L1 · Surface Area
Surface Area — Prisms & Cylinders
Calculate TSA for cubes, rectangular prisms, triangular prisms, trapezoidal prisms and cylinders (open & closed)
⚡ Do Now 8 min · display on board as students enter
1
Area of a circle with r = 6 cm?
2
Area of a triangle: base = 4 cm, height = 3 cm?
3
Area of a rectangle: l = 12 cm, w = 5 cm?
4
Area of a trapezium: a=3, b=7, h=2.6 cm?
5
Circumference of a circle with r = 3 cm?
6
Area of a parallelogram: b = 5 cm, h = 4 cm?
📖 Key Vocabulary & Concepts
| Surface Area (TSA) | The total area of ALL faces of a 3D solid added together |
| Net | A 2D shape that folds to make the 3D solid — draw the net first to identify every face |
| Face | Each flat (or curved) surface of a solid — count them carefully! |
| Curved surface (cylinder) | Unroll it → rectangle with width = circumference = 2πr and height = h. Area = 2πrh |
| Closed cylinder | Both circular ends present → TSA = 2πr² + 2πrh |
| Open top cylinder | Missing top circle → TSA = πr² + 2πrh |
| Open both ends | Missing both circles → TSA = 2πrh (just the curved surface) |
| Prism TSA | Add the area of every face — two identical ends + rectangles for each side edge |
📐 Formulas
Cylinder (closed): TSA = 2πr² + 2πrh | Open top: πr² + 2πrh | Open both: 2πrh
Prism: TSA = sum of ALL faces | Area of circle: A = πr² | Triangle: A = ½bh
Trapezium: A = ½(a+b)h | Parallelogram: A = bh | Kite: A = ½xy
Prism: TSA = sum of ALL faces | Area of circle: A = πr² | Triangle: A = ½bh
Trapezium: A = ½(a+b)h | Parallelogram: A = bh | Kite: A = ½xy
✏️ Worked Examples
Q1(a): Cube, side = 6 cm — find TSA and Volume
1
Identify faces: A cube has 6 identical square faces. Each face = 6 × 6 = 36 cm²
2
TSA = 6 × 36 = 216 cm²
3
Volume = 6³ = 6 × 6 × 6 = 216 cm³
Q1(d): Closed cylinder — r = 3 cm, h = 8 cm
1
Two circular ends: 2 × πr² = 2 × π × 3² = 2 × 28.27 = 56.55 cm²
2
Curved surface: 2πrh = 2 × π × 3 × 8 = 150.80 cm²
3
TSA = 56.55 + 150.80 = 207.35 cm²
4
Volume = πr²h = π × 9 × 8 ≈ 226.19 cm³
Q1(g): Rectangular prism — 4 m × 4.2 m × 5 m
1
Front & back: 2 × (4 × 5) = 40 m²
2
Left & right: 2 × (4.2 × 5) = 42 m²
3
Top & bottom: 2 × (4 × 4.2) = 33.6 m²
4
TSA = 40 + 42 + 33.6 = 115.6 m² | Volume = 4 × 4.2 × 5 = 84 m³
Q1(i): Triangular prism — right triangle base (legs 3 cm, 4 cm, hyp 5 cm), depth = 12 cm
1
2 triangular ends: 2 × (½ × 4 × 3) = 12 cm²
2
3 rectangular faces: 4×12 + 3×12 + 5×12 = 48 + 36 + 60 = 144 cm²
3
TSA = 12 + 144 = 156 cm² | Volume = ½ × 4 × 3 × 12 = 72 cm³
Q1(h): Trapezoidal prism — parallel sides 2 m & 9 m, h = 10.5 m, depth = 9 m, width = 2 m
1
2 trapezoidal ends: 2 × ½(2+9) × 10.5 = 115.5 m²
2
Rectangular faces: Bottom: 9×9=81, Top: 2×9=18, Two slanted sides (approx): calculate from slant lengths
3
Volume: V = A_cross × depth = ½(2+9) × 10.5 × 9 = 57.75 × 9 = 519.75 m³
📝 Q4 — Surface Area of Cylinders
Q4(a): Closed cylinder — diameter = 6 cm (so r = 3 cm), h = 10 cm
1
r = 6 ÷ 2 = 3 cm · Two circles: 2πr² = 2π(9) = 56.55 cm²
2
Curved surface: 2πrh = 2π(3)(10) = 188.50 cm²
3
TSA = 56.55 + 188.50 = 245.04 cm²
Q4(e): Open at the top — r = 4 cm, h = 10 cm
1
Only ONE circle (bottom): πr² = π(16) = 50.27 cm²
2
Curved surface: 2πrh = 2π(4)(10) = 251.33 cm²
3
TSA = 50.27 + 251.33 = 301.59 cm²
Q4(f): Open at both ends — r = 6 cm (diameter=12cm), h = 30 cm
1
r = 12 ÷ 2 = 6 cm. No circles at all.
