Maths MCQs on Expressions and Functions

Algebraic Expressions and Equations

Evaluating Expressions

• To evaluate an expression, substitute the given value of the variable into the expression.
• Example: Evaluate the expression $3x^2 - 5x + 2$ when $x = -2$.
  • Replace $x$ with $-2$ in the expression.
  • Calculate the value of the expression: $3(-2)^2 - 5(-2) + 2 = 3(4) + 10 + 2 = 12 + 10 + 2 = 24$

Function Values

• A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
• To find the value of a function, substitute the input value into the function.
• Examples:
  • Find the value of $f(x) = 2x^2 - 3x + 5$ when $x = 3$.
• Replace $x$ with $3$ in the function: $f(3) = 2(3)^2 - 3(3) + 5 = 2(9) - 9 + 5 = 18 - 9 + 5 = 14$
  • Find the value of $g(x) = 4x^2 + 2x - 6$ when $x = -2$.
• Replace $x$ with $-2$ in the function: $g(-2) = 4(-2)^2 + 2(-2) - 6 = 4(4) - 4 - 6 = 16 - 4 - 6 = 6$

Solving Equations

• An equation is a statement that two expressions are equal.
• To solve an equation, isolate the variable on one side of the equation.
• Example: Solve the equation $5x - 3 = 2x + 7$.
• Add 3 to both sides: $5x = 2x + 10$
• Subtract 2x from both sides: $3x = 10$
• Divide both sides by 3: $x = 10/3$

Simplifying Expressions

• Simplify the expression $4(3x - 2) - 2(2x + 1)$ when $x = 4$.
• Expand the expression: $12x - 8 - 4x - 2 = 8x - 10$
• Substitute $x = 4$ into the simplified expression: $8(4) - 10 = 32 - 10 = 22$