka substitusikan 𝑦=2𝑥+1 ke persamaan parabola 𝑦=𝑥2−6𝑥+𝑘, sehingga diperoleh persamaan kuadrat berikut :
Karena garis singgung dan parabola tersebut saling bersinggungan, maka nilai diskriminan dari
persamaan kuadrat tersebut sama dengan nol (𝐷=0). Sehingga diperoleh nilai 𝑘 sebagai berikut : 𝐷=0 ⇒ 𝑏2−4𝑎𝑐 = 0
⇔(−8)2−4(1)(𝑘−1)=0 ⇔ 64−4(𝑘−1)=0 ⇔ 64−4𝑘+4=0 ⇔68−4𝑘=0 ⇔ 68=4𝑘⇔ 17=𝑘
Jadi, nilai dari 2009 + √𝑘 − 1 = 2009 + √17 − 1 = 2009 + √16 = 2013
12. JAWAB: A
Pembahasan :
Persamaan kuadrat Y = 4 + X - X2
Misalkan titik P(Xa, Xa) dan titik Q(Xb, Yb). Konsep titik pada kurva secara aljabar mengatakan bahwa nilai absis dan ordinat dari titik itu harus memenuhi persamaan kurva yang diberikan. Dalam hal ini kita peroleh
Ya= 4 + (Xa) – (Xa)2 dan Yb = 4 + Xb – Xb2 ...(1)
Kemudian, karena titik asal O(0,0) merupakan titik tengah ruas garis AB, maka berdasarkan konsep titik tengah diperoleh
Xa+ Xb= 0 dan Ya + Yb = 0 ...(2)
Agar persamaan (2) dapat digunakan, maka persamaan pertama dan kedua dalam persamaan(1) harus dijumlahkan sehingga diperoleh
Ya + Yb= 8 + Xa + Xb – (Xa2 + Xb2) atau
Xa2 + Xb2 = 8
Sekali lagi kita perlu konsep (Xa + Xb)2 - 2XaXb = Xa2 + Xb2 = 8 Dengan demikian,
-2XaXb = 8 maka XaXb = –4 atau Xb = –4/Xa
Setelah disubstitusi ke bagian pertama dalam persamaan (2) diperoleh Xa = +-2 dan Xb = -+2. Dari sini, kita memperoleh Ya = +-2 dan Yb = -+2. Dengan demikian, titik P(2, 2) dan Q(–2, –2) atau sebaliknya.
Sehingga jarak A ke B yaitu: = akar [(Xb-Xa)2 + (Yb-Ya)2] = akar [(16) + (16)]
13. JAWAB: B Pembahasan :
9P5 = 9! (9−5)! = 15120
14. JAWAB: D
Pembahasan :
Pernyataan bilangan ganjil sama dengan bilangan genap bernilai salah. Pernyataan 1+2 sama dengan bilangan ganjil benar.
Salah maka benar maka nilainya benar.
Dari 5 opsi yang tersedia yang bernilai benar hanya D.
15. JAWAB: B
Pembahasan :
Diketahui : r bola = 3 cm
Misalkan jari2 alas kerucut adalah 𝑥 dan jarak alas kerucut ke pusat bola adalah 𝑦. Maka 𝑦 = √9 − 𝑥2 , sehingga tinggi kerucut = 𝑡 =(√9 − 𝑥2+ 3) cm
V kerucut = 1
3𝜋𝑥2(√9 − 𝑥2+ 3)
Akan dicari titik stasioner, yaitu saat 𝑉′(𝑥) = 0 ⇒ 𝑉′(𝑥) = 0 ⇒ 1
3𝜋𝑥2(− 𝑥
√9−𝑥2 ) + (√9 − 𝑥2+ 3) 2
3𝜋𝑥 = 0 ⇔ 2√9 − 𝑥2+ 6 = ( 𝑥2
√9−𝑥2 ) ⇔ 2(9 − 𝑥2) + 6√9 − 𝑥2=𝑥2 ⇔ 𝑥4− 8𝑥2= 0 ⇔ 𝑥 = 0 𝑉 𝑥 = 2√2 , 𝑥 = 0 tidak memenuhi. Sehingga :
Vmaks kerucut = 1
PEMBAHASAN BAHASA INDONESIA 18
16. Jawab: C
Opini, ialah pendapat, pikiran, atau pendirian seseorang tentang sesuatu atau dapat menjawab pertanyaan bagaimana. Pernyataan-pernyataan yang merupakan opini adalah Menurut Tom Kennedy, permen lollipop yang baik dihasilkan dari perpaduan 60% sirup jagung dan 40% gula kemudian dipanaskan pada suhu 310 derajat fahrenheit.
