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Grade 11 practice chapters

1. Grade 11 · Chapter 301

   Quadratic sequences · Quadratic coefficient a=1.5; Linear coefficient b=2

   Use index n=6. Calculate u₆, the forward first difference u₇−u₆, and the second difference u₈−2u₇+u₆. Givens: Quadratic coefficient a=1.5; Linear coefficient b=2.

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2. Grade 11 · Chapter 302

   Rescaling data · Scale a=1.5; Shift b=2

   Use the completed transformation, at the end of the animation. Find the transformed mean, population variance, and population standard deviation. Givens: Scale a=1.5; Shift b=2.

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3. Grade 11 · Chapter 303

   Polynomial roots · First root a=1.5; Second root b=2.5

   Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=1.5; Second root b=2.5.

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4. Grade 11 · Chapter 304

   Rational functions · Numerator a=1.5; Pole location b=1

   Evaluate at x=3.5, exactly 2.5 units to the right of the pole. Find the value, derivative, and excluded input. Givens: Numerator a=1.5; Pole location b=1.

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5. Grade 11 · Chapter 305

   Logarithms and domains · Domain boundary a=1.5; Logarithm base b=2.5

   Use x=4.58; the logarithm argument is exactly 3.08. State the domain, evaluate the logarithm, and recover the argument by exponentiation. Givens: Domain boundary a=1.5; Logarithm base b=2.5.

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6. Grade 11 · Chapter 306

   Exponential calibration · Initial value a=2.5; Exponential rate b=0.4

   Evaluate at t=2.4 time units. Find the signal value, tangent slope, and multiplicative change from f(0). Givens: Initial value a=2.5; Exponential rate b=0.4.

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7. Grade 11 · Chapter 307

   Geometric sums · First term a=4.5; Ratio r=0.2

   Include the first n=8 terms, from ar⁰ through ar⁷. Calculate the finite sum, last included term, and infinite-series limit. Givens: First term a=4.5; Ratio r=0.2.

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8. Grade 11 · Chapter 308

   Complex polar form · Modulus r=2.5; Final angle (degrees)=-45

   Evaluate at the signed angle θ=-27° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=2.5; Final angle (degrees)=-45.

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9. Grade 11 · Chapter 309

   Quadratic sequences · Quadratic coefficient a=2; Linear coefficient b=2.5

   Use index n=6. Calculate u₆, the forward first difference u₇−u₆, and the second difference u₈−2u₇+u₆. Givens: Quadratic coefficient a=2; Linear coefficient b=2.5.

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10. Grade 11 · Chapter 310

    Rescaling data · Scale a=2; Shift b=2.5

    Use the completed transformation, at the end of the animation. Find the transformed mean, population variance, and population standard deviation. Givens: Scale a=2; Shift b=2.5.

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11. Grade 11 · Chapter 311

    Polynomial roots · First root a=2; Second root b=3

    Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=2; Second root b=3.

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12. Grade 11 · Chapter 312

    Rational functions · Numerator a=2; Pole location b=1.5

    Evaluate at x=4, exactly 2.5 units to the right of the pole. Find the value, derivative, and excluded input. Givens: Numerator a=2; Pole location b=1.5.

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13. Grade 11 · Chapter 313

    Logarithms and domains · Domain boundary a=2; Logarithm base b=3

    Use x=5.08; the logarithm argument is exactly 3.08. State the domain, evaluate the logarithm, and recover the argument by exponentiation. Givens: Domain boundary a=2; Logarithm base b=3.

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14. Grade 11 · Chapter 314

    Exponential calibration · Initial value a=3; Exponential rate b=0.5

    Evaluate at t=2.4 time units. Find the signal value, tangent slope, and multiplicative change from f(0). Givens: Initial value a=3; Exponential rate b=0.5.

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15. Grade 11 · Chapter 315

    Geometric sums · First term a=5; Ratio r=0.3

    Include the first n=8 terms, from ar⁰ through ar⁷. Calculate the finite sum, last included term, and infinite-series limit. Givens: First term a=5; Ratio r=0.3.

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16. Grade 11 · Chapter 316

    Complex polar form · Modulus r=3; Final angle (degrees)=-30

    Evaluate at the signed angle θ=-18° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=3; Final angle (degrees)=-30.

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17. Grade 11 · Chapter 317

    Trigonometric periods · Amplitude A=3; Angular frequency k=2.5

    Evaluate at x=6π/5 radians, keeping π exact during calculation. Find the signal value, derivative with respect to x, and period. Givens: Amplitude A=3; Angular frequency k=2.5.

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18. Grade 11 · Chapter 318

    Triangle area and angle · Second side b=3.5; Included angle (degrees)=135

    Use the included angle C=87°. Find the area and the side opposite C. Givens: Second side b=3.5; Included angle (degrees)=135.

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19. Grade 11 · Chapter 319

    Quadratic sequences · Quadratic coefficient a=-2; Linear coefficient b=-1

    Use index n=6. Calculate u₆, the forward first difference u₇−u₆, and the second difference u₈−2u₇+u₆. Givens: Quadratic coefficient a=-2; Linear coefficient b=-1.

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20. Grade 11 · Chapter 320

    Polynomial roots · First root a=-3; Second root b=-1.5

    Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=-3; Second root b=-1.5.

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