2
TSA = 2πrh = 2π(6)(30) = 1130.97 cm²
📝 Answer Key — Q1 & Q4
| Shape | TSA | Volume |
|---|---|---|
| a) Cube 6cm | 216 cm² | 216 cm³ |
| b) Cube 9m | 486 m² | 729 m³ |
| c) Cube 2.7m | 43.74 m² | 19.683 m³ |
| d) Cylinder r=3,h=8 | 207.35 cm² | 226.19 cm³ |
| e) Cylinder r=2.5,h=10 | 196.35 mm² | 196.35 mm³ |
| f) Cylinder r=5.2,h=15.4 | 673.19 m² | 1308.95 m³ |
| g) Rect prism 4×4.2×5 | 115.6 m² | 84 m³ |
| h) Trap prism | See worked example | 519.75 m³ |
| i) Tri prism | 156 cm² | 72 cm³ |
| Q4a) d=6,h=10 | 245.04 cm² | — |
| Q4b) d=10,h=20 | 785.40 cm² | — |
| Q4c) d=14,h=14 | 923.63 cm² | — |
| Q4d) d=25 (r=12.5),h=10 | 1767.15 cm² | — |
| Q4e) open top r=4,h=10 | 301.59 cm² | — |
| Q4f) open both d=12,h=30 | 1130.97 cm² | — |
💡 Teacher note: Draw the NET on the board for every new shape — fold and unfold visually. The biggest errors are (1) forgetting to halve the diameter to get r, (2) missing a face on the prism, (3) including circles on an open cylinder. Q4(d) — diameter is 25 cm so r=12.5 cm, not r=10.
L2 · Volume
Volume & Problem Solving
Use V=Ah for all prisms; rearrange to find missing dimensions (Q6); solve worded problems (Q7–Q13)
⚡ Do Now 8 min · display on board as students enter
1
TSA of a closed cylinder: r=5 cm, h=12 cm?
2
Area of a semicircle with r = 40 mm?
3
V = Ah. If A = 25 cm², h = 10 cm, find V.
4
Rectangular prism V=960 cm³, base=128 cm². Find height.
5
π × 7² × 10 = ?
6
∛729 = ?
