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Grade 11 practice chapters

1. Grade 11 · Chapter 101

   Logarithms and domains · Domain boundary a=-1; Logarithm base b=3

   Use x=2.08; 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.

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2. Grade 11 · Chapter 102

   Exponential calibration · Initial value a=3; 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=3; Exponential rate b=0.1.

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3. Grade 11 · Chapter 103

   Complex polar form · Modulus r=3; 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=3; Final angle (degrees)=-90.

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4. Grade 11 · Chapter 104

   Trigonometric periods · Amplitude A=3; Angular frequency k=0.5

   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=3; Angular frequency k=0.5.

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5. Grade 11 · Chapter 105

   Triangle area and angle · Second side b=1.5; Included angle (degrees)=45

   Use the included angle C=33°. Find the area and the side opposite C. Givens: Second side b=1.5; Included angle (degrees)=45.

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6. Grade 11 · Chapter 106

   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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7. Grade 11 · Chapter 107

   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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8. Grade 11 · Chapter 108

   Polynomial roots · First root a=3; Second root b=3

   Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=3; Second root b=3.

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9. Grade 11 · Chapter 109

   Rational functions · Numerator a=2.5; 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=2.5; Pole location b=0.5.

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10. Grade 11 · Chapter 110

    Logarithms and domains · Domain boundary a=-0.5; Logarithm base b=3.5

    Use x=2.58; 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=3.5.

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11. Grade 11 · Chapter 111

    Exponential calibration · Initial value a=0.5; 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=0.5; Exponential rate b=-0.3.

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12. Grade 11 · Chapter 112

    Geometric sums · First term a=2.5; 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=2.5; Ratio r=-0.4.

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13. Grade 11 · Chapter 113

    Complex polar form · Modulus r=0.5; Final angle (degrees)=-150

    Evaluate at the signed angle θ=-90° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=0.5; Final angle (degrees)=-150.

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14. Grade 11 · Chapter 114

    Trigonometric periods · Amplitude A=0.5; Angular frequency k=1.5

    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=0.5; Angular frequency k=1.5.

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15. Grade 11 · Chapter 115

    Triangle area and angle · Second side b=2; Included angle (degrees)=60

    Use the included angle C=42°. Find the area and the side opposite C. Givens: Second side b=2; Included angle (degrees)=60.

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16. Grade 11 · Chapter 116

    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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17. Grade 11 · Chapter 117

    Rescaling data · Scale a=0; Shift b=-0.5

    Use the completed transformation, at the end of the animation. Find the transformed mean, population variance, and population standard deviation. Givens: Scale a=0; Shift b=-0.5.

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18. Grade 11 · Chapter 118

    Polynomial roots · First root a=-3; Second root b=-2.5

    Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=-3; Second root b=-2.5.

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19. Grade 11 · Chapter 119

    Rational functions · Numerator a=3; 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=3; Pole location b=1.

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20. Grade 11 · Chapter 120

    Logarithms and domains · Domain boundary a=0; Logarithm base b=4

    Use x=3.08; the logarithm argument is exactly 3.08. State the domain, evaluate the logarithm, and recover the argument by exponentiation. Givens: Domain boundary a=0; Logarithm base b=4.

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