10,000 ways to practice.
One idea at a time.

Attempt · Explain · Animate

Grade 11 practice chapters

1. Grade 11 · Chapter 241

   Triangle area and angle · Second side b=4; Included angle (degrees)=135

   Use the included angle C=87°. Find the area and the side opposite C. Givens: Second side b=4; Included angle (degrees)=135.

   Question · Worked solution · Animated example

   Open practice chapter

2. Grade 11 · Chapter 242

   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.

   Question · Worked solution · Animated example

   Open practice chapter

3. Grade 11 · Chapter 243

   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.

   Question · Worked solution · Animated example

   Open practice chapter

4. Grade 11 · Chapter 244

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

   Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=-2; Second root b=-1.

   Question · Worked solution · Animated example

   Open practice chapter

5. Grade 11 · Chapter 245

   Rational functions · Numerator a=2; 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; Pole location b=1.

   Question · Worked solution · Animated example

   Open practice chapter

6. Grade 11 · Chapter 246

   Logarithms and domains · Domain boundary a=-2; Logarithm base b=3

   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=3.

   Question · Worked solution · Animated example

   Open practice chapter

7. Grade 11 · Chapter 247

   Geometric sums · First term a=1; 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; Ratio r=-0.5.

   Question · Worked solution · Animated example

   Open practice chapter

8. Grade 11 · Chapter 248

   Complex polar form · Modulus r=2; 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=2; Final angle (degrees)=-75.

   Question · Worked solution · Animated example

   Open practice chapter

9. Grade 11 · Chapter 249

   Trigonometric periods · Amplitude A=2; 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=2; Angular frequency k=1.

   Question · Worked solution · Animated example

   Open practice chapter

10. Grade 11 · Chapter 250

    Triangle area and angle · Second side b=4.5; Included angle (degrees)=150

    Use the included angle C=96°. Find the area and the side opposite C. Givens: Second side b=4.5; Included angle (degrees)=150.

    Question · Worked solution · Animated example

    Open practice chapter

11. Grade 11 · Chapter 251

    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.

    Question · Worked solution · Animated example

    Open practice chapter

12. Grade 11 · Chapter 252

    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.

    Question · Worked solution · Animated example

    Open practice chapter

13. Grade 11 · Chapter 253

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

    Question · Worked solution · Animated example

    Open practice chapter

14. Grade 11 · Chapter 254

    Rational functions · Numerator a=2.5; Pole location b=1.5

    Evaluate at x=4, 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=1.5.

    Question · Worked solution · Animated example

    Open practice chapter

15. Grade 11 · Chapter 255

    Exponential calibration · Initial value a=2.5; 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=2.5; Exponential rate b=0.3.

    Question · Worked solution · Animated example

    Open practice chapter

16. Grade 11 · Chapter 256

    Geometric sums · First term a=1.5; 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=1.5; Ratio r=-0.4.

    Question · Worked solution · Animated example

    Open practice chapter

17. Grade 11 · Chapter 257

    Complex polar form · Modulus r=2.5; 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=2.5; Final angle (degrees)=-60.

    Question · Worked solution · Animated example

    Open practice chapter

18. Grade 11 · Chapter 258

    Trigonometric periods · Amplitude A=2.5; 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=2.5; Angular frequency k=1.5.

    Question · Worked solution · Animated example

    Open practice chapter

19. Grade 11 · Chapter 259

    Triangle area and angle · Second side b=5; Included angle (degrees)=165

    Use the included angle C=105°. Find the area and the side opposite C. Givens: Second side b=5; Included angle (degrees)=165.

    Question · Worked solution · Animated example

    Open practice chapter

20. Grade 11 · Chapter 260

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

    Question · Worked solution · Animated example

    Open practice chapter