📖 Key Vocabulary & Concepts
| V = Ah | Volume = area of cross-section × perpendicular height. Works for ANY prism or cylinder. |
| Cross-section | The identical shape you get if you slice the prism parallel to its base |
| V = πr²h | Volume of a cylinder — the cross-section is a circle with area πr² |
| Rearranging | h = V ÷ A | A = V ÷ h | For cylinder: h = V ÷ (πr²) |
| Cube root | If V = s³ then s = ∛V. E.g. ∛729 = 9 because 9³ = 729 |
| Capacity | 1 cm³ = 1 mL | 1000 cm³ = 1 L. Convert volume to litres by dividing by 1000. |
| Hollow solids | V_solid = V_outer − V_inner. Find both volumes then subtract. |
📐 Formulas
V = Ah (all prisms & cylinders) | Cylinder: V = πr²h
Rearranging: h = V ÷ A | For cube: s = ∛V | For cylinder: h = V ÷ (πr²)
Capacity: 1 cm³ = 1 mL | 1000 cm³ = 1 L
Rearranging: h = V ÷ A | For cube: s = ∛V | For cylinder: h = V ÷ (πr²)
Capacity: 1 cm³ = 1 mL | 1000 cm³ = 1 L
✏️ Worked Examples — Q2 (Volume of prisms)
Q2(a): Half-cylinder — r = 40 mm, length = 75 mm
1
Cross-section area: A = ½πr² = ½ × π × 40² = ½ × 5026.55 = 2513.27 mm²
2
V = A × length = 2513.27 × 75 = 188,495.56 mm³
Q2(d): Trapezoidal prism — parallel sides 3 cm & 7 cm, h = 2.6 cm, depth = 14 cm
1
Cross-section area: A = ½(a+b)h = ½(3+7) × 2.6 = ½ × 10 × 2.6 = 13 cm²
2
V = 13 × 14 = 182 cm³
✏️ Worked Examples — Q6 (Rearranging)
Q6(a): Rectangular prism V = 960 cm³, l = 16 cm, w = 8 cm. Find height.
1
Base area: A = l × w = 16 × 8 = 128 cm²
2
Rearrange V = Ah: h = V ÷ A = 960 ÷ 128 = 7.5 cm
Q6(c): Cylinder V = 785 cm³, r = 7 cm. Find height.
1
Formula: V = πr²h → h = V ÷ (πr²)
2
h = 785 ÷ (π × 49) = 785 ÷ 153.94 ≈ 5.10 cm
Q6(d): Cube V = 729 cm³. Find side length.
1
V = s³ → s = ∛V = ∛729 = 9 cm
✏️ Worked Examples — Worded Problems Q7–Q13
Q7: Box dimensions 85 cm × 62 cm × 36 cm. Air space inside?
1
V = l × w × h = 85 × 62 × 36 = 189,720 cm³
Q8: 25,000 cm³ poured into tank 50×20×20 cm. Overflow?
1
Tank capacity = 50 × 20 × 20 = 20,000 cm³
2
25,000 > 20,000 → YES, it overflows by 5,000 cm³
Q9: Sheet 25×14 cm rolled into cylinder. h = 14 cm, 1 cm overlap each end → circumference = 25 − 2 = 23 cm. Find TSA.
1
Find r: C = 2πr = 23 → r = 23 ÷ (2π) ≈ 3.66 cm
2
Curved surface = 23 × 14 = 322 cm² (circumference × height)
3
Two circular ends: 2 × π × (3.66)² ≈ 2 × 42.08 = 84.17 cm²
4
TSA = 322 + 84.17 = 406.17 cm²
Q10: Cheapest packaging — cost = $0.005/cm². Size A: r=3,h=12.5 | B: r=3.2,h=11 | C: r=3.4,h=9.73
1
A: TSA = 2π(9)+2π(3)(12.5) = 56.55+235.62 = 292.17 cm² → $0.005×292.17 = $1.46
2
B: TSA = 2π(10.24)+2π(3.2)(11) = 64.34+221.07 = 285.41 cm² → $0.005×285.41 = $1.43
3
C: TSA = 2π(11.56)+2π(3.4)(9.73) = 72.63+207.64 = 280.27 cm² → $0.005×280.27 = $1.40
4
Size C is cheapest at $1.40
Q11: Water tank cylinder — diameter = 28 m, h = 12.5 m
1
r = 28 ÷ 2 = 14 m
2
V = πr²h = π × 14² × 12.5 = π × 196 × 12.5 ≈ 7696.90 m³
3
85% capacity: 0.85 × 7696.90 ≈ 6542.37 m³
Q12: Hollow log — outer diameter 60 cm, hollow diameter 20 cm (radius 3m shown = hollow r=10cm after unit note: outer r=30cm, inner r=10cm), length = 300 cm
