Vectors and Planes vs FireAPT

Vectors and Planes App helps visualize and understand 3D linear and quadric structures and their intersections. List of linear structures and combinations: 1. Two vector combination. 2. Plane. 3. Line and plane combination. 4. Two plane combination. 5. Three plane combination. Current list of quadric structures: 1. Two sphere combination. 2. Standard ellipsoid. 3. Ellipsoid in a form of positive-definite matrix. 4. Standard cone. 5. Cone in a form of indefinite matrix. 6. 1-sheet hyperboloid. 7. 1-sheet hyperboloid in a form of indefinite matrix. 8. 2-sheet hyperboloid. 9. 2-sheet hyperboloid in a form of indefinite matrix. 10. Standard cylinder. 11. Cylinder in a form of positive-semidefinite matrix. 12. Hyperbolic paraboloid. 13. Elliptic paraboloid. Current list of combinations of quadric and linear structures: 1. Matrix ellipsoid and line. 2. Standard ellipsoid and plane. 3. Matrix ellipsoid and plane. 4. Matrix cone and line. 5. Standard cone and plane. 6. 1-sheet hyperboloid in matrix form and line. 7. 2-sheet hyperboloid in matrix form and line. 8. Matrix cylinder and line. 9. Elliptic paraboloid and line. 10. Hyperbolic paraboloid and line. Interactive 3D graphs are provided for all of the above. Step by step calculation algorithms are provided for all intersection point sets. Many of the algorithms are based on Linear Algebra concepts. Those, in turn, are explained in our “Matrix Solver Step by Step” app. Version 10 was completely redesigned. Developers hope to get feedback from users at graphmath@aol.com.

FireApt is a focused practice app for anyone preparing for a firefighter aptitude assessments. 1,360 original questions across the four skill areas (Numeracy, Literacy, Abstract & Mechanical), every one with a worked explanation — because knowing you got it wrong teaches you nothing on its own. WHAT'S INSIDE • 1,360 original questions — 340 each in Mechanical Reasoning, Numeracy, Literacy and Abstract Reasoning • A worked explanation for every single question, not just an answer key • Over 1,800 purpose-drawn diagrams: pulleys, gears, levers, circuits, pattern grids • Timed practice exams — 40 questions across all four areas against a 30-minute clock, drawn fresh every time (now customisable) • Reading comprehension built on realistic documents: standard operating procedures, incident reports, safety bulletins, station notices THE FOUR AREAS Mechanical Reasoning — gears, levers, pulleys, hydraulics, forces and how things move. Numeracy — ratios, rates, percentages, unit conversion and the practical calculations the job actually asks for. Literacy — comprehension, inference and clear written communication, including passage sets drawn from the kinds of documents you would read on station. Abstract Reasoning — pattern sequences, matrices and odd-one-out problems that test reasoning independently of prior knowledge. TRACK WHERE YOU STAND Your results are broken down by skill area, with your average, your best and your latest score for each, plus a trend line across every session you have completed. The point is not the score — it is knowing which area to spend your next hour on. BUILT TO STAY OUT OF YOUR WAY • Works completely offline. Every question and diagram ships with the app, so it runs on a train, in a basement, or anywhere with no signal. • No account, no sign-up, no email address. • No ads. No subscriptions. No in-app purchases. You buy the app once and you have all of it. • Nothing is collected about you. Your practice history is saved on your device and never leaves it. WHY IT COSTS WHAT IT COSTS Every question, explanation and diagram here was written and drawn from scratch. There is no recycled question bank behind it, no advertising, and nothing to upsell you once you are inside. One price, everything included, forever. A NOTE ON PREPARATION No practice app can tell you what will be on your assessment. What it can do is make the formats familiar, so that on the day your attention goes on the problem rather than on working out what is being asked. That is what this is for.