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Grade 11 practice chapters

1. Grade 11 · Chapter 41

   Complex polar form · Modulus r=2.5; 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=2.5; Final angle (degrees)=-120.

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2. Grade 11 · Chapter 42

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

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3. Grade 11 · Chapter 43

   Triangle area and angle · Second side b=3.5; Included angle (degrees)=90

   Use the included angle C=60°. Find the area and the side opposite C. Givens: Second side b=3.5; Included angle (degrees)=90.

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4. Grade 11 · Chapter 44

   Quadratic sequences · Quadratic coefficient a=0; 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; Linear coefficient b=-1.

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5. Grade 11 · Chapter 45

   Rescaling data · Scale a=0; 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; Shift b=-1.

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6. Grade 11 · Chapter 46

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

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7. Grade 11 · Chapter 47

   Rational functions · Numerator a=3; 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=3; Pole location b=0.5.

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8. Grade 11 · Chapter 48

   Logarithms and domains · Domain boundary a=0.5; Logarithm base b=4

   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=4.

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9. Grade 11 · Chapter 49

   Exponential calibration · Initial value a=3; Exponential rate b=0

   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.

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10. Grade 11 · Chapter 50

    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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11. Grade 11 · Chapter 51

    Complex polar form · Modulus r=3; Final angle (degrees)=-105

    Evaluate at the signed angle θ=-63° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=3; Final angle (degrees)=-105.

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12. Grade 11 · Chapter 52

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

    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=3.

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13. Grade 11 · Chapter 53

    Triangle area and angle · Second side b=4; Included angle (degrees)=105

    Use the included angle C=69°. Find the area and the side opposite C. Givens: Second side b=4; Included angle (degrees)=105.

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14. Grade 11 · Chapter 54

    Quadratic sequences · Quadratic coefficient a=0.5; Linear coefficient b=-0.5

    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=-0.5.

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15. Grade 11 · Chapter 55

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

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16. Grade 11 · Chapter 56

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

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17. Grade 11 · Chapter 57

    Rational functions · Numerator a=3.5; 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=3.5; Pole location b=1.

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18. Grade 11 · Chapter 58

    Logarithms and domains · Domain boundary a=1; Logarithm base b=4.5

    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=4.5.

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19. Grade 11 · Chapter 59

    Exponential calibration · Initial value a=0.5; Exponential rate b=-0.4

    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=-0.4.

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20. Grade 11 · Chapter 60

    Complex polar form · Modulus r=0.5; Final angle (degrees)=-165

    Evaluate at the signed angle θ=-99° (three fifths of that final angle). Find its real and imaginary components and verify its modulus. Givens: Modulus r=0.5; Final angle (degrees)=-165.

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