Core Module · How to Solve
How to solve Mathematical Equations
Mathematical Equations require solving symbol substitution problems — without a calculator and without scratch paper. Target: 14–16 correct out of 20 in 25 minutes.
THE FORMAT
Each symbol equals a number. Substitute, then solve.
A set of equations defines the value of each geometric symbol (★, ●, ■, etc.). Then a final equation uses those symbols. You must compute the answer entirely mentally — no calculator, no rough paper.
Example
Given: ★ = 4, ● = 7, ■ = 2
Find: ★ × ● − ■ = ?
Solution: 4 × 7 − 2 = 28 − 2 = 26
TECHNIQUE 01
Direct substitution
Write out the symbols' values on your mental notepad, then evaluate left to right with correct BODMAS order. This works for straightforward questions — one substitution, basic arithmetic.
BODMAS reminder
Brackets → Orders (powers/roots) → Division → Multiplication → Addition → Subtraction
Multiplication and division have equal priority — evaluate left to right within the same tier.
TECHNIQUE 02
Elimination method for simultaneous-style questions
Some questions don't give you direct values but instead give multiple equations involving the same symbols. You must solve the system to find the unknown, then compute the final expression.
Strategy
Start with the equation that has the fewest unknowns — ideally one where you can isolate one symbol immediately.
Substitute back into the next equation. Build up values from the simplest equation to the most complex.
If a symbol appears in two equations, subtract or add the equations to eliminate it.
TECHNIQUE 03
Bounded trial for multiple-choice
Since dMAT is multiple choice, you can sometimes use the options to narrow down the answer. If you calculate an approximate value, look at which option it must be closest to. Bounded trial is faster than computing exactly when the arithmetic is cumbersome.
How to apply
Estimate the answer to the nearest 5 or 10. Look at the four options — usually only one falls in that range.
If two options are close together, you need precision. If they're well spread, estimation is enough.
Mental arithmetic tips
Since no calculator or paper is allowed, practise these shortcuts:
- Multiply by 9: Multiply by 10 and subtract the number. 9 × 7 = 70 − 7 = 63.
- Multiply by 11: Multiply by 10 and add the number. 11 × 8 = 80 + 8 = 88.
- Squares to memorise: 1²–25² should be instant. Most answers involve these squares or their products.
- Fractions: Convert to simpler equivalents before computing. 3/4 × 20 = 15 (multiply numerator first).
- Negative numbers: Keep careful track of signs — a common error type is sign errors, not wrong method.