Quiz 1:   Fullscreen Mode Teori dan Rumus Lingkaran Dasar SMA LINGKARAN DASAR LEVEL SMA 1. Pengertian Lingkaran Lingkaran adalah tempat kedudukan titik-titik yang jaraknya sama dari suatu titik tertentu yang disebut pusat lingkaran. Jarak yang sama ini disebut jari-jari lingkaran. O r 2. Unsur-Unsur Lingkaran 2.1 Jari-jari (r) Jari-jari lingkaran adalah jarak dari pusat lingkaran ke titik pada lingkaran. 2.2 Diameter (d) Diameter adalah garis lurus yang menghubungkan dua titik pada lingkaran dan melalui pusat lingkaran. Diameter adalah dua kali jari-jari. d = 2r 2.3 Busur Lingkaran Busur lingkaran adalah garis lengkung yang merupakan bagian dari lingkaran. Busur lingkaran dibedakan menjadi: Busur kecil (busur...

Kalkulator Luas Segitiga Kalkulator Luas Segitiga Nilai a = Nilai b = Nilai c = Hitung Luas Segitiga Hasil Perhitungan:

Quiz 1:   Fullscreen Mode Quiz 2:   Fullscreen Mode      SASMO: Singapore and Asian Schools Math Olympiad                    SASMO: Singapore and Asian Schools Math Olympiad          The Singapore and Asian Schools Math Olympiad (SASMO) is one of the largest and most prestigious mathematics competitions in Asia, attracting over 35,000 participants from 38 countries in recent years. Established in 2006, SASMO aims to discover, encourage, and challenge mathematically gifted students from Singapore and other Asian countries.          Overview of SASMO          SASMO is organized by the Singapore International Math Contests Centre (SIMCC) and supported by non-profit foundations such as the Scholastic Trust Singapore (STS) and the SASMO Advisory Council (SAC). The competition is designed to stretch the untapped thinking potential of students, enhancing their performance in school mathematics and developing higher-order thinking skills (HOTS).              ...

Quiz 1:   Fullscreen Mode Teori Lengkap Garis dan Sudut 1. Konsep Dasar Garis Dalam geometri Euclidean, garis didefinisikan sebagai himpunan titik-titik yang memanjang tak terbatas ke kedua arah. Teori fundamental menyatakan: Melalui dua titik berbeda hanya dapat dibuat satu garis lurus [1] 2. Relasi Antar Garis Pada bidang datar, dua garis dapat memiliki tiga jenis hubungan: - Sejajar: Tidak pernah berpotongan - Berpotongan: Bertemu di satu titik - Berimpit: Semua titik sama [2] 3. Garis Bersilangan Konsep unik dalam geometri 3D: Dua garis bersilangan jika tidak sejajar dan tidak berpotongan [3] 4. Anatomi Sudut Sudut = Dua garis bertemu di titik pangkal [4] 5. Penulisan Sudut ∠ABC = ∠CBA = ∠B Titik tengah (B) adalah vertex [5] 6. Sistem Besaran Sudut 1° = 60' = 3600" \(1^{\circ}=60^{\prime}=3600^{\prime\prime}\) [6] 7. Klasifikasi Sudut Sudut siku...

Quiz 1:   Fullscreen Mode Geometric Transformations Theory 1. Reflections Definition: Mirror image over a line Key Formulas: - Vertical line x=a: (x,y) → (2a-x,y) - Horizontal line y=b: (x,y) → (x,2b-y) - Line y=x: (x,y) → (y,x) - Line y=-x: (x,y) → (-y,-x) 2. Rotations Definition: Turning around a center point Rotation Matrices: 90° clockwise: \(\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\) 180° rotation: \(\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}\) 3. Translations Definition: Sliding without rotation Vector Notation: Translation vector \( \binom{a}{b} \): (x,y) → (x+a, y+b) 4. Enlargements Scale Factor Formula: For center (h,k) and scale factor s: x' = h + s(x - h) y' = k + s(y - k) Combined...

Quiz 1:   Fullscreen Mode Teori Lengkap Fungsi Matematika A. Relasi (Hubungan) Definisi: Aturan yang menghubungkan anggota dua himpunan (A dan B) Contoh Diagram Panah Relasi "Hobi Anak" Contoh Pasangan Berurutan { (Eva, merah), (Roni, hitam), (Tia, merah), (Dani, biru) } Notasi: (Nama, Warna) Domain: {Eva, Roni, Tia, Dani} Kodomain: {merah, hitam, biru} B. Fungsi (Pemetaan) Syarat Fungsi: 1. Setiap domain punya pasangan 2. Setiap domain hanya punya 1 pasangan Komponen Fungsi Domain (D f ): {1,2,3} Kodomain: {1,2,3,4} Range (R f ): {2,3,4} Contoh Fungsi ...

