Application of Calculus

Curriculum details

Strand

Calculus (Strand 3)

Sub-strand

Application of Calculus (3.2)

Content standard

3.3.2.CS.1 - Demonstrate conceptual Find the area under a constant function, curves and distinguish between total, net and understanding of integration to find distances, areas under curve, volumes and other related real life problems. 3.3.2.LO.1 Determine distance, area under curve and solid of volumes formed under revolution.

Indicator

3.3.2.LI.3 - Find the volume of a solid formed after rotation about horizontal or vertical axis.

Suggested placement

Semester 2, Week 7 (Week 27 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Source document note

The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

• exemplars - p.528: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page

Curriculum reference

NaCCA curriculum document, p. 528

Exemplars (from the NaCCA curriculum)

Talk for Learning, Think-pair-share, Experiential Learning; and Group Work/Collaborative Learning.
Suppose the downward velocity of a sky diver is given by 𝑣(𝑡) = 30(1 − 𝑒 *G )𝑓/𝑠 for the first 5
- seconds of a jump. Compute the distance fallen.
Solution: . 𝑑 = ∫ ( 30(1 − 𝑒 *G ) 𝑑 = [30𝑡 + 30𝑒 *G ]5 0 = (150 + 30𝑒 *. ) − (0 + 30𝑒 ( ) = 120 + 30𝑒 *. ≈ 120.2𝑓
- Suppose that water can flow in and out of a storage tank. The net rate of change of water is 𝑓(𝑡) = 20(𝑡 ) − 1) gallons per minute.
- For 0 ≤ 𝑡 ≤ 3, determine when the water level is increasing and when the water level is decreasing.
- If the tank has 200 gallons of water at time 𝑡 = 0, determine how many gallons are in the tank at time 𝑡 = 3.
Solution:: Let 𝑤(𝑡) be the number of gallons in the tank at time 𝑡.
- Water level decreases if 𝑤 - (𝑡) = 𝑓(𝑡) < 0. 𝑓(𝑡) = 20(𝑡 ) − 1) < 0, 𝑖 0 ≤ 𝑡 < 1 Water level increases if 𝑤 - (𝑡) = 𝑓(𝑡) > 0. 𝑓(𝑡) = 20(𝑡 ) − 1) > 0, 𝑖 1 < 𝑡 ≤ 3
" "
- ∫ ( 𝑤 - (𝑡) 𝑑 = ∫ ( 20(𝑡 ) − 1) 𝑑 G " 𝑤(3) − 𝑤(0) = 20 i − 𝑡j 3 0 " Since we have 𝑤(0) = 200, 𝑡ℎ𝑒
𝑤(3) − 200 = 20(9 − 3) = 120 Hence, 𝑤(3) = 200 + 120 = 320 The tank will have 320 gallons at time 3
Teaching and Learning Resources:
- Reading resource colour pens
- Notebook
- Graph sheets
- Mathematical sets,
- Technological tools.
- Curriculum
- Cardboard
Assessment (3.3.2.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.