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Grade 11 practice chapters

1. Grade 11 · Chapter 461

   Complex polar form · Modulus r=1; 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=1; Final angle (degrees)=-30.

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2. Grade 11 · Chapter 462

   Triangle area and angle · Second side b=2.5; Included angle (degrees)=135

   Use the included angle C=87°. Find the area and the side opposite C. Givens: Second side b=2.5; Included angle (degrees)=135.

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3. Grade 11 · Chapter 463

   Quadratic sequences · Quadratic coefficient a=-2; Linear coefficient b=0

   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.

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4. Grade 11 · Chapter 464

   Rescaling data · Scale a=-2; Shift b=0

   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.

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5. Grade 11 · Chapter 465

   Rational functions · Numerator a=3.5; Pole location b=-0.5

   Evaluate at x=2, 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=-0.5.

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6. Grade 11 · Chapter 466

   Logarithms and domains · Domain boundary a=-2; Logarithm base b=4.5

   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=4.5.

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7. Grade 11 · Chapter 467

   Exponential calibration · Initial value a=0.5; 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=0.5; Exponential rate b=0.4.

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8. Grade 11 · Chapter 468

   Geometric sums · First term a=1; 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=1; Ratio r=-0.2.

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9. Grade 11 · Chapter 469

   Complex polar form · Modulus r=1.5; Final angle (degrees)=-15

   Evaluate at the signed angle θ=-9° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=1.5; Final angle (degrees)=-15.

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10. Grade 11 · Chapter 470

    Triangle area and angle · Second side b=3; Included angle (degrees)=150

    Use the included angle C=96°. Find the area and the side opposite C. Givens: Second side b=3; Included angle (degrees)=150.

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11. Grade 11 · Chapter 471

    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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12. Grade 11 · Chapter 472

    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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13. Grade 11 · Chapter 473

    Polynomial roots · First root a=-3; 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=-3; Second root b=-0.5.

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14. Grade 11 · Chapter 474

    Rational functions · Numerator a=4; Pole location b=0

    Evaluate at x=2.5, exactly 2.5 units to the right of the pole. Find the value, derivative, and excluded input. Givens: Numerator a=4; Pole location b=0.

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15. Grade 11 · Chapter 475

    Logarithms and domains · Domain boundary a=-1.5; Logarithm base b=5

    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=5.

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16. Grade 11 · Chapter 476

    Geometric sums · First term a=1.5; Ratio r=-0.1

    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=-0.1.

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17. Grade 11 · Chapter 477

    Complex polar form · Modulus r=2.5; Final angle (degrees)=15

    Evaluate at the signed angle θ=9° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=2.5; Final angle (degrees)=15.

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18. Grade 11 · Chapter 478

    Triangle area and angle · Second side b=3.5; Included angle (degrees)=165

    Use the included angle C=105°. Find the area and the side opposite C. Givens: Second side b=3.5; Included angle (degrees)=165.

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19. Grade 11 · Chapter 479

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

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20. Grade 11 · Chapter 480

    Rescaling data · Scale a=-1; Shift b=1

    Use the completed transformation, at the end of the animation. Find the transformed mean, population variance, and population standard deviation. Givens: Scale a=-1; Shift b=1.

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