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Grade 11 practice chapters

1. Grade 11 · Chapter 161

   Rational functions · Numerator a=1.5; 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=1.5; Pole location b=0.

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2. Grade 11 · Chapter 162

   Logarithms and domains · Domain boundary a=-2; Logarithm base b=2.5

   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=2.5.

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3. Grade 11 · Chapter 163

   Exponential calibration · Initial value a=0.5; 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=0.5; Exponential rate b=-0.2.

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4. Grade 11 · Chapter 164

   Geometric sums · First term a=1; 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=1; Ratio r=-0.6.

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5. Grade 11 · Chapter 165

   Complex polar form · Modulus r=0.5; Final angle (degrees)=-135

   Evaluate at the signed angle θ=-81° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=0.5; Final angle (degrees)=-135.

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6. Grade 11 · Chapter 166

   Trigonometric periods · Amplitude A=0.5; Angular frequency k=2

   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=0.5; Angular frequency k=2.

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7. Grade 11 · Chapter 167

   Triangle area and angle · Second side b=5; Included angle (degrees)=150

   Use the included angle C=96°. Find the area and the side opposite C. Givens: Second side b=5; Included angle (degrees)=150.

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8. Grade 11 · Chapter 168

   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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9. Grade 11 · Chapter 169

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

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10. Grade 11 · Chapter 170

    Polynomial roots · First root a=0; 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=0; Second root b=0.5.

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11. Grade 11 · Chapter 171

    Rational functions · Numerator a=2; 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=2; Pole location b=0.5.

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12. Grade 11 · Chapter 172

    Logarithms and domains · Domain boundary a=-1.5; Logarithm base b=3

    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=3.

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13. Grade 11 · Chapter 173

    Geometric sums · First term a=1.5; 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=1.5; Ratio r=-0.5.

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14. Grade 11 · Chapter 174

    Complex polar form · Modulus r=1; Final angle (degrees)=-120

    Evaluate at the signed angle θ=-72° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=1; Final angle (degrees)=-120.

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15. Grade 11 · Chapter 175

    Trigonometric periods · Amplitude A=1; Angular frequency k=2.5

    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; Angular frequency k=2.5.

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16. Grade 11 · Chapter 176

    Triangle area and angle · Second side b=5.5; Included angle (degrees)=165

    Use the included angle C=105°. Find the area and the side opposite C. Givens: Second side b=5.5; Included angle (degrees)=165.

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17. Grade 11 · Chapter 177

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

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18. Grade 11 · Chapter 178

    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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19. Grade 11 · Chapter 179

    Polynomial roots · First root a=0.5; Second root b=1

    Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=0.5; Second root b=1.

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20. Grade 11 · Chapter 180

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

    Evaluate at x=3.5, 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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