1
V_outer = π × 30² × 300 = π × 900 × 300 = 848,230 cm³
2
V_inner = π × 10² × 300 = π × 100 × 300 = 94,248 cm³
3
V_solid = 848,230 − 94,248 = 753,982 cm³
Q13: Cylindrical roller — diameter 60 cm (r = 30 cm = 0.3 m), width = 1 m
1
(a) Curved SA = 2πrh = 2π × 0.3 × 1 ≈ 1.885 m²
2
(b) 20 revolutions: each revolution presses 1.885 m². Total = 20 × 1.885 ≈ 37.70 m²
📝 Full Answer Key — Q6
| Q6 | Answer |
|---|---|
| a) Rect prism V=960, l=16, w=8 | h = 7.5 cm |
| b) Tri prism V=400, A=20 | h = 20 cm |
| c) Cylinder V=785, r=7 | h ≈ 5.10 cm |
| d) Cube V=729 | s = 9 cm |
| e) Cube V=1000 | s = 10 cm |
| f) Fish tank V=2400, l=30, w=10 | h = 8 cm |
| g) Cylinder can V=250, r=3 | h ≈ 8.84 cm |
| h) Cereal box V=3600, l=20, h=30 | w = 6 cm |
| i) Tri prism V=500, depth=10, base=5 | tri height = 20 cm |
💡 Teacher note: Emphasise V=Ah works for EVERYTHING — cylinder cross-section is a circle (A=πr²), half-cylinder is ½πr², trapezium is ½(a+b)h. Q8 overflow is great for discussion. Q10 is the standout extension — cheapest ≠ smallest. Q12: outer r=30cm, inner hole r=10cm from diagram (3m label is the visible hollow section). Q13 units: diameter given in cm but length in m — convert first.
L9 · T2 Week 4
Ways to Earn Money
Name and calculate different types of income: wages, salary, commission, piecework
⚡ Do Now 8 min · display on board as students enter
1
What is 10% of $200?
2
What is 25% of $80?
3
Write 15% as a decimal.
4
$450 × 1.5 = ?
5
$120 − 20% of $120 = ?
📖 Key Vocabulary
| Wage | Paid per hour — hours can vary week to week |
| Salary | Fixed annual amount — paid fortnightly or monthly |
| Commission | A percentage (%) of total sales made |
| Piecework | Paid per item completed |
📐 Formula / Rule
Wage = rate × hours | Weekly salary = annual ÷ 52 | Commission = rate% × sales
✏️ Worked Examples teacher-led · reveal steps one at a time
Alex earns $19.50/hr and works 8 hours. Total pay?
→Pay = rate × hours
→Pay = $19.50 × 8 = $156
Salary = $72,800/year. Weekly pay?
→Weekly = $72,800 ÷ 52 = $1,400
Commission 3% on a $24,000 sale.
→Commission = 3% × $24,000 = 0.03 × 24,000 = $720
📝 Practice Questions
1
Emma earns $24/hr and works 35 hrs. Weekly pay?
2
Salary $46,800/year. Fortnightly pay (÷ 26)?
3
Commission rate 4%. Sales = $15,000. Commission?
4
Piecework: $2.80 per item. 75 items. Pay?
5
Jordan earns $21.60/hr and works 12 hours. Total?
6
Salary $58,500/year. Weekly pay?
7
Commission 5% on $32,000 in sales.
8
Piecework: $3.50 per box × 120 boxes.
🎯 Exit Ticket
1
Name 3 types of income with a real-life example of each.
2
Jordan earns $21.60/hr and works 12 hours. How much does she earn?
💡 Teacher note: Use real job examples: retail, fast food, car wash. Ask 'Who knows someone on commission?' Students engage when maths feels real.
L10 · T2 Week 4
⚠️ Measurement Test + Wages Intro
Complete the Measurement Test, then begin wage and salary calculations
⚡ Do Now 8 min · display on board as students enter
See lesson plan — test or special activity this lesson.
