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Grade 11 practice chapters

1. Grade 11 · Chapter 321

   Rational functions · Numerator a=2.5; Pole location b=2

   Evaluate at x=4.5, exactly 2.5 units to the right of the pole. Find the value, derivative, and excluded input. Givens: Numerator a=2.5; Pole location b=2.

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2. Grade 11 · Chapter 322

   Logarithms and domains · Domain boundary a=-2; Logarithm base b=3.5

   Use x=1.08; 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=3.5.

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3. Grade 11 · Chapter 323

   Exponential calibration · Initial value a=0.5; Exponential rate b=0.1

   Evaluate at t=2.4 time units. Find the signal value, tangent slope, and multiplicative change from f(0). Givens: Initial value a=0.5; Exponential rate b=0.1.

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4. Grade 11 · Chapter 324

   Geometric sums · First term a=1; Ratio r=-0.4

   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=1; Ratio r=-0.4.

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5. Grade 11 · Chapter 325

   Complex polar form · Modulus r=0.5; Final angle (degrees)=-90

   Evaluate at the signed angle θ=-54° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=0.5; Final angle (degrees)=-90.

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6. Grade 11 · Chapter 326

   Triangle area and angle · Second side b=4; Included angle (degrees)=150

   Use the included angle C=96°. Find the area and the side opposite C. Givens: Second side b=4; Included angle (degrees)=150.

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7. Grade 11 · Chapter 327

   Quadratic sequences · Quadratic coefficient a=-1.5; Linear coefficient b=-0.5

   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=-0.5.

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8. Grade 11 · Chapter 328

   Rescaling data · Scale a=-1.5; Shift b=-0.5

   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=-0.5.

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9. Grade 11 · Chapter 329

   Polynomial roots · First root a=-2.5; Second root b=-1

   Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=-2.5; Second root b=-1.

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10. Grade 11 · Chapter 330

    Rational functions · Numerator a=3; Pole location b=-2

    Evaluate at x=0.5, exactly 2.5 units to the right of the pole. Find the value, derivative, and excluded input. Givens: Numerator a=3; Pole location b=-2.

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11. Grade 11 · Chapter 331

    Logarithms and domains · Domain boundary a=-1.5; Logarithm base b=4

    Use x=1.58; 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=4.

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12. Grade 11 · Chapter 332

    Exponential calibration · Initial value a=1; Exponential rate b=0.2

    Evaluate at t=2.4 time units. Find the signal value, tangent slope, and multiplicative change from f(0). Givens: Initial value a=1; Exponential rate b=0.2.

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13. Grade 11 · Chapter 333

    Geometric sums · First term a=1.5; 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=1.5; Ratio r=-0.3.

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14. Grade 11 · Chapter 334

    Complex polar form · Modulus r=1; Final angle (degrees)=-75

    Evaluate at the signed angle θ=-45° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=1; Final angle (degrees)=-75.

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15. Grade 11 · Chapter 335

    Triangle area and angle · Second side b=4.5; Included angle (degrees)=165

    Use the included angle C=105°. Find the area and the side opposite C. Givens: Second side b=4.5; Included angle (degrees)=165.

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16. Grade 11 · Chapter 336

    Polynomial roots · First root a=-2; Second root b=-0.5

    Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=-2; Second root b=-0.5.

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17. Grade 11 · Chapter 337

    Rational functions · Numerator a=3.5; Pole location b=-1.5

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

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18. Grade 11 · Chapter 338

    Logarithms and domains · Domain boundary a=-1; Logarithm base b=4.5

    Use x=2.08; the logarithm argument is exactly 3.08. State the domain, evaluate the logarithm, and recover the argument by exponentiation. Givens: Domain boundary a=-1; Logarithm base b=4.5.

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19. Grade 11 · Chapter 339

    Exponential calibration · Initial value a=1.5; Exponential rate b=0.3

    Evaluate at t=2.4 time units. Find the signal value, tangent slope, and multiplicative change from f(0). Givens: Initial value a=1.5; Exponential rate b=0.3.

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20. Grade 11 · Chapter 340

    Geometric sums · First term a=2; 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=2; Ratio r=-0.2.

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