Calculus Applications Worksheet for Grade 7
Mathematics
General
3 questions
~6 mins
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About This Worksheet
This medium level calculus worksheet is designed for grade 7 to develop key mathematical skills. It includes 10 engaging problems covering essential concepts in calculus. Perfect for classroom practice, homework, or assessment preparation. This worksheet helps students build confidence and proficiency in mathematics through structured practice with clear solutions provided.
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Calculus Applications Worksheet for Grade 7
Subject: MathematicsGrade: General
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Calculus Applications Worksheet for Grade 7
Mathematics
Instructions: Read each question carefully. For multiple-choice questions, select the best answer. For calculation questions, show your work clearly in the grid provided. Use your calculator if needed.
A
Differentiation in Real Life
This section explores how derivatives represent rates of change in everyday situations.
1.
A car is traveling along a highway. Its speed is increasing at a rate of 4 miles per hour squared. What does this rate tell us about the car's movement?
[2 marks]AThe car is moving slower over time
BThe car is stationary
CThe car's speed is increasing by 4 miles per hour each hour
DThe car's speed is decreasing
2.
What is the derivative of f(x) = 3x^2 + 5x?
[2 marks]Af'(x) = 3x + 5
Bf'(x) = 6x + 3
Cf'(x) = 3x^2 + 5
Df'(x) = 6x + 5
3.
Find the rate of change of the function f(x) = x^3 at x = 2.
[2 marks]Af'(2) = 8
Bf'(2) = 16
Cf'(2) = 12
Df'(2) = 24
B
Calculating Areas Under Curves
This section shows how integration helps find the area under a curve, useful in real-world measurements.
1.
Estimate the area under the graph of y = x between x=0 and x=3 using the rectangles method with 3 equal parts.
[2 marks]A6
B9
C7.5
D4.5
2.
What is the integral of f(x) = 2x from x=1 to x=4?
[2 marks]A∫2x dx = x^2 + C; answer = 22
B∫2x dx = x^2 + C; answer = 14
C∫2x dx = x^2 + C; answer = 15
D∫2x dx = 2x^2 + C; answer = 30
C
Real-Life Applications
Applying calculus to solve practical problems related to motion and areas.
1.
A balloon rises at a rate given by the function h(t) = 5t + 2, where t is in minutes. What is the rate of change of height with respect to time?
[2 marks]AThe balloon's height is increasing by 2 meters per minute
BThe rate of change varies with time
CThe balloon is rising at 5 meters per minute
DThe balloon is descending
2.
Calculate the total area under the curve y=4x from x=0 to x=2.
[2 marks]A8
B4
C16
D2
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Details
- Created
- 10/4/2025
- Updated
- 12/29/2025
- Type
- worksheet