📖 Key Vocabulary
| Measurement Test | Covers: area, perimeter, composite shapes, Pythagoras, converse, word problems |
📐 Formula / Rule
After test: Wage = rate × hours | Weekly salary = annual ÷ 52 | Fortnightly = annual ÷ 26
✏️ Worked Examples teacher-led · reveal steps one at a time
After test — Sam earns $22/hr and works 38 hours. Weekly pay?
→Pay = $22 × 38 = $836
📝 Practice Questions
1
$18/hr × 40 hrs = ?
2
Salary $52,000/year. Weekly pay?
3
$23.50/hr × 6 hrs = ?
4
Salary $78,000/year. Fortnightly pay?
🎯 Exit Ticket
1
You earn $20/hr. You work 9 hours. How much do you earn?
💡 Teacher note: TEST: seating plan strictly enforced, clear desks, formula sheet provided. Ahmed A — extra time if needed. After test: keep intro light and engaging.
L11 · T2 Week 4
Wages & Penalty Rates
Calculate wages including time and a half, double time and mixed weeks
⚡ Do Now 8 min · display on board as students enter
1
$18 × 6 = ?
2
$18 × 1.5 = ?
3
$18 × 2 = ?
4
$22.50 × 8 = ?
5
What does 'time and a half' mean?
📖 Key Vocabulary
| Normal time | ×1 — standard hourly rate |
| Time and a half | ×1.5 — common for Saturday shifts |
| Double time | ×2 — common for Sunday and public holidays |
| Double time and a half | ×2.5 — public holiday premium |
📐 Formula / Rule
Penalty pay = hourly rate × multiplier × hours worked
✏️ Worked Examples teacher-led · reveal steps one at a time
Jake earns $17/hr. Mon–Fri 8 hrs/day, Sat 4 hrs (T&H), Sun 3 hrs (DT). Total?
→Mon–Fri: $17 × 8 × 5 = $680
→Saturday (×1.5): $17 × 1.5 × 4 = $102
→Sunday (×2): $17 × 2 × 3 = $102
→Total: $680 + $102 + $102 = $884
📝 Practice Questions
1
$20/hr, 5 hrs Saturday (time & half). Pay?
2
$25/hr, 4 hrs public holiday (double time). Pay?
3
$16/hr. 38 normal hrs + 3 hrs time & half. Total?
4
$22/hr. Mon–Fri 7 hrs/day. Sat 5 hrs (time & half). Total?
5
Mia $19.50/hr. Tue–Sat 8 hrs. Sat = time & half. Total?
6
$24/hr. 3 hrs double time and a half. Pay?
🎯 Exit Ticket
1
You earn $21/hr. 6 hours on Sunday at double time. How much?
2
What multiplier is used for time and a half?
💡 Teacher note: Real-world connection: which shifts pay the most and why? The 'Your Roster' activity works well here.
L12 · T2 Week 4
Payslips — Reading & Calculating
Read a payslip and calculate gross pay, tax, super and net pay
⚡ Do Now 8 min · display on board as students enter
1
$850 − $125 = ?
2
10% of $960 = ?
3
11% of $840 = ?
4
$1,200 − $312 − $96 = ?
📖 Key Vocabulary
| Gross Pay | Total earnings BEFORE any deductions |
| Tax | Money withheld for the government (ATO) |
| Superannuation (Super) | 11% employer contribution — goes into your retirement fund |
| Net Pay | What you actually receive — gross minus deductions |
| YTD | Year to Date — total earned since 1 July |
📐 Formula / Rule
Net Pay = Gross − Tax − Other Deductions | Super = 11% × Gross (employer pays this separately)
✏️ Worked Examples teacher-led · reveal steps one at a time
Gross = $1,400. Tax = $285. Super = 11% of gross. Find net pay and super.
→Super = 11% × $1,400 = $154 (employer pays this on top)
→Net Pay = $1,400 − $285 = $1,115
📝 Practice Questions
1
Gross=$960, Tax=$142, Other=$20. Net pay?
