Print a formula sheet for your class
Each formula sheet is organised by topic with plain-English explanations and worked examples. Open a level below, then press Ctrl+P (Windows) or ⌘P (Mac) to print. The print layout removes navigation and renders a clean A4 document.
Errors your students are definitely making
These five errors appear in almost every SA matric exam marking session. Photocopy and hand them out before the November exam — or send the link to your class.
Confusing sin²(x) with sin(x²)
Grade 11–12sin²(x) means [sin(x)]² — the square of the sine value. sin(x²) means apply sine to x². These are not equal.
Write sin²(x) = (sin x)(sin x). Never move the exponent inside the argument.
sin²(30°) = (0.5)² = 0.25. But sin(30²) = sin(900°) ≈ 0.866
Cancelling instead of factorising
Grade 10–12Students write (x² + 4x) / x = x + 4x — they cancel x from the top and bottom of the fraction incorrectly.
Factorise first: (x² + 4x)/x = x(x + 4)/x = x + 4. Division by zero (x = 0) must be excluded.
(x² + 4x)/x ≠ x + 4x. Correct: factorise → x(x+4)/x = x+4, x ≠ 0
Wrong compound interest vs simple interest
Grade 10–12Simple interest: A = P(1 + ni). Compound interest: A = P(1 + i)ⁿ. Students confuse them on exam questions.
Identify the keyword: "simple interest" → A = P(1+ni). "Compound interest" or no qualifier → A = P(1+i)ⁿ.
P=R1000, 10% for 3 years. Simple: 1000(1+0.3)=1300. Compound: 1000(1.1)³≈1331.
Derivative of product — forgetting the product rule
Grade 12Students write d/dx[f(x)g(x)] = f'(x)g'(x). This is wrong. The product rule applies.
d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x). Always expand or use the product rule.
d/dx[x·sin(x)] = 1·sin(x) + x·cos(x) = sin x + x cos x. NOT cos(x) alone.
Area under curve and negative values
Grade 12When a function dips below the x-axis, ∫f(x)dx gives a negative value. Students report this as area.
Area = |∫f(x)dx| for regions below the axis. Split the integral at x-intercepts and sum absolute values.
∫from 0 to 2π sin(x)dx = 0 (areas cancel). Actual area = 4 square units.
In-depth concept pages — shareable links
Each Explore page is a curated, research-backed one-pager on a specific concept. Send the link to struggling students or display in class before introducing a topic.
The full curriculum is on The Continuum
The Continuum hosts the complete SA mathematics curriculum — interactive workspaces, guided practice, and adaptive learning paths — for students who want to go further than the classroom.