Quick Read
- 20 equation questions, 25 minutes, 75 seconds each, no negative marking
- Every system follows a 3-step method: find the anchor equation, express every other variable through it, then substitute into the longest equation last
- No calculator, notes, or rough paper is allowed; hold A, B, C, D in your head
- To practice: solve each system mentally first, then open the solution path to check your route, not before
- Read the full substitution method walkthrough first, then attempt the 15 free practice questions below that.
Start the 15 Practice Questions ↓
What Are dMAT Mathematical Equations?
Mathematical Equations is the second subtest of the dMAT Core Module, sitting between Figure Sequences and Latin Squares, and every candidate answers it regardless of degree background. You see a small system of linked equations and must work out the values of the variables A, B, C, and sometimes D. According to the official preparatory materials, you get 20 questions in 25 minutes, which is 75 seconds per question.
The arithmetic itself is school-level. What the dMAT Mathematical Equations subtest actually measures is working memory and method: you must hold several variable values in your head because no notes or rough paper is allowed anywhere in the exam.
After finishing this page, you should continue with the dMAT practice test hub, the dMAT Core Module explained guide, and the full dMAT exam pattern.
| Feature | Detail |
|---|---|
| Position in exam | Second subtest of the Core Module |
| Questions | 20 |
| Time | 25 minutes (75 seconds per question) |
| Format | System of 2 to 4 linked equations, single-choice answers |
| Variables | A, B, C, and D are always whole numbers |
| Aids allowed | None. No calculator, notes or rough paper |
The Substitution Method for dMAT Mathematical Equations
Every dMAT Mathematical Equations system, from 2 variables to 4, falls to the same three steps.
- Find the anchor. One equation is always solvable on its own or expressible in a single variable, such as B − 2 = 4 or 3 × B = A. Solve or rewrite it first, never the longest equation.
- Express, do not solve. Turn every other variable into an expression of the anchor variable: A = 3B, C = B + 5. You are collecting substitutions, not answers.
- Collapse the long equation last. Substitute everything into the longest equation. It reduces to one small calculation, such as 4B = 12, and the remaining variables follow in seconds.
Worked example: 6 + A = 10, B ÷ A = 3, C = B − A. The anchor gives A = 4 right away. Then B = 3 × 4 = 12, and C = 12 − 4 = 8. Total time with the method: under 30 seconds.
Speed on this section transfers directly from pattern training, too, so pair your drills with dMAT Figure Sequences practice questions in the same sitting.
dMAT Mathematical Equations Practice Questions with Answers (Free)
There are no dMAT past papers, so format-accurate practice is the only realistic preparation. The 15 original dMAT Mathematical Equations questions below mirror the official preparatory materials: the same 2-variable to 4-variable systems, whole-number answers throughout, and worked solution paths in the official style. Attempt each question mentally, then open the solution path to compare your route.
Question 1 Low
Solve the system of equations in your head, no calculator or notes. What are the values of A and B?
B − A = 4
- a) A = 7, B = 3
- b) A = 7, B = 11
- c) A = 17, B = 21
- d) A = 5, B = 9
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Answer: b. The first equation is the anchor: subtract 5 on both sides, so A = 7. Substitute into the second: B − 7 = 4, so B = 11.
Question 2 Low
Solve the system of equations in your head, no calculator or notes. What are the values of A and B?
B − A = 6
- a) A = 3, B = 6
- b) A = 12, B = 6
- c) A = 6, B = 12
- d) A = 6, B = 8
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Answer: c. From the first equation B = 2A. Substituting into the second: 2A − A = 6, so A = 6 and B = 12.
Question 3 Low
Solve the system of equations in your head, no calculator or notes. What are the values of A and B?
A + B = 16
- a) A = 4, B = 12
- b) A = 12, B = 4
- c) A = 4, B = 10
- d) A = 6, B = 10
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Answer: a. Replace B with 3A in the second equation: A + 3A = 16, so 4A = 16 and A = 4. Then B = 3 × 4 = 12.
Question 4 Low
Solve the system of equations in your head, no calculator or notes. What are the values of A and B?
A + B = 15
- a) A = 9, B = 24
- b) A = 5, B = 10
- c) A = 1, B = 14
- d) A = 9, B = 6
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Answer: d. The anchor gives A = 9 directly. Substitute into the second equation: 9 + B = 15, so B = 6.