2
Gross=$2,100, Tax=$385. Net pay?
3
Gross=$780. Super=11%. How much super does employer pay?
4
Net=$1,260. Tax=$194. What was the gross?
5
Jake: 38 hrs at $23/hr. Tax=18% of gross. Find gross, tax, net.
🎯 Exit Ticket
1
What is the difference between gross and net pay?
2
Gross=$1,050, Tax=$210, Super=11%. Find net pay and employer super.
💡 Teacher note: Key misconception: super is paid BY the employer ON TOP of gross — not deducted from wages. Say: 'It's a bonus put into a retirement account you can't touch yet.'
L13 · T2 Week 5
Commission & Piecework
Calculate commission (with and without base pay) and piecework earnings
⚡ Do Now 8 min · display on board as students enter
1
4% of $30,000 = ?
2
2.5% of $12,000 = ?
3
$3.20 × 45 = ?
4
Gross = $920, Tax = $158. Net pay?
📖 Key Vocabulary
| Base + commission | Fixed amount plus a % of sales on top |
| Piecework rate | Fixed $ per item or task completed |
| Compare income | Calculate totals for each option — then decide |
📐 Formula / Rule
Commission = rate% × total sales | Piecework = rate per item × number of items
✏️ Worked Examples teacher-led · reveal steps one at a time
Real estate agent: base $800/week + 1.5% commission. Sold a house for $620,000.
→Commission: 1.5% × $620,000 = 0.015 × 620,000 = $9,300
→Total: $800 + $9,300 = $10,100
Piecework: $4.20 per board. 180 boards Monday, 210 Tuesday. Total pay?
→Total boards: 180 + 210 = 390
→Pay: 390 × $4.20 = $1,638
📝 Practice Questions
1
Commission 6% on sales of $45,000.
2
Base $500/week + 2% commission on $28,000.
3
Piecework: $1.80/item × 340 items.
4
Which is better: (A) $25/hr × 40 hrs OR (B) $5/item × 220 items?
5
Commission 3.5% on $80,000 + base $1,200/month. Monthly total?
6
Piecework: $2.10/kg × 670 kg (380 Mon + 290 Tue).
🎯 Exit Ticket
1
Commission rate 5% on $32,000 sales. Calculate.
2
Which pays more: $28/hr × 38 hrs OR $20/hr × 38 hrs + Sat 5 hrs T&H?
💡 Teacher note: 'Which job pays more?' discussion is engaging here. Remind students there are also non-financial factors in choosing work.
L14 · T2 Week 5
Percentages Review + Intro to Interest
Identify P, R and T in interest problems and convert time periods correctly
⚡ Do Now 8 min · display on board as students enter
1
5% of $600 = ?
2
8% of $2,500 = ?
3
12.5% of $800 = ?
4
Write 4.5% as a decimal.
5
Write 0.075 as a percentage.
📖 Key Vocabulary
| Principal (P) | The original amount borrowed or saved |
| Rate (R) | Annual interest rate — always convert to a decimal |
| Time (T) | How long in YEARS — convert months: ÷ 12 |
| Interest (I) | The extra money charged or earned |
📐 Formula / Rule
6 months = 0.5 yrs | 3 months = 0.25 | 9 months = 0.75 | 18 months = 1.5
✏️ Worked Examples teacher-led · reveal steps one at a time
Identify P, R and T: 'Sarah borrows $5,000 at 6% per year for 3 years.'
→P = $5,000
→R = 6% = 0.06
→T = 3 years
Identify P, R and T: '$1,500 saved at 3.5% p.a. for 18 months.'
→P = $1,500
→R = 3.5% = 0.035
→T = 18 ÷ 12 = 1.5 years
📝 Practice Questions
1
Identify P, R, T: $8,000 at 4% p.a. for 2 years.
2
Identify P, R, T: $12,000 at 7.2% p.a. for 4 years.
3
Identify P, R, T: $500 at 2% p.a. for 9 months.
