Mathematics · Grades 9–10
Algebra · Formula sheet
Rules, conditions and small examples in one printable reference.
Remember this
Substitute into an expression
Substitute with brackets, then follow the order of operations.
ax + b → a × (value of x) + b
9 × (-2) + 12 = -6
Combine like terms
Only terms with the same variable part can be combined this way.
ax + bx = (a + b)x
(32 + 33)x = 65x
Equations with x on both sides
Perform the same operation on both sides. Here a is different from c.
ax + b = cx + d → (a − c)x = d − b
7x = 49 → x = 7
Simultaneous equations
Add the equations to eliminate y, then solve for x.
x + y = s; x − y = d → x = (s + d)/2
2x = 50 → x = 25
Inverse linear functions
Undo addition first, then undo multiplication.
f⁻¹(y) = (y − b)/a, a ≠ 0
(-9 − (15)) ÷ 6 = -4
Compose two functions
Apply the inside function first.
(f ∘ g)(x) = f(g(x))
g(7) = 30; f(30) = 117
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.