A defined-operation question invents a symbol, such as a ⊕ b = a·b + a + b, and asks you to use it. Nothing in it is new maths: it is substitution done carefully. The examples below are EXAMEV practice in the TR-YÖS style, not ÖSYM questions.
The rules
- 1Copy the rule and replace a and b with the numbers, keeping their order.
- 2Work from the inside out when operations are nested, like brackets.
- 3If the answer is known and a number is missing, write the rule as an equation and solve.
- 4Check whether the rule is symmetric: if swapping a and b changes the result, order matters.
Example 1: substitution
a ⊕ b = a·b + a + b. Find 3 ⊕ 4. Answer: 3·4 + 3 + 4 = 12 + 7 = 19.
Example 2: nested operations
With the same rule, find (1 ⊕ 2) ⊕ 0. Inside first: 1 ⊕ 2 = 2 + 1 + 2 = 5. Then 5 ⊕ 0 = 0 + 5 + 0 = 5.
Example 3: find the unknown
If x ⊕ 2 = 14, find x. Write the rule: 2x + x + 2 = 14, so 3x = 12 and x = 4. Check: 4 ⊕ 2 = 8 + 4 + 2 = 14.
Look for a shortcut: a·b + a + b = (a + 1)(b + 1) − 1. So 3 ⊕ 4 = 4·5 − 1 = 19 in one step.
Common mistake: with a rule like a ∗ b = 2a − b, assuming order does not matter. 3 ∗ 1 = 5, but 1 ∗ 3 = −1.
How EXAMEV helps
The EXAMEV TR-YÖS bank has 64 defined-operation questions among its 1,300+ practice questions, with explanations and timed sessions. See also our guide to TR-YÖS number sequences.