Practice maths class test — Year 2: the line in the coordinate plane.
15 questions drawn at random from a bank of 25, on the block of the programme your teacher is finishing: every attempt is a different test. No penalty for wrong answers, so answer even if you are not sure. At the end you receive by email the correct answer to every question and your weak topics — with an account you see them straight away here on the page. The step-by-step solution unlocks with your first lesson.
A class test is the written test an Italian high-school class sits after each block of the programme; this practice version is multiple choice.
Test in ItalianThe questions of this simulator are in Italian, as in the real exam.
Programme covered by the test
- Distance between two points and midpoint of a segment
- Explicit and implicit form, gradient
- Line through a point and line through two points
- Conditions for parallel and perpendicular lines
- Lines parallel to the axes and lines with no gradient
- Distance of a point from a line
- Proper and improper families of lines
- Perpendicular bisector of a segment and area of a triangle from coordinates
Two worked examples from the test
Qual è il coefficiente angolare della retta di equazione
Solution
- Porta l'equazione in forma esplicita isolando la : .
- Dividi tutto per : .
- Il coefficiente angolare è il numero che moltiplica la , cioè .
- Il segno meno sparisce perché anche il termine viene diviso per : dimenticarlo è l'errore che produce .
Scrivi l'equazione della retta passante per con coefficiente angolare .
Solution
- Usa la formula del fascio proprio: .
- Sostituisci: , cioè .
- Isola la : .
- L'opzione nasce dallo scrivere invece di : l'ordinata del punto è , quindi il segno si ribalta.
In the online practice test you will find 13 more questions like these; the correct answer to every question arrives by email.
Prefer paper? Download the test as a PDF (15 questions, 4 pages · 77 KB, ready to print). You receive the solutions by email after taking it online.
Download the PDFWhat a maths test on the line in the plane looks like
The line through two points, lines parallel and perpendicular to a given line, point-to-line distance, the perpendicular bisector of a segment and often the area of a triangle given its three vertices. There is almost always a family of lines with a parameter.
The mistake that costs the grade
For perpendicular lines, using the opposite of the gradient instead of the negative reciprocal: you need m′ = −1/m, not −m. And forgetting that the vertical line x = k has no gradient, so the formulas do not apply to it.
How to use this practice test
Take it once cold, without revising and with the timer on: it is there to show you where you stand, not to look good. Then look at your weak topics, revise only those — usually two or three, not the whole chapter — and retake it after a few days. The 15 questions are drawn from a bank of 25, so the second attempt is not the same test and the scores are genuinely comparable.
Is the score not enough?
See which topics lost you the most marks, then read how to handle test anxiety — or we look at your results together: the diagnostic is free.