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MTK TKA Flashcards

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1
Q

Kisi-kisi TKA Matematika

A

topik utama ::: Algebra, Aritmetika, Fungsi, Trigonometri, Geometri (bangun datar & ruang), Peluang & Statistika, Kalkulus dasar (limit/derivatif sederhana), Barisan & deret

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2
Q

Rumus luas lingkaran

A

L = πr². (π = 3.14159 atau 22/7)

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3
Q

Contoh: Luas lingkaran r=7 cm

A

L = πr² = π×7² = 49π ≈ 153.94 cm²

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4
Q

Rumus keliling lingkaran

A

K = 2πr atau K = πd

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5
Q

Rumus luas segitiga

A

L = 1/2 × alas × tinggi

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6
Q

Contoh: Luas segitiga a=10 t=6

A

L = 1/2×10×6 = 30

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7
Q

Teorema Pythagoras

A

Untuk segitiga siku-siku: a² + b² = c², c = hipotenusa

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8
Q

Contoh Pythagoras a=3 b=4

A

c = √(3²+4²) = √25 = 5

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9
Q

Rumus luas persegi

A

L = s²

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10
Q

Rumus volume kubus

A

V = s³

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11
Q

Rumus luas permukaan kubus

A

L_perm = 6s²

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12
Q

Rumus volume tabung

A

V = πr²h

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13
Q

Rumus luas permukaan tabung

A

L = 2πr(h + r)

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14
Q

Rumus trigonometri dasar

A

sinθ = o/h, cosθ = a/h, tanθ = o/a

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15
Q

Identitas trigonometri dasar

A

sin²θ + cos²θ = 1

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16
Q

Rumus peluang sederhana

A

P(A) = jumlah kejadian A / jumlah ruang sampel

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17
Q

Rumus rata-rata aritmetika

A

μ = (x₁ + x₂ + … + xₙ)/n

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18
Q

Rumus deret aritmetika

A

Sₙ = n/2 (2a₁ + (n-1)d)

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19
Q

Rumus deret geometri

A

Sₙ = a₁(1 - rⁿ)/(1 - r)

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20
Q

Contoh deret: a1=3, d=2, n=5

A

S5 = 35

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21
Q

Rumus perubahan persen

A

Nilai akhir = nilai awal × (1 ± persen/100)

