MathScope vs Citizenship Test Germany 2026

MathScope turns equations into graphs you can see and play with. Type a formula and its graph appears instantly; drag a slider and watch it change. From a textbook parabola to a Klein bottle, it all renders smoothly at your fingertips. Free to download: graph y = f(x) and implicit curves, plot 3D surfaces z = f(x, y), animate parameters with sliders, mark zeros and extrema, and explore part of the gallery at no cost. Upgrade to MathScope Pro when you want the full toolkit. 2D GRAPHING • One smart input box: y = x², x² + y² = 9, r = 2sin(3θ) and (cos 3t, sin 2t) are recognized automatically as explicit, implicit, polar or parametric • Overlay several functions, each with its own color and one-tap show/hide • Parameter sliders: write a, b or k in a formula and a slider appears; tap ▶ to animate it • Analysis tools: mark zeros, extrema and intersections; long-press a curve to trace coordinates and the tangent line; show the symbolic derivative f′(x); shade a definite integral with draggable bounds • A keyboard designed for math, so input is fast and accurate 3D SPACE • Surfaces z = f(x, y), implicit surfaces F(x, y, z) = 0, parametric surfaces and space curves • C++-accelerated Marching Cubes engine generates complex implicit surfaces in seconds • Cinematic rendering: physically based materials, environment reflections, bloom, 7 color maps, wireframe mesh and auto-rotate CURATED GALLERY 50+ classic and surprising shapes: cardioid, rose curves, butterfly curve, spirograph, Fourier square wave, Taylor expansions, Mexican hat, Möbius strip, Klein bottle, trefoil knot and more. Tap one to open, edit and animate it. FAVORITES & EXPORT Save the graphs you like, with history kept automatically, and export images to share with friends. MATHSCOPE PRO Unlocks parametric and polar curves, the full 3D space, intersections / derivative / integral tools, the entire gallery, all color maps and ultra-high-resolution meshes, 4K export without watermark, and unlimited functions and favorites. • Yearly (includes a 3-day free trial) and Monthly: auto-renewing subscriptions. Payment is charged to your Apple ID account. A subscription renews automatically unless auto-renew is turned off at least 24 hours before the end of the current period. Manage or cancel anytime in your App Store account settings. • Lifetime: a one-time purchase, yours to keep. Privacy Policy: https://vaca.vip/mathscope/privacy Terms of Use: https://www.apple.com/legal/internet-services/itunes/dev/stdeula/

Pass the German citizenship test (Einbürgerungstest) on your first try! COMPLETE QUESTION BANK All 460 official BAMF questions with answers and explanations. Includes 300 general knowledge questions plus 10 state-specific questions for each of the 16 Bundesländer. REALISTIC EXAM SIMULATION Practice with timed mock exams that match the official format: 33 questions, 60 minutes, passing score of 17 correct answers. Get instant results and detailed feedback after each attempt. SMART STUDY MODE Study at your own pace with flashcard-style learning. Mark difficult questions for focused review. Track your progress across all categories: Politics, History, Society, and State-specific topics. DETAILED STATISTICS See your strengths and weaknesses at a glance. Track completion rates by category, monitor your improvement over time, and know exactly when you're ready for the real exam. KEY FEATURES - All 460 official BAMF questions - State-specific questions for all 16 Bundesländer - Realistic exam simulation with timer - Smart study mode with progress tracking - Detailed statistics and performance analysis - Works offline - no internet required - Clean, distraction-free design Perfect for immigrants preparing for German naturalization (Einbürgerung). Whether you're studying for the Einbürgerungstest or the Orientierungstest, this app has everything you need to pass confidently. PREMIUM & PRICING Einbürgerungstest is free to download. Premium unlocks the full question bank and all features. Choose between: - Premium Monthly or Premium Yearly: an auto-renewable subscription - Lifetime Premium: an optional one-time purchase. Pay once, no subscription, no renewal. Subscription terms: - Payment is charged to your Apple ID account at confirmation of purchase. - The subscription automatically renews unless auto-renew is turned off at least 24 hours before the end of the current period. - Your account is charged for renewal within 24 hours prior to the end of the current period. - You can manage or cancel your subscription in your Apple ID Account Settings after purchase. - Any unused portion of a free trial period, if offered, is forfeited when you purchase a subscription. Privacy Policy: https://techconcepts.org/einbuergerungstest/privacy Terms of Use (EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/