4
Identify P, R, T: $25,000 at 9.25% p.a. for 3 years.
5
Convert: 15 months to years.
6
Convert: 8% to a decimal.
🎯 Exit Ticket
1
Write the simple interest formula and explain each letter.
2
Identify P, R, T: '$3,000 at 5.5% p.a. for 30 months'
💡 Teacher note: Time conversion is the biggest trap. Spend 3 mins on it: write on board — 3 months=0.25, 6=0.5, 9=0.75, 18=1.5.
L15 · T2 Week 6
Simple Interest Formula: I = PRT
Calculate simple interest and total amount using I = P × R × T
⚡ Do Now 8 min · display on board as students enter
1
Write I = PRT in full words.
2
Convert 9 months to years.
3
Write 7.5% as a decimal.
4
$2,000 × 0.05 × 3 = ?
📖 Key Vocabulary
| I = PRT | Simple Interest = Principal × Rate × Time |
| A = P + I | Total Amount = Principal + Interest |
| p.a. | Per annum = per year |
📐 Formula / Rule
I = P × R × T A = P + I (R as decimal, T in years)
✏️ Worked Examples teacher-led · reveal steps one at a time
Find the interest on $4,000 at 5% p.a. for 3 years.
→P = $4,000 R = 0.05 T = 3
→I = 4000 × 0.05 × 3 = $600
→A = $4,000 + $600 = $4,600
$9,000 at 4.5% p.a. for 18 months. Find I and A.
→P = $9,000 R = 0.045 T = 1.5 (18 ÷ 12)
→I = 9000 × 0.045 × 1.5 = $607.50
→A = $9,000 + $607.50 = $9,607.50
📝 Practice Questions
1
P=$3,000, R=4%, T=2 yrs. Find I and A.
2
P=$7,500, R=6%, T=3 yrs. Find I and A.
3
P=$1,200, R=8%, T=6 months. Find I.
4
P=$5,000, R=3.5%, T=4 yrs. Find I and A.
5
P=$2,500, R=5%, T=30 months. Find I and A.
6
P=$10,000, R=9.25%, T=3 yrs. Find I then monthly interest.
🎯 Exit Ticket
1
Car loan: $14,500 at 9.25% p.a. for 3 years. Find total interest and total amount.
2
How much interest per month on the loan above?
💡 Teacher note: Make students write EVERY line of working. Write on board and leave there: R = decimal, T = years.
L16 · T2 Week 6
⚠️ Finance Test Prep + Review
Review all financial maths topics and prepare for the Finance Test
⚡ Do Now 8 min · display on board as students enter
1
Write the simple interest formula.
2
Write the total amount formula.
3
What multiplier is time and a half?
4
Difference between gross and net pay?
5
Convert 9 months to years.
📖 Key Vocabulary
| Finance Test | THIS WEEK — covers all income types, payslips and simple interest |
📐 Formula / Rule
Wage=rate×hrs | ×1.5/×2/×2.5 | Net=Gross−Tax | Super=11%×Gross | I=PRT | A=P+I
📝 Practice Questions
1
$21/hr × 37 hrs = ?
2
$18/hr, 6 hrs Saturday (time & half). Pay?
3
Commission 5% on $32,000 sales.
4
Gross=$1,350, Tax=$212. Net pay?
5
Super at 11% on gross = $2,000.
6
P=$5,000, R=6%, T=4. Find I.
7
P=$8,000, R=3.5%, T=2.5 yrs. Find A.
8
$3,500 at 4.2% p.a. for 2 yrs. Interest and total.
🎯 Exit Ticket
1
List 5 formulas or rules from this Finance unit.
💡 Teacher note: FINANCE TEST: confirm exact timing with class teacher. Covers all income types, payslips and simple interest.
