WAEC Mathematics questions: Binary operations

13 questions with answers and explanations. Tap an option to check yourself.

All topics Binary operations · 13 Coordinate geometry · 20 Euclidean geometry · 26 Fractions, decimals, approximations and percentages · 29 Indices, logarithms and surds · 29 Inequalities · 17 Loci · 12 Mensuration · 27 Number bases · 24 Polynomials · 29 Probability · 23 Progressions · 22 Sets · 22 Statistics · 26 Trigonometry · 26 Variation · 19

Question 1· Binary operations· WAEC
If x Δ y = x² − 2y, evaluate (3 Δ 1) Δ 2.
Explanation and discussion
Question 2· Binary operations· WAEC
An operation △ is defined by p △ q = p² + q². Evaluate (1 △ 2) △ 1.
Explanation and discussion
Question 3· Binary operations· WAEC
If a ⊕ b = 2a + b², evaluate 3 ⊕ 2.
Explanation and discussion
Question 4· Binary operations· WAEC
The operation x ∗ y = (x + y)/2 is defined on the real numbers. Which statement is true?
Explanation and discussion
Question 5· Binary operations· WAEC
If x ∗ y = x raised to the power y, find 2 ∗ 3.
Explanation and discussion
Question 6· Binary operations· WAEC
A binary operation * is defined on the real numbers by a * b = a + b − ab. Find 3 * 4.
Explanation and discussion
Question 7· Binary operations· WAEC
Find the identity element of the operation a ∘ b = a + b − 2 on the real numbers.
Explanation and discussion
Question 8· Binary operations· WAEC
A binary operation ⊕ is defined by a ⊕ b = 3a − b. Find 5 ⊕ 7.
Explanation and discussion
Question 9· Binary operations· WAEC
An operation ⊙ is defined by m ⊙ n = m − n + mn. Find 2 ⊙ (−1).
Explanation and discussion
Question 10· Binary operations· WAEC
On the set {1, 2, 3, 4}, a ⊗ b is the remainder when ab is divided by 5. Find 3 ⊗ 4.
Explanation and discussion
Question 11· Binary operations· WAEC
A binary operation is defined by m ∘ n = m² − 2n. Evaluate (−3) ∘ 4.
Explanation and discussion
Question 12· Binary operations· WAEC
Under the operation a ∘ b = a + b − 2, whose identity element is 2, find the inverse of 5.
Explanation and discussion
Question 13· Binary operations· WAEC
Find the identity element of the operation a ∗ b = ab/2 on the non-zero real numbers.
Explanation and discussion

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WAEC Mathematics questions: Binary operations

If x Δ y = x² − 2y, evaluate (3 Δ 1) Δ 2.

An operation △ is defined by p △ q = p² + q². Evaluate (1 △ 2) △ 1.

If a ⊕ b = 2a + b², evaluate 3 ⊕ 2.

The operation x ∗ y = (x + y)/2 is defined on the real numbers. Which statement is true?

If x ∗ y = x raised to the power y, find 2 ∗ 3.

A binary operation * is defined on the real numbers by a * b = a + b − ab. Find 3 * 4.

Find the identity element of the operation a ∘ b = a + b − 2 on the real numbers.

A binary operation ⊕ is defined by a ⊕ b = 3a − b. Find 5 ⊕ 7.

An operation ⊙ is defined by m ⊙ n = m − n + mn. Find 2 ⊙ (−1).

On the set {1, 2, 3, 4}, a ⊗ b is the remainder when ab is divided by 5. Find 3 ⊗ 4.

A binary operation is defined by m ∘ n = m² − 2n. Evaluate (−3) ∘ 4.

Under the operation a ∘ b = a + b − 2, whose identity element is 2, find the inverse of 5.

Find the identity element of the operation a ∗ b = ab/2 on the non-zero real numbers.