Question 5 Low
Solve the system of equations in your head, no calculator or notes. What are the values of A and B?
A − B = 7
- a) A = 7, B = 14
- b) A = 14, B = 7
- c) A = 10, B = 5
- d) A = 12, B = 6
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Answer: b. Replace A with 2B in the second equation: 2B − B = 7, so B = 7 and A = 14. The swapped pair is the trap option.
Question 6 Medium
Solve the system of equations in your head, no calculator or notes. What are the values of A, B and C?
A − B = 10
A ÷ B = C
- a) A = 15, B = 5, C = 3
- b) A = 12, B = 4, C = 3
- c) A = 15, B = 5, C = 5
- d) A = 9, B = 3, C = 3
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Answer: a. From equation 1, A = 3B. Substituting into equation 2: 3B − B = 10, so B = 5 and A = 15. Then C = 15 ÷ 5 = 3.
Question 7 Medium
Solve the system of equations in your head, no calculator or notes. What are the values of A, B and C?
B − 2 = 4
2 × B = C
- a) A = 6, B = 8, C = 16
- b) A = 8, B = 6, C = 10
- c) A = 8, B = 6, C = 12
- d) A = 10, B = 4, C = 8
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Answer: c. Equation 2 is the anchor: B = 6. Then A = 14 − 6 = 8, and C = 2 × 6 = 12.
Question 8 Medium
Solve the system of equations in your head, no calculator or notes. What are the values of A, B and C?
C − A = 8
B = A + C
- a) A = 4, B = 16, C = 12
- b) A = 3, B = 12, C = 9
- c) A = 4, B = 14, C = 12
- d) A = 6, B = 24, C = 18
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Answer: a. From equation 1, C = 3A. Substituting into equation 2: 3A − A = 8, so A = 4 and C = 12. Then B = 4 + 12 = 16.
Question 9 Medium
Solve the system of equations in your head, no calculator or notes. What are the values of A, B and C?
B + A = 15
C = B − A
- a) A = 3, B = 12, C = 4
- b) A = 5, B = 20, C = 15
- c) A = 4, B = 16, C = 12
- d) A = 3, B = 12, C = 9
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Answer: d. Replace B with 4A in equation 2: 4A + A = 15, so A = 3 and B = 12. Then C = 12 − 3 = 9.
Question 10 Medium
Solve the system of equations in your head, no calculator or notes. What are the values of A, B and C?
3 × A = C
B + C = 20
- a) A = 4, B = 8, C = 12
- b) A = 2, B = 4, C = 6
- c) A = 5, B = 10, C = 15
- d) A = 4, B = 12, C = 8
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Answer: a. Express B and C in A, then substitute into equation 3: 2A + 3A = 20, so A = 4. Then B = 8 and C = 12.
Question 11 High
Solve the system of equations in your head, no calculator or notes. What are the values of A, B, C and D?
C − B = 5
A − B + C = 17
A ÷ B = D
- a) A = 16, B = 4, C = 9, D = 4
- b) A = 8, B = 2, C = 7, D = 4
- c) A = 12, B = 3, C = 8, D = 4
- d) A = 12, B = 3, C = 5, D = 4
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Answer: c. Express everything in B: A = 4B and C = B + 5. Substitute into equation 3: 4B − B + B + 5 = 17, so 4B = 12 and B = 3. Then A = 12, C = 8 and D = 12 ÷ 3 = 4.
Question 12 High
Solve the system of equations in your head, no calculator or notes. What are the values of A, B, C and D?
2 × A = B
C = A + 2
D = B − C
- a) A = 4, B = 8, C = 6, D = 2
- b) A = 3, B = 6, C = 5, D = 1
- c) A = 4, B = 8, C = 6, D = 14
- d) A = 5, B = 10, C = 7, D = 3
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Answer: a. Express B and C in A, then substitute into equation 1: A + 2A + A + 2 = 18, so 4A = 16 and A = 4. Then B = 8, C = 6 and D = 8 − 6 = 2.
Question 13 High
Solve the system of equations in your head, no calculator or notes. What are the values of A, B, C and D?
