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Grade 11 practice chapters
221–240 of 600 matching chapters · Page 12 of 30
Clear filtersGrade 11 · Chapter 221
Geometric sums · First term a=4; 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; Ratio r=0.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 222
Complex polar form · Modulus r=0.5; 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=0.5; Final angle (degrees)=-120.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 223
Trigonometric periods · Amplitude A=0.5; 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=0.5; Angular frequency k=2.5.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 224
Triangle area and angle · Second side b=3; Included angle (degrees)=105
Use the included angle C=69°. Find the area and the side opposite C. Givens: Second side b=3; Included angle (degrees)=105.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 225
Quadratic sequences · Quadratic coefficient a=1.5; 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=1.5; Linear coefficient b=1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 226
Rescaling data · Scale a=1.5; 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=1.5; Shift b=1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 227
Polynomial roots · First root a=-3; Second root b=-2
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.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 228
Logarithms and domains · Domain boundary a=1.5; Logarithm base b=2
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=2.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 229
Exponential calibration · Initial value a=1; 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; Exponential rate b=0.
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Open practice chapterGrade 11 · Chapter 230
Geometric sums · First term a=4.5; 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=4.5; Ratio r=0.1.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 231
Complex polar form · Modulus r=1; 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; Final angle (degrees)=-105.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 232
Triangle area and angle · Second side b=3.5; Included angle (degrees)=120
Use the included angle C=78°. Find the area and the side opposite C. Givens: Second side b=3.5; Included angle (degrees)=120.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 233
Quadratic sequences · Quadratic coefficient a=2; Linear coefficient b=2
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=2.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 234
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.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 235
Polynomial roots · First root a=-2.5; Second root b=-1.5
Evaluate at x=0.8. Find the function value, tangent slope, and vertical line of symmetry. Givens: First root a=-2.5; Second root b=-1.5.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 236
Logarithms and domains · Domain boundary a=2; Logarithm base b=2.5
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=2.5.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 237
Exponential calibration · Initial value a=1.5; 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=1.5; Exponential rate b=0.1.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 238
Geometric sums · First term a=5; Ratio r=0.2
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=0.2.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 239
Complex polar form · Modulus r=1.5; 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=1.5; Final angle (degrees)=-90.
Question · Worked solution · Animated example
Open practice chapterGrade 11 · Chapter 240
Trigonometric periods · Amplitude A=1.5; 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=1.5; Angular frequency k=0.5.
Question · Worked solution · Animated example
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