Free diagnostic exams
Find your true starting point in mathematics
Timed, exam-style diagnostics for IGCSE, A-Level, AP and SAT, written by The Complete Equation's tutors to show you exactly what to work on next.
Written and marked by The Complete Equation's own tutors
Diagnostics across the curricula we teach
New · Digital SAT practice
Practice in an interface that feels like test day
Full-length SAT modules in a Bluebook-style player, followed by a report that shows your estimated section score, your pacing on every question, and the SAT domains that need work.
Real module timing
22 math questions in 35 minutes, with a timer you can hide and a five-minute warning you can't.
Desmos and the reference sheet
The same built-in graphing calculator and formula sheet you'll have on test day.
Mark for review and cross out
Bookmark questions, eliminate answer choices and check your work on the review page before you submit.
Why students use it
A diagnosis, not just a score
Real exam conditions
Every diagnostic is timed. The clock starts when you do and the paper submits itself when time is up, just like the real thing.
Instant scoring
Your paper is marked the moment you submit, with a question-by-question breakdown and worked explanations.
Know where you stand
A skill-by-skill report with the time you spent on every question shows exactly what cost you marks and what to work on next.
The studio behind the papers
A real tutoring studio, not a question bank
Every diagnostic here is written, marked and followed up by The Complete Equation, a 1:1 online mathematics tutoring studio. Watch the short intro, then put a paper to the test.
Courses covered
Pick your course, sit the paper
Digital SAT Practice Tests
Full-length digital SAT modules in a Bluebook-style test interface: timer, Desmos calculator, reference sheet, mark for review and answer eliminator.
Middle School Math: Checkpoint 1
Grade 5 skills: place value, whole-number operations, time, Roman numerals, squares and area.
Middle School Math: Checkpoint 2
Grade 6 skills: long multiplication and division, two-digit divisors, and fraction operations.
Middle School Math: Checkpoint 3
Grade 7 skills: statistics (mean, median, mode, range), exponents, order of operations, and fraction multiplication and division.
IBDP Math Readiness: Pre-IB
Checks readiness for IB DP Mathematics: probability, sets, algebra, functions, sequences and trigonometry.
SAT Math
Digital SAT math: algebra, advanced math, problem solving and data analysis, geometry.
How it works
From diagnostic to a plan in three steps
Take a free diagnostic
Pick your course (IGCSE, A-Level, AP or SAT) and sit a short timed paper written by our tutors.
See your skill report
Instant marking shows your score and a breakdown by skill, so the gaps are obvious.
Fix the gaps 1:1
Book a free demo class and the tutor who wrote your paper builds a plan around your report.
After your diagnostic
Turn your skill report into a plan
Book a demo class
Your first lesson is free. Bring your skill report: it tells the tutor exactly where to start.
Meet the tutor
Get to know your tutor 1:1 and experience the teaching approach live before you decide anything.
Start learning
Lessons are built around the exact gaps your diagnostic found, nothing generic.
Inside a real lesson
The whiteboards your lessons happen on
Unedited screenshots from real 1:1 lessons, taught by the same tutors who write and mark these diagnostics.
Twenty minutes now saves months later
Sign in with Google and take your first diagnostic free. No card, no commitment.
Start free