Variables and algebraic expressions

Evaluate $2x^2 - 5x$ when $x = -3$.

Simplify $4x + 3y - x + 5y - 2$.

Kofi sells bags of oranges at a market in Kumasi for $12$ cedis each. He pays $15$ cedis a day for his stall. Which expression gives his profit, in cedis, on a day when he sells $x$ bags?

Expand $(x + 5)(x - 2)$ and write it as $x^2 + bx + c$. What is $b$?

Which is the complete factorisation of $12x + 18$?

Which of these are equal to $2^{12}$? (Choose all that apply.)

Zainab tests the rule $(a + b)^2 = a^2 + b^2$ with $a = 0, b = 7$ and with $a = 5, b = 0$. It works both times. What is the right conclusion?

Which Lean statement says that $(a + b)^2 = a^2 + 2ab + b^2$ is an identity for the integers?

Write find_counterexample(f, g, values) that returns the first v in values with f(v) != g(v), or None if f and g agree on all of them. Then think: if it returns None, have you proved that f and g are equivalent?

A row of hexagons is made from matchsticks; neighbouring hexagons share one side. How many matchsticks are needed for a row of $20$ hexagons? (Find an expression for $n$ hexagons first.)