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Grade 11 practice chapters

1. Grade 11 · Chapter 441

   Rescaling data · Scale a=1; 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=1; Shift b=2.5.

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2. Grade 11 · Chapter 442

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

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3. Grade 11 · Chapter 443

   Logarithms and domains · Domain boundary a=1; Logarithm base b=3

   Use x=4.08; 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=3.

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4. Grade 11 · Chapter 444

   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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5. Grade 11 · Chapter 445

   Geometric sums · First term a=4; 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; Ratio r=0.3.

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6. Grade 11 · Chapter 446

   Complex polar form · Modulus r=3; 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=3; Final angle (degrees)=15.

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7. Grade 11 · Chapter 447

   Triangle area and angle · Second side b=1.5; Included angle (degrees)=105

   Use the included angle C=69°. Find the area and the side opposite C. Givens: Second side b=1.5; Included angle (degrees)=105.

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8. Grade 11 · Chapter 448

   Quadratic sequences · Quadratic coefficient a=1.5; 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=1.5; Linear coefficient b=3.

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9. Grade 11 · Chapter 449

   Rescaling data · Scale a=1.5; 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=1.5; Shift b=3.

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10. Grade 11 · Chapter 450

    Polynomial roots · First root a=0; Second root b=2

    Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=0; Second root b=2.

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11. Grade 11 · Chapter 451

    Rational functions · Numerator a=2.5; 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=2.5; Pole location b=-1.5.

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12. Grade 11 · Chapter 452

    Logarithms and domains · Domain boundary a=1.5; Logarithm base b=3.5

    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=3.5.

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13. Grade 11 · Chapter 453

    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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14. Grade 11 · Chapter 454

    Geometric sums · First term a=4.5; 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=4.5; Ratio r=0.4.

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15. Grade 11 · Chapter 455

    Complex polar form · Modulus r=0.5; 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=0.5; Final angle (degrees)=-45.

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16. Grade 11 · Chapter 456

    Triangle area and angle · Second side b=2; Included angle (degrees)=120

    Use the included angle C=78°. Find the area and the side opposite C. Givens: Second side b=2; Included angle (degrees)=120.

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17. Grade 11 · Chapter 457

    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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18. Grade 11 · Chapter 458

    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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19. Grade 11 · Chapter 459

    Polynomial roots · First root a=0.5; 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=0.5; Second root b=2.5.

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20. Grade 11 · Chapter 460

    Geometric sums · First term a=5; Ratio r=0.5

    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=0.5.

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