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Grade 11 practice chapters

1. Grade 11 · Chapter 381

   Geometric sums · First term a=4.5; 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=4.5; Ratio r=0.3.

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2. Grade 11 · Chapter 382

   Complex polar form · Modulus r=1; Final angle (degrees)=-60

   Evaluate at the signed angle θ=-36° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=1; Final angle (degrees)=-60.

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3. Grade 11 · Chapter 383

   Triangle area and angle · Second side b=2.5; Included angle (degrees)=120

   Use the included angle C=78°. Find the area and the side opposite C. Givens: Second side b=2.5; Included angle (degrees)=120.

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4. Grade 11 · Chapter 384

   Quadratic sequences · Quadratic coefficient a=2; Linear coefficient b=3

   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=3.

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5. Grade 11 · Chapter 385

   Rescaling data · Scale a=2; Shift b=3

   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=3.

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6. Grade 11 · Chapter 386

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

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7. Grade 11 · Chapter 387

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

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8. Grade 11 · Chapter 388

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

   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=3.5.

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9. Grade 11 · Chapter 389

   Geometric sums · First term a=5; 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=5; Ratio r=0.4.

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10. Grade 11 · Chapter 390

    Complex polar form · Modulus r=1.5; 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=1.5; Final angle (degrees)=-45.

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11. Grade 11 · Chapter 391

    Triangle area and angle · Second side b=3; Included angle (degrees)=135

    Use the included angle C=87°. Find the area and the side opposite C. Givens: Second side b=3; Included angle (degrees)=135.

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12. Grade 11 · Chapter 392

    Quadratic sequences · Quadratic coefficient a=-2; 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=-2; Linear coefficient b=-0.5.

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13. Grade 11 · Chapter 393

    Rescaling data · Scale a=-2; 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=-2; Shift b=-0.5.

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14. Grade 11 · Chapter 394

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

    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=3.

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15. Grade 11 · Chapter 395

    Rational functions · Numerator a=3; 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; Pole location b=-1.5.

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16. Grade 11 · Chapter 396

    Logarithms and domains · Domain boundary a=-2; Logarithm base b=4

    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=4.

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17. Grade 11 · Chapter 397

    Exponential calibration · Initial value a=2; 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=2; Exponential rate b=0.5.

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18. Grade 11 · Chapter 398

    Geometric sums · First term a=1; 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; Ratio r=-0.3.

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19. Grade 11 · Chapter 399

    Complex polar form · Modulus r=2; 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=2; Final angle (degrees)=-30.

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20. Grade 11 · Chapter 400

    Triangle area and angle · Second side b=3.5; Included angle (degrees)=150

    Use the included angle C=96°. Find the area and the side opposite C. Givens: Second side b=3.5; Included angle (degrees)=150.

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