17. Jawab: E
Pernyataan berikut yang tidak relevan dengan maksud paragraf di atas adalah Waduk Jatiluhur digunakan untuk olahraga ski air, kano, dayung, perahu naga dan lain-lain karena tidak sesuai dengan kalimat utama Waduk Jatiluhur merupakan salah satu tempat wisata di Jawa Barat yang patut dikunjungi. Jawaban A, B, C, dan D berhubungan dengan kalimat utama karena koheren (sesuai) dengan masalah yang dibicarakan yaitu penjelasan.
18. Jawab: A
Kalimat yang termasuk kalimat efektif adalah kalimat A, sedangkan kalimat yang lain seharusnya B) Tempat wisata di Jawa Timur terdiri dari wisata religi, wisata pemandangan alam dan wisata budaya, dan wisata balai konservasi pelestarian fauna langka. C) Kegagalan proyek itu karena perancangan tidak baik dan pengawasan yang kurang cermat. D)Meskipun negara itu penghasil kapas nomor satu dunia, harga tekstilnya sangat tinggi. E) Pendidikan antikorupsi akan dilaksanakan segera di seluruh jenjang pendidikan mulai tahun ajaran baru 2012/2013 (tidak ada P = dilaksanakan).
19. Jawab: A
Kerangka Karangan adalah rencana garis besar karangan berdasarkan tingkat kepentingannya, pokok- pokok yang akan dibicarakan, pedoman bagi pembaca untuk mengetahui isi suatu karangan. Kerangka karangan yang paling runtut berdasarkan pola deduktif adalah pentingnya pembiasaan berperilaku tertib lalu lintas, manfaat pembiasaan berperilaku tertib lalu lintas, bentuk pembiasaan berperilaku tertib lalu lintas, sasaran pembiasaan berperilaku tertib lalu lintas, langkah pembiasaan berperilaku tertib lalu lintas.
20. Jawab: E
PEMBAHASAN BAHASA INGGRIS 18
31.
The nomination of the Vice President candidates takes place...
(A) on the same day as that of the President’s candidate
(B) on the day preceding that of the President’s candidate
(C) on the day following that of the President’s candidate
(D) either (b) or (c)
(E) on Sunday
32. Harry Truman is mentioned here to show that...
(A) a president may die while in office
(B) a vice President is considered equally important as a President
(C) a vice President has assumed new duties and importance
(D) all of the above
(E) none of the above
33. How are the requirements for the Vice President candidate and the President
candidate?
(A) the same
(B) completely different
(C) the same except for one requirement
(D) both (b) and (c)
(E) the difference
THE ELECTION OF VICE PRESIDENT
After the convention chooses the Presidential candidate, the nominee for Vice President is selected the next day. This is usually accomplished on the first ballot. The Vice President is the only public official in the United States, other than the President, who is elected by all the states. The
names of a party’s candidates for President and Vice President are placed together on the ballot. Thus,
a vote for one is a vote for the other. Usually the Presidential candidate has a great authority in
deciding who the Vice President candidate will be as the two men will have to work closely together. The constitutional requirements for the Vice President are practically the same as those for the President. However, he may not come from the same state as President.
In recent years the Vice President has assumed new duties and importance. Since several American Presidents have died in office, it is believed that the candidate for Vice President should be considered in the same light as the candidate for President. In 1945, when Franklin D. Roosevelt died,
34. What does the text tell us about?
(A) all materials including ice cream have sense of heat
(B) the molecules in the hot chocolate and the cold ice-cream move very fast
(C) the molecules in cool water can move faster than molecules in other things
(D) swallowing fast-moving molecules is good for children
(E) the
molecules in cool materials can’t move freely
35. When you swallow
those fast-moving
molecules they give you some of their heat
energy
—
they make you feel warm. (par. 3). The italic phrase can he meant as
(A) the molecules
(B) the molecules that are in the ice-cream
(C) the molecules that in cool water
(D) the molecules in the hot chocolate
(E) the molecules in the ice-cream and cool water
Which is hottest—ice cream, a glass of cool water or a streaming cup of chocolate? The
chocolate is hottest of course. But it wouldn’t be quite right to say that the ice-cream and the water
aren’t hot at all. Each one has some heat. All things have heat, even very cold things. But some things
have more heat than the others. So when we use words like hot and cold we aren’t really talking
about two different ideas. We are simply telling how much energy something has. The molecules in the hot chocolates are moving very fast, they have a lot of energy. When you swallow those fast moving molecules they give you some of their heat energy. They make you feel warm.
The molecules in the cold ice-cream are moving very slowly, but they are moving! They have a small amount of heat energy. Because your body has much more heat energy that the ice cream
36. What is the topic of the text above?
(A) Long-life span
(B) Survival
(C) youth
(D) Old age span.
