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Grade 11 practice chapters

1. Grade 11 · Chapter 501

   Complex polar form · Modulus r=1; 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; Final angle (degrees)=-15.

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2. Grade 11 · Chapter 502

   Triangle area and angle · Second side b=5.5; Included angle (degrees)=60

   Use the included angle C=42°. Find the area and the side opposite C. Givens: Second side b=5.5; Included angle (degrees)=60.

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3. Grade 11 · Chapter 503

   Quadratic sequences · Quadratic coefficient a=0.5; 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=0.5; Linear coefficient b=2.5.

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4. Grade 11 · Chapter 504

   Polynomial roots · First root a=-1; Second root b=1.5

   Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=-1; Second root b=1.5.

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5. Grade 11 · Chapter 505

   Rational functions · Numerator a=2; 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; Pole location b=-1.5.

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6. Grade 11 · Chapter 506

   Logarithms and domains · Domain boundary a=0.5; Logarithm base b=3

   Use x=3.58; the logarithm argument is exactly 3.08. State the domain, evaluate the logarithm, and recover the argument by exponentiation. Givens: Domain boundary a=0.5; Logarithm base b=3.

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7. Grade 11 · Chapter 507

   Exponential calibration · Initial value a=3; 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=3; Exponential rate b=-0.2.

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8. Grade 11 · Chapter 508

   Geometric sums · First term a=3.5; 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=3.5; Ratio r=0.3.

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9. Grade 11 · Chapter 509

   Complex polar form · Modulus r=2; 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; Final angle (degrees)=15.

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10. Grade 11 · Chapter 510

    Triangle area and angle · Second side b=6; Included angle (degrees)=75

    Use the included angle C=51°. Find the area and the side opposite C. Givens: Second side b=6; Included angle (degrees)=75.

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11. Grade 11 · Chapter 511

    Quadratic sequences · Quadratic coefficient a=1; 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; Linear coefficient b=3.

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12. Grade 11 · Chapter 512

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

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

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13. Grade 11 · Chapter 513

    Rational functions · Numerator a=2.5; Pole location b=-1

    Evaluate at x=1.5, 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=-1.

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14. Grade 11 · Chapter 514

    Logarithms and domains · Domain boundary a=1; Logarithm base b=3.5

    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=3.5.

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15. Grade 11 · Chapter 515

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

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16. Grade 11 · Chapter 516

    Geometric sums · First term a=4; 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; Ratio r=0.4.

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17. Grade 11 · Chapter 517

    Complex polar form · Modulus r=2.5; 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=2.5; Final angle (degrees)=30.

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18. Grade 11 · Chapter 518

    Triangle area and angle · Second side b=1; Included angle (degrees)=105

    Use the included angle C=69°. Find the area and the side opposite C. Givens: Second side b=1; Included angle (degrees)=105.

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19. Grade 11 · Chapter 519

    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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20. Grade 11 · Chapter 520

    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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