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Grade 11 practice chapters
181–200 of 600 matching chapters · Page 10 of 30
Clear filtersGrade 11 · Chapter 181
Logarithms and domains · Domain boundary a=-1; Logarithm base b=3.5
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=3.5.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 182
Exponential calibration · Initial value a=1.5; 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=1.5; Exponential rate b=0.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 183
Geometric sums · First term a=2; 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; Ratio r=-0.4.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 184
Complex polar form · Modulus r=1.5; 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=1.5; Final angle (degrees)=-105.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 185
Trigonometric periods · Amplitude A=1.5; 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=1.5; Angular frequency k=3.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 186
Triangle area and angle · Second side b=1; Included angle (degrees)=45
Use the included angle C=33°. Find the area and the side opposite C. Givens: Second side b=1; Included angle (degrees)=45.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 187
Quadratic sequences · Quadratic coefficient a=-1; 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; Linear coefficient b=-1.
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Open practice chapterGrade 11 · Chapter 188
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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Open practice chapterGrade 11 · Chapter 189
Rational functions · Numerator a=3; 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=3; Pole location b=1.5.
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Open practice chapterGrade 11 · Chapter 190
Logarithms and domains · Domain boundary a=-0.5; Logarithm base b=4
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=4.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 191
Exponential calibration · Initial value a=2; 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; Exponential rate b=0.1.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 192
Geometric sums · First term a=2.5; 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=2.5; Ratio r=-0.3.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 193
Complex polar form · Modulus r=2; 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; Final angle (degrees)=-90.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 194
Trigonometric periods · Amplitude A=2; 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=2; Angular frequency k=0.5.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 195
Triangle area and angle · Second side b=1.5; Included angle (degrees)=60
Use the included angle C=42°. Find the area and the side opposite C. Givens: Second side b=1.5; Included angle (degrees)=60.
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Open practice chapterGrade 11 · Chapter 196
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.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 197
Rescaling data · Scale a=0; Shift b=0
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.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 198
Polynomial roots · First root a=1.5; Second root b=2
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=2.
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Open practice chapterGrade 11 · Chapter 199
Rational functions · Numerator a=3.5; Pole location b=2
Evaluate at x=4.5, 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=2.
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Open practice chapterGrade 11 · Chapter 200
Logarithms and domains · Domain boundary a=0; Logarithm base b=4.5
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=4.5.
Question · Worked solution · Animated example
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