(E) Health secrets
37. Which of the following is true about the information in the text?
(A) Gene quality contributes much more to life
(B) Okinawa people look younger at their actual
(C) All alcoholic drinks decrease life expectation.
(D) All of Dr. Perls' subjects are self-reliant.
(E) Superold people normally can exceed 100.
Scientists are as obsessed with the question of why the superold survive and thrive as Ponce de Leon was to find the Fountain of Youth. They want to understand why the Japanese islands of Okinawa are home to the world's largest population of centenarians, with almost 600 of its 1.3 million
inhabitants living into their second century-many of them active and looking decades younger than their actual years. Like weekend visitors on the summer ferry to Martha's Vineyard, scientists and sociologists block the boats to Sardinia and Nova Scotia, Canada, to see why those craggy locales hide vast clusters of the superold. As well as studying these populations intensively to unlock their secrets, scientists have also taken a hard look at the very old in the U.S., most notably in the New England Centenarian Study. led by Dr. Thomas Perls, a geriatrician at Boston University. While the very old are
happy to offer homespun explanations for 10 their longevity-HI never took a drink"; "I drank a shot of whiskey every day"-experts are trying to unravel and understand the biological factors that allow some people to reach while others drop off in their 70s or 80s. Researchers are particularly interested in determining which factors allow up to 30% of those who
reach 100 to do so in sufficient mental and physical health: a whopping 90% of centenarians, according
to Perls. remain functionally independent up to age 92.
It is pretty obvious even to nonscientists that how you get there depends partly on the genes you are born with and partly on lifestyle-what and how much you eat, where you live and what types of stress and trauma you experience. How much depends on each factor, though, was unknown until Swedish scientists tackled the problem in 1998. They did it by looking at the only set of people who share genes but not lifestyle: identical twins who were separated at birth and reared apart. If genes
38. ln writing the text, the writer's tone could be best described as ...
(A) conservative.
(B) informative.
(C) persuasive.
(D) descriptive.
(E) evaluative
39. ln the text above the writer deals with a topic on ...
(A) prevalence of autism among children.
(B) possible biological causes of autism.
(C) research findings on mental disorders.
(D) maternal age and autism in children.
(E) negative effects of delayed pregnancy.
It is common knowledge that as women get older, pregnancy becomes a riskier enterprise. Advanced maternal age is linked to a number of developmental disorders in children, such as Down's syndrome. Now, a study has confirmed that older mothers are more likely to give birth to a child with autism, too. The authors of the epidemiological study, published February 8 in Autism Research,
examined the parental age of more than 12,000 children with autism and nearly five million"control" children between 1990 and 1999, all living in California. The researchers found that mothers over 40 had a 51 percent higher risk of having a child with autism than mothers 25 to 29, and a 77 percent higher risk than mothers under 25.
Autism-a developmental disorder characterized by impaired social interactio" and communication-appears to be on the rise. The U.S. Centers for Disease Control and Prevention now
estimates that as many as one in 110 children in the U.S. has an autistic spectrum disorder-a group of developmental disorders including autism, Asperger's syndrome and pervasive developmental disorder. The prevalence of autistic spectrum disorders in California in 2007 was 12 times that from 1987, representing an average annual growth of 13 percent, according to a report from the California Department of Developmental Services. Only a fraction of these extra cases can be explained by changes to diagnostic criteria and earlier diagnoses.
Maternal age is also increasing in the U.S. A California-based study reported a three-fold increase in the number of births to women aged 40 to 44 between 1982 and 2004. But this trend toward delayed childbearing accounted for less than 5 percent of the total increase in autism diagnoses in California over the decade, according to the study-a finding that surprised Janie Shelton, a doctoral student in University of California, Davis's Department of Public Health Sciences and the study's lead author. "I would have expected to see more of a contribution, because age is a risk factor and women are having kids later," she says. Earlier work had suggested that both maternal and
40. It can be concluded from the text that ...
(A) a big age difference of parents of 40 years or beyond may result in autism.
(B) several mental disorders can be prevented by having kids earlier.
(C) women today show a general trend in delaying pregnancy.
(D) the paternal age only partly explains the case of mental disorders among children.
(E) the case of autism among children remains a mystery among scientists.
41. From the information in the first and second paragraphs, it can be inferred that ...
(A) developmental disorders in children are close to delayed pregnancy.
(B) modified diagnosis criteria can detect many cases of autism.
(C) many of the children in the US obviously suffer from autism.
(D) asperger's syndrome is not related in any way to autism.
(E) studies on autism have not successfully revealed its causes.
