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Grade 11 practice chapters

1. Grade 11 · Chapter 581

   Rational functions · Numerator a=3; 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=3; Pole location b=0.

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2. Grade 11 · Chapter 582

   Logarithms and domains · Domain boundary a=1; Logarithm base b=4

   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=4.

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3. Grade 11 · Chapter 583

   Geometric sums · First term a=4; 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=4; Ratio r=0.5.

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4. Grade 11 · Chapter 584

   Complex polar form · Modulus r=2; 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; Final angle (degrees)=45.

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5. Grade 11 · Chapter 585

   Triangle area and angle · Second side b=6; Included angle (degrees)=90

   Use the included angle C=60°. Find the area and the side opposite C. Givens: Second side b=6; Included angle (degrees)=90.

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6. Grade 11 · Chapter 586

   Quadratic sequences · Quadratic coefficient a=1.5; 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=1.5; Linear coefficient b=-2.5.

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7. Grade 11 · Chapter 587

   Rescaling data · Scale a=1.5; 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=1.5; Shift b=-2.5.

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8. Grade 11 · Chapter 588

   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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9. Grade 11 · Chapter 589

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

   Evaluate at x=3, 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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10. Grade 11 · Chapter 590

    Geometric sums · First term a=4.5; Ratio r=0.6

    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=0.6.

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11. Grade 11 · Chapter 591

    Complex polar form · Modulus r=2.5; 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=2.5; Final angle (degrees)=60.

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12. Grade 11 · Chapter 592

    Triangle area and angle · Second side b=1; Included angle (degrees)=120

    Use the included angle C=78°. Find the area and the side opposite C. Givens: Second side b=1; Included angle (degrees)=120.

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13. Grade 11 · Chapter 593

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

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14. Grade 11 · Chapter 594

    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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15. Grade 11 · Chapter 595

    Logarithms and domains · Domain boundary a=2; Logarithm base b=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=5.

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16. Grade 11 · Chapter 596

    Geometric sums · First term a=5; Ratio r=0.7

    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=0.7.

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17. Grade 11 · Chapter 597

    Complex polar form · Modulus r=3; 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=3; Final angle (degrees)=75.

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18. Grade 11 · Chapter 598

    Triangle area and angle · Second side b=1.5; Included angle (degrees)=135

    Use the included angle C=87°. Find the area and the side opposite C. Givens: Second side b=1.5; Included angle (degrees)=135.

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19. Grade 11 · Chapter 599

    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 600

    Rescaling data · Scale a=-2; 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=-2; Shift b=1.

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