Year 9 Maths · Surface Area & Volume
Lesson 2: Volume & Problem Solving
Use V=Ah for all prisms; rearrange to find missing dimensions; solve worded problems
Name: _____________________________
Date: _______________
Formulas: V = Ah (all prisms) | Cylinder: V = πr²h | Rearranging: h = V ÷ A | Cube: s = ∛V
1 cm³ = 1 mL | 1000 cm³ = 1 L | Hollow: V = V_outer − V_inner
1 cm³ = 1 mL | 1000 cm³ = 1 L | Hollow: V = V_outer − V_inner
QUESTION 2 — Volume of Solids
a) Half-cylinder: r = 40 mm, length = 75 mm
V = _____________
b) Parallelogram prism: b=2.8cm, h=5.1cm, length=8cm
V = _____________
d) Trapezoidal prism: a=3cm, b=7cm, h=2.6cm, depth=14cm
V = _____________
e) Trapezoidal prism: a=0.8mm, b=4.4mm, h=3.5mm, depth=4.2mm
V = _____________
QUESTION 3 — Cross-section area given, find Volume
d) Area = 82.5 cm², length = 10 cm
V = _____________
e) Area = 46 mm², length = 8.3 mm
V = _____________
f) Area = 17.5 mm², length = 7.2 mm
V = _____________
QUESTION 6 — Find the Missing Dimension
a) Rectangular prism V=960 cm³, l=16 cm, w=8 cm. Find height.
h = _____________
b) Triangular prism V=400 cm³, cross-section area=20 cm². Find height.
h = _____________
c) Cylinder V=785 cm³, r=7 cm. Find height.
h = _____________
d) Cube V=729 cm³. Find side length. (Hint: ∛729 = ?)
s = _____________
e) Cube V=1000 cm³. Find side length.
s = _____________
f) Fish tank V=2400 cm³, l=30 cm, w=10 cm. Find height.
h = _____________
g) Cylinder V=250 cm³, r=3 cm. Find height.
h = _____________
h) Cereal box V=3600 cm³, l=20 cm, height=30 cm. Find width.
w = _____________
i) Triangular prism V=500 cm³, depth=10 cm, triangle base=5 cm. Find perpendicular height of triangle.
h_tri = _____________
QUESTIONS 7–13 — Worded Problems
Q7. How much air space is inside a rectangular cardboard box: 85 cm × 62 cm × 36 cm?
V = _____________
Q8. 25,000 cm³ of water is poured into a tank that is 50 cm long, 20 cm wide and 20 cm high. Will it overflow? Prove your answer with calculations.
Tank capacity = _____________ Will it overflow? YES / NO By how much? _____________
Q9. Kiara rolls a 25×14 cm sheet of cardboard into a cylinder (height=14 cm, 1 cm overlap each end → circumference = 23 cm). Find the surface area of the finished cylinder.
r ≈ _____________ TSA ≈ _____________
Q10. Cost = $0.005/cm². Find the TSA and cost for each size. Which is cheapest?
SIZE A: r=3cm, h=12.5cm SIZE B: r=3.2cm, h=11cm SIZE C: r=3.4cm, h=9.73cm
SIZE A: r=3cm, h=12.5cm SIZE B: r=3.2cm, h=11cm SIZE C: r=3.4cm, h=9.73cm
A: TSA=_____ Cost=_____ B: TSA=_____ Cost=_____ C: TSA=_____ Cost=_____ Cheapest: _____
Q11. Water tank cylinder: diameter = 28 m, height = 12.5 m.
(a) Find the volume of the tank. (b) At 85% capacity, how much water can be stored?
(a) Find the volume of the tank. (b) At 85% capacity, how much water can be stored?
(a) V = _____________ (b) 85% capacity = _____________
Q12. A hollow log: outer diameter = 60 cm, hollow inner diameter = 20 cm, length = 300 cm. Find the volume of solid wood.
V = _____________
Q13. Cylindrical roller: diameter = 60 cm, width = 1 m.
(a) Find the curved surface area. (b) Area pressed in 20 revolutions?
(a) Find the curved surface area. (b) Area pressed in 20 revolutions?
(a) Curved SA = _____________ (b) Area after 20 rev = _____________