Introduction to algebra: Practice Questions

If a number \( n \) is multiplied by 5 and then decreased by 8, which expression represents the final result?

Evaluate the expression \( \frac{x^2 - 2y}{x + y} \) when \( x = -3 \) and \( y = 4 \).

If \( n \) is any integer, which of the following expressions will always result in an odd number?

A shop sells apples for \( a \) cents each and oranges for \( r \) cents each. Write an expression for the total cost, in cents, of 4 apples and 7 oranges.

Solve the following equation for \( x \):
\( \frac{x - 1}{2} - \frac{x - 2}{3} = \frac{x + 1}{4} \)

Write an algebraic expression for a number that is 5 less than three times \( n \).

Find the value of the expression \( \frac{b^2 - 4ac}{2a} \) when \( a = -2 \), \( b = -6 \), and \( c = 3 \).

Expand and simplify the expression \( (x + 2)(x - 1)(x + 3) \).

A taxi service charges a fixed booking fee of $$ \$5 $$ and an additional $$ \$2.50 $$ for every kilometre travelled.

(a) Write an algebraic expression for the total cost, $$ C $$, of a journey that covers $$ x $$ kilometres.

(b) Calculate the total cost of a journey of $$ 15 $$ kilometres.

(c) If a customer paid $$ \$40 $$ for a journey, how many kilometres did they travel?

(a) Simplify the algebraic fraction fully: \( \frac{x^2 + 5x - 24}{3x^2 - 192} \).

(b) Write as a single fraction in its simplest form: \( \frac{3}{x+1} - \frac{2}{x-2} \).

(c) Factorise completely the expression: \( 2ay - 6by + 4ax - 12bx \).