dMAT Mathematical Equations: Free Practice Questions & Papers

Mathematical Equations is the third subtest inside the dMAT Core Module, alongside Figure Sequences and Latin Squares. It gives you a short system of equations built from letters instead of named variables, and asks you to work out the value each letter must take so that every equation in the system holds true.

In this guide, you will learn how the Mathematical Equations subtest in the dMAT exam works, how to solve linked equations using the substitution method, and sample questions, tips, and a study plan.

Key Highlights:

• The dMAT Mathematical Equations subtest has 20 questions to solve in 25 minutes, allowing around 75 seconds per question.
• Each dMAT Mathematical Equations system uses letters to represent the whole numbers from 1 to 20, with one valid solution.
• The substitution method provides a systematic way to solve dMAT Mechanical Equations by identifying an anchor equation and substituting values step by step.
• Speed and accuracy are essential in dMAT Mathematical Equations, as the subtest does not allow notes or rough work.

dMAT Mathematical Equations Section: Overview

The Mathematical Equations section in dMAT Core Module presents you with two to four linked equations, each built from letters such as A, B, C and D, and asks you to find the value of one specified letter. Every letter in the system must be a whole number between 1 and 20, and each system has exactly one valid solution, so there is never a need to consider multiple possible answers for a given letter.

The dMAT Mathematical Equation subtest does not test algebra beyond the secondary school level. Instead, it tests whether you can hold two or three linked equations in your head and solve them within a fixed time limit, without using notes. 

The table below provides a brief overview of the dMAT mathematical section.

Since every mathematical equation resolves to a single answer, the section rewards a repeatable method over creative problem-solving. The next section breaks that method down into three steps you can apply to almost every item you see.

How to Solve dMAT Mathematical Equations Using the Substitution Method?

The substitution method for dMAT Mathematical Equations involves isolating a variable and replacing it in the other equations to solve the system step by step. This approach helps simplify complex-looking systems by reducing them to one variable.

• Step 1: Start with the simplest equation: Look for an equation that gives a variable directly, such as B = 6, or can be rearranged easily, such as C − 4 = 9.
• Step 2: Express the other variables using the anchor: Use the known variable to rewrite the remaining equations. For example, if B = 6 and A + 2 = B, rewrite it as A = B − 2.
• Step 3: Substitute into the final equation: Once the variables are expressed in terms of the anchor variable, substitute them into the remaining equation to reduce the system to a single calculation.

Example: Take the system B = 5, A = B + 3, and C = 2 × A. Find C.

Since B = 5, substitute directly into the second equation to get A = 5 + 3 = 8. Substitute A into the third equation to get C = 2 × 8 = 16. The full chain resolves in three short steps and never requires solving more than one unknown at a time.

Tip: Solve only the letter the question actually asks for, rather than working out every letter in the system by default. And use the 1 to 20 constraint as a check on your working, since any answer that falls outside that range signals an arithmetic error rather than a valid alternative solution.

dMAT Mathematical Equations Sample Paper PDF 

The dMAT Mathematical Equations sample paper reflects the question style and format of the actual subtest, with an answer key for quick evaluation. Download the PDF to practise linked equations, familiarise yourself with the format, and improve speed through timed practice.

[Download the dMAT Mathematical Practice Paper]

dMAT Mathematical Equations Practice Questions With Answers

 The following dMAT Mathematical Equations practice questions help you test how quickly you can identify relationships, substitute values, and solve linked equations. You will find questions with answers and step-by-step solutions so you can check your final answer.

Sample Question 1 (two variables) 

B = 9. A + 3 = B. What is A?

1. 5
2. 6
3. 7
4. 12

Sample Question 2 (three variables)

A = 2 × B. A + B = 9. C = 4 × B. What is C?

1. 8
2. 12
3. 16
4. 18 

Sample Question 3 (four variables)

C = 3 × B. A = B + 4. D = A − 1. A − B + C − D = 9. What is D?

1. 5
2. 6
3. 7
4. 8 

Answer key:

• Question 1: B = 9, so A + 3 = 9 gives A = 6.
• Question 2: Substituting A = 2 × B into A + B = 9 gives 3 × B = 9, so B = 3 and A = 6. C = 4 × B = 12.
• Question 3: Express C, A and D in terms of B: C = 3 × B, A = B + 4, D = B + 3. Substituting into the fourth equation gives (B + 4) − B + 3 × B − (B + 3) = 9, which simplifies to 2 × B + 1 = 9, so B = 4. This gives A = 8, C = 12 and D = 7.

dMAT Mathematical Equations Study Plan 

A 4-week preparation plan for dMAT Mathematical Equations should gradually move you from untimed accuracy to full-speed, no-notes practice. You can use the first two weeks to build equation-solving accuracy and familiarity, then focus on timed sets and exam-style practice in the final two weeks.

Tip: Repeat difficult question types within each week rather than moving on once you get one right, since the subtest rewards a method you can reproduce under pressure, not a method you understood once.

Tips to Solve dMAT Mathematical Equations

To solve a dMAT Mathematical Equations question under 75 seconds requires cutting unnecessary steps rather than calculating faster.

• Scan before you write: Spend the first five seconds identifying the anchor equation rather than starting your substitution from the first line of the system. Systems are not always listed in solving order.
• Solve for the asked letter only: If the system defines four letters but the question asks for one, stop your substitution chain as soon as you reach that letter. Solving the full system wastes time.
• Keep values in short verbal chunks: Hold intermediate results as short phrases, such as "B is four, so A is seven," rather than tracking several unlabelled numbers at once. This reduces the working-memory load that causes most errors under time pressure.
• Guess and move on if you are stuck: There is no negative marking across the dMAT Core Module, so an unanswered question costs you the same as a wrong one. If a question is not resolving within your allotted time, choose your best estimate and continue rather than losing time on one question.

From the Desk of Yocket

The Mathematical Equations subtest is one of the easier parts of the dMAT exam to learn, since it follows a fixed problem-solving method rather than open-ended reasoning. Once you become familiar with the substitution steps, you can focus on improving your speed and accuracy through timed practice. 

If you want more structured dMAT practice, use Yocket Prep to work on exam-style questions and build speed across the Core Module. Regular practice can help you become more comfortable with the question formats and manage the time pressure more effectively.