Free IB Maths AI HL baseline test: start of DP2

Find out where a student is starting from at the start of DP2. 20 multiple-choice questions on the AI HL content usually taught in DP1: finance, complex numbers, matrices, models, 3D geometry, vectors, statistics, probability distributions and calculus, marked instantly, with a report that shows which topics are secure and which need work.

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What it covers

The test is written for the start of DP2 of IB Maths AI HL. It covers the AI HL content usually taught in DP1: finance, complex numbers, matrices, models, 3D geometry, vectors, statistics, probability distributions and calculus. Each question is tagged with the topic it tests, so the report maps straight onto the course:

Standard form
Upper and lower bounds
Infinite geometric series
Compound interest
Complex numbers
Determinant of a matrix
Multiplying matrices
Straight-line models
Exponential decay
Interpreting a quadratic model
Distance in 3D
The cosine rule
Area of a triangle
Angle between vectors
Mean from a frequency table
Using a regression line
Bayes' theorem
The binomial distribution
The chain rule
Area under a curve

How it works

20 questions, four options each, one mark per question, about 40 minutes. Calculator allowed.
Online or on paper, alone or with a class: how the baseline tests work, and the questions students and teachers ask.

Two sample questions

These are like the questions in the test, with different numbers. They are not in the test itself.

Sample 1 · Straight-line models

What is the equation of the straight line through $(1, 5)$ and $(4, 11)$ ?

$y = 2 x + 3$
$y = 2 x + 7$
$y = \frac{1}{2} x + 3$
$y = - 2 x + 7$

Show the answer and working

Answer: A

Gradient $2$ ; substitute a point to find $c = 3$ : $y = 2 x + 3$ .

B is what you get if you made a sign error finding c. C is what you get if you found the gradient upside down. D is what you get if you made a sign error in the gradient.

Sample 2 · Determinant of a matrix

$M = (\begin{matrix} 3 & 2 \\ - 1 & 4 \end{matrix})$ . What is $det M$ ?

$10$
$14$
$- 14$
$6$

Show the answer and working

Answer: B

$3 \times 4 - 2 \times (- 1) = 14$ .

A is what you get if you subtracted 2 instead of adding. C is what you get if you worked out bc − ad. D is what you get if you added the diagonals.

What the report looks like

Example report (made-up results for one student):

Score 13 / 20 (65%)

Standard formGap
Upper and lower boundsGap
Infinite geometric seriesDeveloping
Compound interestDeveloping
Complex numbersSecure
Determinant of a matrixSecure

Questions students and teachers ask

How long does it take?

20 multiple-choice questions, about 40 minutes. A calculator is allowed. A teacher can set it as a timed test.

What does the result show?

The score, a topic-by-topic report with the weakest topics first, the common mistake behind each wrong answer, and links to practise each weak topic. It shows where a student is starting from; it is not a grade prediction.

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