C = 2 × B
A + B + C = 21
D = C ÷ A
- a) A = 3, B = 6, C = 12, D = 4
- b) A = 4, B = 7, C = 14, D = 3
- c) A = 3, B = 6, C = 12, D = 2
- d) A = 6, B = 9, C = 18, D = 3
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Answer: a. Express A and C in B: A = B − 3 and C = 2B. Substitute into equation 3: B − 3 + B + 2B = 21, so 4B = 24 and B = 6. Then A = 3, C = 12 and D = 12 ÷ 3 = 4.
Question 14 High
Solve the system of equations in your head, no calculator or notes. What are the values of A, B, C and D?
B = D − 5
A + B = 11
C = A + B
- a) A = 3, B = 4, C = 7, D = 9
- b) A = 4, B = 7, C = 28, D = 12
- c) A = 5, B = 6, C = 11, D = 15
- d) A = 4, B = 7, C = 11, D = 12
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Answer: d. Express B in A: D = 3A, so B = 3A − 5. Substitute into equation 3: A + 3A − 5 = 11, so 4A = 16 and A = 4. Then D = 12, B = 7 and C = 4 + 7 = 11.
Question 15 High
Solve the system of equations in your head, no calculator or notes. What are the values of A, B, C and D?
2 × B = A
C = 3 × B
D = B + 4
- a) A = 6, B = 3, C = 9, D = 7
- b) A = 10, B = 5, C = 15, D = 9
- c) A = 8, B = 4, C = 12, D = 8
- d) A = 8, B = 4, C = 10, D = 8
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Answer: c. Express everything in B and substitute into equation 1: 2B − B + 3B − B − 4 = 8, so 3B = 12 and B = 4. Then A = 8, C = 12 and D = 8.
dMAT Mathematical Equations Study Plan Before 26 September 2026
The dMAT is on 26 September 2026, and registration closes on 15 September.
Check the dMAT exam dates and registration deadline, then work backward with this dMAT Mathematical Equations plan:
| Weeks before test | Focus |
|---|---|
| 6 to 5 | Learn the substitution method: 2-variable systems untimed, no paper |
| 4 to 3 | 3-variable systems; start 75-second pacing per question |
| 2 | 4-variable systems; classify every error into the four mistake buckets |
| 1 | Two full-time 20-question sets; review only your slowest question type |
| Test week | Short daily warm-ups only; no new difficulty |
Frequently Asked Questions About dMAT Mathematical Equations
How many Mathematical Equations questions are in the dMAT?
The Core Module includes 20 Mathematical Equations questions to be solved in 25 minutes, about 75 seconds each. It is the second of the three Core Module subtests, and every dMAT candidate answers it regardless of their degree or chosen subject module.
Is a calculator allowed for this section?
The dMAT permits no aids of any kind: no calculator, no rough paper, and no notes. Every official system uses small whole numbers precisely so that mental arithmetic is enough, which is why practicing without a pen from your first session matters more than question volume.
How hard is the math itself?
The operations never go beyond addition, subtraction, multiplication, and division. The difficulty is structural: holding three or four variable values in working memory while substituting between equations, under a 75-second clock. Method and pacing, not mathematical ability, decide your score.
Do the answers always come out as whole numbers?
In the official preparatory materials, every system resolves to small whole numbers. A fraction or decimal mid-solution is a reliable signal that you have made a slip, so treat it as a prompt to restart from the anchor equation rather than forcing an answer.
What is the fastest way to solve dMAT equation systems?
Anchor first: find the equation solvable in one step or expressible in one variable, rewrite every other variable through it, and substitute into the longest equation last. The long equation then collapses to a single small calculation, and the remaining values follow immediately.
How is this technique different from school algebra?
The technique is identical to solving simultaneous equations in school, with two twists: everything happens mentally, and the answer options are engineered around your likely errors, including swapped pairs and sign slips. School speed with paper does not automatically transfer to the dMAT Mathematical Equations.
Do commerce and business students also face Mathematical Equations?
The Core Module is identical for every candidate, so commerce, finance, and business graduates taking the dMAT for APS purposes solve the same 20 systems as engineers. If you are unsure whether the exam applies to you, see how dMAT and APS certification fit together.
What should I do if a system looks unsolvable?
Re-read it for the anchor you missed, because every official system has exactly one solution. If it still does not open within your 75 seconds, eliminate options with obviously wrong values, guess, and move on. There is no negative marking, so a blank answer is the only truly wrong move.
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