The most common arithmetic errors on the GDC come from missing brackets - especially with fractions, negatives and powers.
In short: Brackets, powers and roots must be entered so the calculator follows the same order of operations you would use by hand. Put brackets around any numerator, denominator or exponent made of more than one term, and use the dedicated power and root keys. Most lost marks come from a missing bracket, not from the maths itself.
When you'd use this
A fraction where the numerator or denominator has more than one term, e.g. (a+b)/(c-d).
A negative number raised to a power, where the bracket changes the sign of the result.
A compound exponent such as 2x+1 in x^(2x+1) - without brackets, only part of it is treated as the power.
A multi-term expression under a root, e.g. √(a+b), not just the first term.
Here's a real IB-style question that uses exactly this technique.
EasyCalculatorPaper 1[2 marks]
Evaluate (2 + 3) ÷ (4 − 1)², giving your answer as a fraction.
5/9
Mark it
Correct2 / 2 marks
Worked solution & mark scheme:
M1 Correct bracketing of numerator and denominator
A1 5/9
Common questions
When would I need to use brackets, powers and roots correctly in IB Maths?
The most common arithmetic errors on the GDC come from missing brackets - especially with fractions, negatives and powers. A fraction where the numerator or denominator has more than one term, e.g. (a+b)/(c-d). A negative number raised to a power, where the bracket changes the sign of the result.
How do I use brackets, powers and roots correctly on a TI-84 Plus CE?
1. Use brackets whenever you have a fraction, a negative, or a compound expression in an exponent. 2. Fraction: type (3+5)÷(2−1) not 3+5÷2−1 - the calculator respects order of operations, so division binds tightly. 3. Power: type (2x+1)^3 not 2x+1^3 - without brackets only the 1 is cubed. 4. Square root: the √ key only captures what immediately follows - use √(expression) with a closing bracket for multi-term expressions. 5. Powers: use the ^ key. Square root: 2nd → √ then close the bracket. Cube root: MATH → 4:∛( or x^(1/3). 6. Always check the answer makes sense - a wildly large or small result usually means a missing bracket.
How do I use brackets, powers and roots correctly on a Casio fx-CG50 and fx-CG100?
1. Use brackets whenever you have a fraction, a negative, or a compound expression in an exponent. 2. Fraction: type (3+5)÷(2−1) not 3+5÷2−1 - the calculator respects order of operations, so division binds tightly. 3. Power: type (2x+1)^3 not 2x+1^3 - without brackets only the 1 is cubed. 4. Square root: the √ key only captures what immediately follows - use √(expression) with a closing bracket for multi-term expressions. 5. Powers: use the ^ key (x□ key). Square root: SHIFT → √. Fractions: use the fraction template (SHIFT → ÷) for clean stacked fractions. 6. Always check the answer makes sense - a wildly large or small result usually means a missing bracket.
How do I use brackets, powers and roots correctly on a TI-Nspire CX?
1. Use brackets whenever you have a fraction, a negative, or a compound expression in an exponent. 2. Fraction: type (3+5)÷(2−1) not 3+5÷2−1 - the calculator respects order of operations, so division binds tightly. 3. Power: type (2x+1)^3 not 2x+1^3 - without brackets only the 1 is cubed. 4. Square root: the √ key only captures what immediately follows - use √(expression) with a closing bracket for multi-term expressions. 5. Powers: use the ^ key or the exponent template. Roots: use the √ template from the maths palette (ctrl+B or the template key). 6. Always check the answer makes sense - a wildly large or small result usually means a missing bracket.
What should I watch out for when I use brackets, powers and roots correctly?
When in doubt, add extra brackets. (3+5)÷(2) and 3+5÷2 give different answers - the first is almost always what you mean.
How are marks awarded when I use brackets, powers and roots correctly in an IB exam?
In the worked example on this page (2 marks, Paper 1), the marks are: M1: Correct bracketing of numerator and denominator; A1: 5/9.
