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Grade 11 practice chapters

1. Grade 11 · Chapter 141

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

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2. Grade 11 · Chapter 142

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

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

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3. Grade 11 · Chapter 143

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

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4. Grade 11 · Chapter 144

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

   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=1.5.

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5. Grade 11 · Chapter 145

   Exponential calibration · Initial value a=2.5; Exponential rate b=0.1

   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=0.1.

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6. Grade 11 · Chapter 146

   Geometric sums · First term a=4.5; 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=4.5; Ratio r=0.

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7. Grade 11 · Chapter 147

   Complex polar form · Modulus r=2.5; Final angle (degrees)=-90

   Evaluate at the signed angle θ=-54° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=2.5; Final angle (degrees)=-90.

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8. Grade 11 · Chapter 148

   Triangle area and angle · Second side b=4; Included angle (degrees)=120

   Use the included angle C=78°. Find the area and the side opposite C. Givens: Second side b=4; Included angle (degrees)=120.

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9. Grade 11 · Chapter 149

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

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10. Grade 11 · Chapter 150

    Rescaling data · Scale a=2; 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=2; Shift b=1.5.

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11. Grade 11 · Chapter 151

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

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12. Grade 11 · Chapter 152

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

    Evaluate at x=2, 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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13. Grade 11 · Chapter 153

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

    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=2.

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14. Grade 11 · Chapter 154

    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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15. Grade 11 · Chapter 155

    Geometric sums · First term a=5; 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=5; Ratio r=0.1.

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16. Grade 11 · Chapter 156

    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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17. Grade 11 · Chapter 157

    Triangle area and angle · Second side b=4.5; Included angle (degrees)=135

    Use the included angle C=87°. Find the area and the side opposite C. Givens: Second side b=4.5; Included angle (degrees)=135.

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18. Grade 11 · Chapter 158

    Quadratic sequences · Quadratic coefficient a=2; 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=2; Linear coefficient b=1.5.

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19. Grade 11 · Chapter 159

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

    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=-2.

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20. Grade 11 · Chapter 160

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

    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=0.

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