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1 Number and algebra

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  1. 1.1 Number and algebra - SL content

    1. • Use numbers in the form a x 10^k where 1 <= a < 10 and k is an integer. • Calculator/computer notation such as 5.2E30 is not acceptable.

    2. • Use nth-term, finite-sum and sigma notation for arithmetic sequences. • Identify first term and common difference; apply to contexts such as simple interest.

    3. • Use nth-term, finite-sum and sigma notation for geometric sequences. • Identify first term and common ratio; apply to growth/decay contexts.

    4. • Apply geometric sequences to compound interest and annual depreciation. • Use technology/financial packages; consider inflation and compounding frequency.

    5. • Use laws of exponents with integer exponents. • Understand base-10 and natural logarithms; ax=b is equivalent to log_a(b)=x.

    6. • Use decimal places, significant figures and appropriate accuracy. • Work with upper/lower bounds of rounded numbers. • Calculate percentage errors and judge whether results are reasonable.

    7. • Use technology for amortization and annuity problems. • Payments are made at the end of each period in examinations. • Knowing the annuity formula may help, but it is not examined.

    8. • Use technology to solve systems of up to three linear equations. • Use technology to solve polynomial equations. • Know terms such as roots and zeros; exam systems have unique solutions.

  2. 1.2 Number and algebra - AHL content

    1. AHL 1.9 (HL)—Logarithm laws

      • Use logarithm laws for products, quotients and powers. • In examinations, logarithm bases are 10 or e.

    2. AHL 1.10 (HL)—Rational exponents

      • Simplify numerical and algebraic expressions with rational exponents. • Include negative and fractional powers.

    3. AHL 1.11 (HL)—Infinite geometric sequences

      • Find sums of infinite geometric sequences. • Connect convergence to limits, fractals and Markov chains.

    4. AHL 1.12 (HL)—Complex numbers

      • Use i where i^2=-1 and Cartesian form z=a+bi. • Calculate sums, differences, products, quotients and powers of complex numbers. • Use Argand diagrams and complex roots of real-coefficient quadratics with negative discriminant.

    5. AHL 1.13 (HL)—Complex forms and applications

      • Use polar form z=r(cos theta+i sin theta)=r cis theta and Euler form z=re^(i theta). • Convert between Cartesian, polar and exponential forms. • Use products, quotients and integer powers; roots are not required. • Interpret complex operations geometrically and model sinusoidal phase shifts.

    6. AHL 1.14 (HL)—Matrices

      • Use matrix terminology, order, equality, addition, subtraction, scalar multiplication and multiplication. • Know identity/zero matrices, determinants and inverses; hand calculation is limited to 2x2 inverses/determinants. • Write systems as Ax=b and solve with inverse matrices; apply matrices to coding, decoding and systems.

    7. AHL 1.15 (HL)—Eigenvalues and eigenvectors

      • Find eigenvalues/eigenvectors and characteristic polynomial for 2x2 matrices. • Diagonalize 2x2 matrices with distinct real eigenvalues. • Use M^n=PD^nP^-1 for powers and applications such as population movement or predator-prey models.