Binary operations

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1. 1Binary operationsWorking out a binary operation, testing whether it is associative, completing and reading its table, and finding the identity element and inverses on the real numbers.Done20 min

Past questions (13)

From 2010–2023: 11 WAEC, 2 NECO. Theory questions first, then objective, newest first.

Theory (9)

• NECO 2023 · Paper 2 · Q10Resolve $\dfrac{2x^3 + 5x^2 - 6x + 4}{(x - 1)(x + 2)}$ into partial fractions.
• WAEC 2022 · Paper 2 · Q1A binary operation $*$ is defined on the set $T = \{-2, -1, 1, 2\}$ by $p * q = p^2 + 2pq - q^2$, where $p, q \in T$.
• WAEC 2022 · Paper 2 · Q1A binary operation $\Delta$ is defined on the set of real numbers, $\mathbb R$, by $p\,\Delta\,q = pq + p + q$ for $p, q \in \mathbb R$.
• WAEC 2019 · Paper 2 · Q9Solve the equations $3\log_2 x = y$ and $\log_2 4x = y + 4$ simultaneously.
• WAEC 2019 · Paper 2 · Q3A binary operation $*$ is defined on the set of real numbers, $\mathbb R$, by $x * y = x + y - 3xy$, where $x, y \in \mathbb R$. Find the identity …
• WAEC 2016 · Paper 2 · Q1A binary operation $*$ is defined on the set $\mathbb R$ of real numbers by $m * n = m + n + 2$. Find the:
• WAEC 2015 · Paper 2 · Q1A binary operation $\Delta$ is defined on the set of real numbers $\mathbb R$ by $a\,\Delta\,b = a^3 - b^3$. Without using a calculator, find …
• WAEC 2014 · Paper 2 · Q2A binary operation $*$ is defined on the set of rational numbers by $m * n = \dfrac{m^2 - n^2}{2mn}$, $n \ne 0$ and $m \ne 0$.
• WAEC 2010 · Paper 2 · Q1A binary operation $*$ is defined on the set $\mathbb{R}$ of real numbers by $x * y = \dfrac{x^2}{x + y}$, where $x, y \in \mathbb{R}$.

Objective (4)

• NECO 2023 · Paper 1 · Q7A binary operation $*$ with identity element zero is defined on the set $\mathbb{R}$ of real numbers by $p * q = p + q + 3pq$. For what value …
• WAEC 2023 · Paper 1 · Q32The table shows the operation $*$ on the set $\{x, y, z, w\}$.
• WAEC 2022 · Paper 1 · Q1A binary operation $\Delta$ is defined on the set of real numbers, $R$, by $x \Delta y = \sqrt{x + y - \dfrac{xy}{4}}$, where $x, y \in R$. Find …
• WAEC 2020 · Paper 1 · Q1A binary operation $*$ is defined on the set of real numbers, $\mathbb{R}$, by $x * y = x^2 - y^2 + xy$, where $x, y \in \mathbb{R}$. Evaluate …