Practice mixed test — Year 4: the whole first term.
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
- Associated angles, addition and double-angle formulas
- Trigonometric equations and inequalities, including linear ones
- Right-angled triangles, the laws of sines and cosines
- The chord theorem and trigonometry problems
- Exponentials and logarithms: rules, equations, domain
Two worked examples from the test
Quanto vale
Solution
Passo 1 — Converto in gradi. siamo nel secondo quadrante.
Passo 2 — Segno. Nel secondo quadrante il coseno è negativo (l'ascissa del punto sulla circonferenza goniometrica sta a sinistra dell'asse ).
Passo 3 — Arco associato. , quindi
Il è il valore del seno di o il coseno di : si ottiene scambiando con nella riduzione.
Se , quanto vale ?
Solution
Passo 1 — Scelgo la formula di duplicazione più comoda. Conosco solo il coseno, quindi uso la versione che ne fa a meno del seno:
Passo 2 — Sostituisco.
Passo 3 — Calcolo.
Il è di chi si ferma prima di sottrarre ; il di chi crede che , che è falso.
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 · 85 KB, ready to print). You receive the solutions by email after taking it online.
Download the PDFWhat a maths test on mixed test looks like
The Year 4 end-of-term test: associated angles, addition and double-angle formulas, trigonometric equations and inequalities including linear ones, the laws of sines and cosines, the chord theorem and exponentials and logarithms.
The mistake that costs the grade
Giving a single solution to a trigonometric equation instead of the whole family, with +2kπ or +kπ depending on the case — and then not selecting the ones that fall in the requested interval. It is the mistake that costs the most marks in Year 4.
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.