42. Which of the following best describes the author's purpose in this study?
(A) To reveal that the case of autism among children is prevalent
(B) To analyse how delayed pregnancy brings about
autism
(C) To make the readers aware of the consequence of delayed pregnancy
(D) To refute a common misconception about the cause of autism
43. From the second paragraph, it can be inferred that....
(A) Wesley is a successful prestigious school.
(B) the students at Wesley are from the haves.
(C) the students at Wesley are mostly colored.
(D) the colored students usually perform better.
(E) wesley curriculum is adopted by other schools
44. ln writing the text, the writer's tone could be best described as
(A) persuasive
(B) descriptive
(C) informative
(D) evaluative
(E) conservative
Many modern educational experts claim that teaching facts and academic skills is less
important than achieving other social objectives. For some liberals, the schools must first change attitudes or provide nurturing in place of failed families or help establish equality and social justice. For some conservatives, the school must first prepare kids for the workplace by molding them into supple corporate citizens, while others want the focus to be on family values, a competitive spirit, or other social or behavioral objectives. But the idea of simply educating kids seems to have taken a backseat to most educational experts and administrators.
They miss the point that kids with real academic skills, especially skills in reading, writing, and
mathematics, are more likely to overcome social barriers, more likely to have genuine self esteem, and most likely to be genuinely prepared for the challenges of life and the workplace. By emphasizing so many things besides a genuine, classical education, tile educational establishment tends to soli our kids short and bring about many of the problems they claim to be solving consider the case of Wesley Elemontary School in Houston. According to Richard Nadlor in the article, "Failing Grade", Wesley has all the demographic markers of a school bound for failure. Over 80% of the students qualify for
subsidized lunches, and nearly all are minorities (92% black, 7% Hispanic). Yet it ranks among the best schools of Houston, with first-graders placing at the 82nd percentile level in reading tests which is 50 points higher than the expected level for similar at-risk schools.
What has made Wesley so successful? The answer is classical education in the form of Direct Instruction curriculum designed by Siegfried Engelmann, an example of the much ridiculed
45. Which of the following best reflects the author's opinion about schools?
(A) Teaching social skills is more important than academic skills
(B) Schools must be able to change the attitude of the students.
(C) Teaching academic skills is more important than social skills
PEMBAHASAN SOAL TPA PAKET 18
BAGIAN TPA SINONIM
46. A. EKLIPS = GERHANA
47. B. MUKJIZAT = BARAKAH
48. B. DEDIKASI = PENGABDIAN
49. C. PROVOKASI = PANCINGAN
50. E. DEHIDRASI = PENYUSUTAN AIR
ANTONIM
51. D. GEGAI >< KUAT
52. E. CANGGIH >< SEDERHANA
53. A. KONVEKS >< KONKAF
54. D. PERINTIS >< PEWARIS
55. D. TINGGI >< RENDAH
ANALOGI 56. E.
SEKUMPULAN BUNGA DALAM BUKET = SEKUMPULAN KERTAS DALAM BUKU
57. C.
RUMPUT ADA DI LAPANGAN = BINTANG ADA DI ANGKASA
58. D.
ULAT : KEPOMPONG : KUPU-KUPU = BAYI : KANAK-KANAK : REMAJA
59. C.
TUKANG MENGGUNAKAN GERGAJI DAN PALU = MONTIR MENGGUNAKAN OBENG DAN TANG
60. E.
BURUNG TERBANG DI UDARA = IKAN BERENANG DI LAUT
NUMERIKAL 61. C.
1/9 , 1/3 , 1, 3, 9, , 27 , 81, 243
Merupakan deret geometri dengan rasio 3
62. D.
18, 9, 3, 8, 4, 2, 7, 31
𝟐
Merupakan deret dengan pola dibagi 2, diakarkan, ditambah 5 dan seterusnya
63. D.
10, 30, 32, 16, 48, 50, 25, 75
Merupakan deret dengan pola dikalikan 3, ditambah 2, dibagi 2, dan seterusnya 64. B.
15, 10, 5, 20, 15, 10, 40, 35
65. B.
A, B, D, B, B, D, C, B, D, D, B, D, E, B Merupakan deret dengan pola sebagai berikut A, B, D, B, B, D, C, B, D, D, B, D, E, B
Berlaku hubungan komutatif sehingga M = N 72. B.
“Menyusul” berarti menempuh jarak yang sama. Misal waktu yang dibutuhkan truk = T
Maka waktu yang dibutuhkan sedan = T-1/2 Sehingga memenuhi persamaan GLB
Misal jari- jari tabung B adalah R. dan Tinggi Tabung B adalah T Volume A/ Volume B = π. (RA)2 . TA/ π.(R)2.T
Volume A/ Volume B = π.(R2/4).4T / π.R2.T
Sehingga Volume A : Volume B = 1 : 1 76. B.