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22
Q

Rumus limit sederhana

A

lim x→a f(x) = L

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23
Q

Tips hafalan rumus matematika

A

Buat mindmap tiap topik, hafal 10 rumus inti/minggu, latihan 5 soal per rumus

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24
Q

Kesalahan umum

A

Lupa satuan, tanda negatif, urutan operasi

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25
Contoh soal: 5x - 3 = 2x + 9
x = 4
26
Soal cepat: 2x² - 8 = 0
x = ±2
27
Rumus luas segitiga sama sisi
(√3/4)a²
28
Contoh: sisi 6
9√3 ≈ 15.6
29
Kisi-kisi fungsi
Domain, range, komposisi, invers
30
Contoh fungsi: f(x)=2x+1, g(x)=x², f(g(2))
2(4)+1=9
31
Kisi-kisi peluang
Frekuensi relatif, kombinasi, aturan perkalian
32
Rumus kombinasi
C(n,r)=n!/(r!(n−r)!)
33
Contoh: C(5,2)
10
34
Kisi-kisi statistika
Mean, median, modus
35
Contoh: 2,4,6,8
mean=5
36
Kisi-kisi utama
Aritmetika, Aljabar, Fungsi, Trigonometri, Geometri Datar & Ruang, Barisan & Deret, Logika, Statistika, Peluang, Limit, Persamaan, Pertidaksamaan, Transformasi, Matriks & Vektor.
37
Rumus persentase
persen = (bagian / total) × 100%
38
Rumus diskon
harga_akhir = harga_awal × (1 - diskon%)
39
Rumus bunga tunggal
B = (P × i × t)/100
40
Rumus bunga majemuk
A = P(1 + i/100)^t
41
Rumus rata-rata (mean)
μ = (Σx)/n
42
Median
Nilai tengah data setelah diurutkan
43
Modus
Nilai yang paling sering muncul
44
Rumus pembulatan nilai
ke puluhan terdekat jika satuan ≥5 naik
45
Rumus kuadrat umum
ax² + bx + c = 0
46
Rumus akar-akar persamaan kuadrat
x = (-b ± √(b² - 4ac)) / 2a
47
Diskriminan
D = b² - 4ac → D>0 dua akar nyata, D=0 satu akar, D<0 tak nyata
48
Jumlah akar
x₁ + x₂ = -b/a
49
Hasil kali akar
x₁ × x₂ = c/a
50
Rumus faktorisasi cepat
a² - b² = (a + b)(a - b)
51
Rumus (a + b)²
a² + 2ab + b²
52
Rumus (a - b)²
a² - 2ab + b²
53
Rumus (a + b)(a - b)
a² - b²
54
Pertidaksamaan kuadrat
cari akar lalu uji interval tanda
55
Fungsi linear
f(x) = ax + b
56
Gradien garis lurus
m = (y₂ - y₁)/(x₂ - x₁)
57
Persamaan garis melalui dua titik
y - y₁ = m(x - x₁)
58
Fungsi kuadrat
f(x) = ax² + bx + c → puncak di (−b/2a, f(−b/2a))
59
Transformasi fungsi
translasi, refleksi, rotasi, dilatasi
60
Komposisi fungsi
(f ∘ g)(x) = f(g(x))
61
Invers fungsi
f⁻¹(x) → g(f(x)) = x
62
Luas segitiga
½ × alas × tinggi
63
Luas persegi
s²
64
Luas persegi panjang
p × l
65
Luas jajar genjang
alas × tinggi
66
Luas trapesium
½ × (jumlah sisi sejajar) × tinggi
67
Luas lingkaran
πr²
68
Keliling lingkaran
2πr
69
Luas belah ketupat
½ × d₁ × d₂
70
Keliling belah ketupat
4s
71
Luas layang-layang
½ × d₁ × d₂
72
Teorema Pythagoras
a² + b² = c²
73
Rumus jarak dua titik
√((x₂−x₁)² + (y₂−y₁)²)
74
Rumus titik tengah
((x₁+x₂)/2, (y₁+y₂)/2)
75
Volume kubus
s³
76
Volume balok
p × l × t
77
Volume prisma
Luas alas × tinggi
78
Volume limas
⅓ × luas alas × tinggi
79
Volume tabung
πr²t
80
Volume kerucut
⅓πr²t
81
Volume bola
4/3 πr³
82
Luas permukaan bola
4πr²
83
Diagonal ruang kubus
s√3
84
Diagonal bidang kubus
s√2
85
Perbandingan sudut siku-siku
sin = o/h, cos = a/h, tan = o/a
86
Hubungan penting
sin²θ + cos²θ = 1
87
Rumus sudut jumlah
sin(A ± B) = sinAcosB ± cosAsinB
88
Rumus cos(A ± B)
cosAcosB ∓ sinAsinB
89
Rumus tan(A ± B)
(tanA ± tanB)/(1 ∓ tanA tanB)
90
Rumus luas segitiga trigonometri
½ ab sinC
91
Rumus tinggi segitiga trigonometri
h = a sinB = b sinA
92
Rumus identitas dasar
cot = 1/tan, sec = 1/cos, csc = 1/sin
93
Barisan aritmetika
Un = a + (n − 1)d
94
Jumlah n suku aritmetika
Sn = n/2(2a + (n − 1)d)
95
Barisan geometri
Un = a × r^(n − 1)
96
Jumlah n suku geometri
Sn = a(1 − rⁿ)/(1 − r)
97
Jumlah tak hingga (|r|<1)
S∞ = a/(1 − r)
98
Negasi (¬p)
kebalikan pernyataan p
99
Konjungsi (p ∧ q)
benar jika keduanya benar
100
Disjungsi (p ∨ q)
benar jika salah satunya benar
101
Implikasi (p → q)
salah hanya jika p benar dan q salah
102
Rumus himpunan
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
103
Rumus dasar
P(A) = n(A)/n(S)
104
P(A atau B)
P(A) + P(B) − P(A∩B)
105
P(A dan B)
P(A) × P(B) jika independen
106
Permutasi
P(n,r) = n!/(n − r)!
107
Kombinasi
C(n,r) = n!/(r!(n − r)!)
108
Mean
μ = Σx/n
109
Median
tengah dari data terurut
110
Modus
data terbanyak muncul
111
Kuartil Q1, Q3
pembagi data 25% dan 75%
112
Simpangan baku (σ)
√(Σ(x−μ)²/n)
113
Rumus limit dasar
lim x→a k = k
114
lim x→a x
a
115
lim x→a [f(x) ± g(x)]
L ± M
116
Turunan fungsi polinomial
d/dx (xⁿ) = n xⁿ⁻¹
117
Turunan hasil kali
(uv)' = u'v + uv'
118
Turunan hasil bagi
(u/v)' = (u'v − uv')/v²
119
Turunan trigonometri dasar
(sinx)' = cosx, (cosx)' = −sinx, (tanx)' = sec²x
120
Kesalahan umum
Lupa substitusi tanda negatif, lupa prioritas operasi, tidak konversi satuan.
121
Tips hafalan cepat
Hafal per topik (10 rumus per hari), latihan substitusi sederhana.
122
Rumus keliling bangun ruang dasar
Kubus 12s, Balok 4(p+l+t)
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