✅ MASTERING YOUR CALCULATOR
Cambridge IGCSE Mathematics — Notes, Advanced Examples, Quizzes & Solutions
👩🎓 What You Will Learn
- Correct calculator usage for multi-step problems.
- Apply BODMAS with powers, roots, and fractions.
- Round correctly to significant figures and decimal places.
- Solve advanced expressions involving sums, differences, numerators, denominators.
- Handle standard form and complex mixed operations efficiently.
1. Why Your Calculator is Important
It saves time and reduces errors in complex calculations.
Example: Without a calculator: finding \(\sqrt{98.6}\) is tedious. With a calculator: \(\sqrt{98.6}=9.929...\)
2. The BODMAS Rule
Follow this order: Brackets → Orders → Division/Multiplication → Addition → Subtraction.
Example:
\[ (15.4 + 8.6) \times 2^3 \]
- \(15.4 + 8.6 = 24\)
- \(2^3 = 8\)
- \(24 \times 8 = 192\)
3. Rounding Correctly
Significant Figures (s.f.): Count from the first non-zero digit.
Decimal Places (d.p.): Count digits after the decimal point.
- \(0.004532\) to 3 s.f. → \(0.00453\)
- \(23.6789\) to 2 d.p. → \(23.68\)
4. Standard Form
Write as \(a \times 10^n\), where \(1 \le a < 10\).
Example: \(1,230,000 = 1.23 \times 10^6\)
5. Calculator Keys You Must Know
EXPor×10^x→ Standard form√→ Square rootx²→ Square a number
Example: \(3.5^2 = 12.25\)
✅ Basic Worked Examples
- \((45.6 + 23.78) - 12.45 = 56.93\)
- \(\sqrt{75.3} = 8.678...\approx8.68\) (2 d.p.)
- \(\dfrac{254.67}{13.2} = 19.283...\approx19.3\) (3 s.f.)
- \(\dfrac{7.5^3}{15} = 28.125\approx28\) (2 s.f.)
🔥 Advanced Multi-step Examples
Example A
\[ \dfrac{\big(4.8^2+3.6^2\big)-(7.2\times1.5)}{12.5-8.75} \]
Solution: \(4.8^2=23.04,\ 3.6^2=12.96,\) sum=36; subtract \(10.8\)=25.2; divide by \(3.75\)=6.72.
Example B
\[ \dfrac{(2.35\times10^3)+(4.8\times10^2)}{(6.5-2.7)^2} \]
Solution: Numerator=2830; denominator=\(3.8^2=14.44\); result≈196.
Example C
\[ \dfrac{\sqrt{15.2^2+9.6^2}+3.5^3}{(18.4\div2.3)-5} \]
Solution: root≈17.98; cube=42.875; sum=60.85; denominator=3; result=20.3.
✅ Practice Section — Test Yourself
Part C — Advanced Challenge
- \[ \dfrac{(5.4^2+7.8^2)-(3.6\times2.1)}{12.6-8.4} \]
- \[ \dfrac{3.1^3+2.8^2}{(6.3\div2.1)-1.5} \]
- \[ \Bigg(\dfrac{2}{3}+\dfrac{4}{5}-\dfrac{7}{10}\Bigg)\times\dfrac{(3.2^2-2.8^2)}{0.08} \]
- \[ \dfrac{(0.0062\times10^4)+(1.8\times10^3)}{(7.5-3.2)^2} \]
Show Solutions
1. 19.6 (3 s.f.)
2. 25.1 (3 s.f.)
3. 23
4. 101 (3 s.f.)