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Grade 11 practice chapters

1. Grade 11 · Chapter 281

   Rational functions · Numerator a=4; 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=4; Pole location b=-1.5.

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2. Grade 11 · Chapter 282

   Geometric sums · First term a=3; 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=3; Ratio r=-0.1.

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3. Grade 11 · Chapter 283

   Triangle area and angle · Second side b=1.5; Included angle (degrees)=75

   Use the included angle C=51°. Find the area and the side opposite C. Givens: Second side b=1.5; Included angle (degrees)=75.

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4. Grade 11 · Chapter 284

   Quadratic sequences · Quadratic coefficient a=0.5; 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=0.5; Linear coefficient b=1.

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5. Grade 11 · Chapter 285

   Rescaling data · Scale a=0.5; 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=0.5; Shift b=1.

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6. Grade 11 · Chapter 286

   Polynomial roots · First root a=0.5; 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=0.5; Second root b=1.5.

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7. Grade 11 · Chapter 287

   Logarithms and domains · Domain boundary a=0.5; Logarithm base b=1.5

   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=1.5.

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8. Grade 11 · Chapter 288

   Exponential calibration · Initial value a=1.5; 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=1.5; Exponential rate b=0.2.

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9. Grade 11 · Chapter 289

   Geometric sums · First term a=3.5; Ratio r=0

   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.

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10. Grade 11 · Chapter 290

    Complex polar form · Modulus r=1.5; 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=1.5; Final angle (degrees)=-75.

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11. Grade 11 · Chapter 291

    Trigonometric periods · Amplitude A=1.5; Angular frequency k=1

    Evaluate at x=6π/5 radians, keeping π exact during calculation. Find the signal value, derivative with respect to x, and period. Givens: Amplitude A=1.5; Angular frequency k=1.

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12. Grade 11 · Chapter 292

    Triangle area and angle · Second side b=2; Included angle (degrees)=90

    Use the included angle C=60°. Find the area and the side opposite C. Givens: Second side b=2; Included angle (degrees)=90.

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13. Grade 11 · Chapter 293

    Quadratic sequences · Quadratic coefficient a=1; Linear coefficient b=1.5

    Use index n=6. Calculate u₆, the forward first difference u₇−u₆, and the second difference u₈−2u₇+u₆. Givens: Quadratic coefficient a=1; Linear coefficient b=1.5.

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14. Grade 11 · Chapter 294

    Rescaling data · Scale a=1; Shift b=1.5

    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=1.5.

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15. Grade 11 · Chapter 295

    Polynomial roots · First root a=1; Second root b=2

    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.

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16. Grade 11 · Chapter 296

    Rational functions · Numerator a=1; 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=1; Pole location b=0.5.

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17. Grade 11 · Chapter 297

    Exponential calibration · Initial value a=2; Exponential rate b=0.3

    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=0.3.

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18. Grade 11 · Chapter 298

    Geometric sums · First term a=4; 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=4; Ratio r=0.1.

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19. Grade 11 · Chapter 299

    Complex polar form · Modulus r=2; 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; Final angle (degrees)=-60.

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20. Grade 11 · Chapter 300

    Triangle area and angle · Second side b=2.5; Included angle (degrees)=105

    Use the included angle C=69°. Find the area and the side opposite C. Givens: Second side b=2.5; Included angle (degrees)=105.

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