Quiz 1   Fullscreen Mode Persamaan dan Pertidaksamaan Nilai Mutlak Teori Dasar Nilai mutlak (|x|) merupakan jarak bilangan real dari titik 0 pada garis bilangan. Sifat utama: |x| ≥ 0 untuk semua x ∈ ℝ |x| = |-x| √(x²) = |x| Rumus Fundamental Jenis Rumus Persamaan |f(x)| = a ⇨ f(x) = a atau f(x) = -a Pertidaksamaan |f(x)| |f(x)| > a ⇨ f(x) a Contoh Soal Contoh 1: Selesaikan |2x - 3| = 5 Penyelesaian: 2x - 3 = 5 ⇒ x = 4 2x - 3 = -5 ⇒ x = -1 Contoh 2: Selesaikan |x + 2| ≤ 3 Penyelesaian: -3 ≤ x + 2 ≤ 3 ⇒ -5 ≤ x ≤ 1

Quiz 1   Fullscreen Mode Pythagoras Theorem: Complete Theory and Formulas Fundamental Theorem In any right-angled triangle: a² + b² = c² Where: - a, b = legs (shorter sides) - c = hypotenuse (longest side) Derived Formulas Find hypotenuse (c): c = √(a² + b²) Find leg (a): a = √(c² - b²) Example Problems Example 1: Find hypotenuse (c) when a=6cm, b=8cm 6² + 8² = c² 36 + 64 = 100 → c = √100 = 10cm Example 2: Find leg (a) when b=5cm, c=12cm a² = 12² - 5² a² = 144 - 25 = 119 → a ≈ 10.9cm (3 s.f.) 3D Applications Space diagonal in cuboid: d² = l² + w² + h² Example: For 6×5×4 cuboid: AG = √(6² + 5² + 4²) = √77 ≈ 8.77cm Practice Exercises Calcu...

Quiz 1   Fullscreen Mode Teori dan Rumus Aritmatika Sosial Teori dan Rumus Aritmatika Sosial 1. Untung dan Rugi Untung terjadi ketika harga jual lebih besar dari harga beli. Rugi terjadi ketika harga jual lebih kecil dari harga beli. Rumus: Untung = Harga Jual - Harga Beli Rugi = Harga Beli - Harga Jual Persentase Untung = (Untung / Harga Beli) × 100% Persentase Rugi = (Rugi / Harga Beli) × 100% 2. Bruto, Neto, dan Tara Bruto adalah berat kotor (berat barang + kemasan). Neto adalah berat bersih (berat barang saja). Tara adalah berat kemasan. Rumus: Bruto = Neto + Tara Neto = Bruto - Tara Tara = Bruto - Neto 3. Bunga Tunggal Bunga Tunggal adalah bunga yang dihitung berdasarkan modal awal. Rumus: Bunga = (Modal × Bunga...

 Rumus refleksi titik (x,y) terhadap garis y= mx+n Aplikasi untuk Refleksi titik terhadap garis Point Reflection Calculator x: y: m: n: Calculate Aplikasi untuk Refleksi garis terhadap garis

Desktop site for perfect viewing Quiz 1   Fullscreen Mode Binomial and Geometric Distributions Two Special Discrete Distributions In statistics, there are two discrete distributions commonly used to model situations involving success or failure outcomes: binomial distribution and geometric distribution . Both involve repeated independent trials with a constant probability of success. Binomial Distribution The binomial distribution is used to calculate the number of successes in a fixed number of trials. For example, if we roll a die 4 times and want to know how many times we get a six, we can define the random variable R as the number of sixes rolled. Here, R can take values 0, 1, 2, 3, or 4. Parameters of Binomial Distribution: n : Number of trials (e.g., n = 4 ) p : Probability of success in each trial (e.g., rolling a six is p = 1/6 ) q : Probability of failure ( q = 1 - p = 5/6 ) ...

Quiz 1   Fullscreen Mode Discrete Random Variables and Probability Distribution Discrete Random Variables A discrete random variable is a variable whose values are countable or finite, and these values occur randomly. Examples include: The number of broken eggs in a carton. The number of sixes rolled when throwing four dice. Characteristics of Discrete Random Variables Values are integers (e.g., 0, 1, 2, etc.). Each value has a specific probability of occurring. For example, when flipping two coins, the number of heads that appear is a discrete random variable X , with possible values X ∈ {0, 1, 2} . Probability Distribution A probability distribution describes the likelihood of each value of a random variable. For discrete random variables, the probability distribution can be presented as a table, bar graph, or function. Example: Flippin...

Quiz 1   Fullscreen Mode Further Differentiation Further Differentiation 1. Increasing and Decreasing Functions A function y = f(x) is: Increasing : If dy/dx > 0 throughout the interval. Decreasing : If dy/dx < 0 throughout the interval. 2. Stationary Points Stationary points , also known as turning points, occur when: dy/dx = 0 3. First Derivative Test for Maximum and Minimum Points At a maximum point: dy/dx = 0 The gradient is positive to the left and negative to the right of the point. At a minimum point: dy/dx = 0 The gradient is negative to the left and positive to the right of the point. 4. Second Derivative Test for Maximum and Minimum Points If dy/dx = 0 and d²y/dx² < 0 , the point is a maximum. If dy/dx = 0 and d²y/dx² > ...

Quiz 1   Fullscreen Mode Additional exercise Differentiation Rules and Concepts Differentiation Rules and Concepts Gradient of a Curve The gradient of a curve is represented as: dy/dx This represents the rate of change of the curve \( y = f(x) \). The Four Rules of Differentiation 1. Power Rule If \( y = x^n \), then: d/dx (x^n) = n * x^(n-1) 2. Scalar Multiple Rule If \( y = kf(x) \), where \( k \) is a constant, then: d/dx [kf(x)] = k * d/dx [f(x)] 3. Addition/Subtraction Rule If \( y = f(x) ± g(x) \), then: d/dx [f(x) ± g(x)] = d/dx [f(x)] ± d/dx [g(x)] 4. Chain Rule If \( y = f(u) \) and \( u = g(x) \), then: dy/dx = (dy/du) * (du/dx) Tangen...