Surface Area
This formula is used to find the total area of all the faces of a 3D object
What is surface area?
This is the term for money you earn from work
What is income?
These are the three main trigonometric ratios used in right-angled triangles
What are sine, cosine and tangent
This theorem states that in a right-angled triangle, a2+b2=c2
What is Pythagoras’ Theorem?
This financial term describes the amount of money you owe after borrowing
What is debt
A rectangular prism has dimensions 4 cm × 3 cm × 2 cm. Its total surface area is this many square centimetres.
What is 52 cm²
SA = 2(lw + lh + wh) = 2(12 + 8 + 6) = 52 cm²)
The simple interest on $500 at 5% per year for 2 years
What is $50
I = Prt = 500 × 0.05 × 2 = $50
In a right triangle, if opposite = 6 cm and hypotenuse = 10 cm, this is the value of sin θ.
What is 0.6
sin θ = 6/10 = 0.6
A right-angled triangle has legs 3 cm and 4 cm. The hypotenuse is this length
What is 5 cm
32+42=25→c=5
In a right triangle, this side is always directly opposite the right angle
What is the hypotenuse
This is the total surface area of a cylinder with radius 5 cm and height 10 cm
What is 471 cm²
SA = 2πr² + 2πrh = 2(3.14)(25) + 2(3.14)(5)(10) = 157 + 314 = 471 cm²)
A student spends $60 on food, $40 on phone credit and saves $30 from a $150 allowance. This is the amount they have left over unspent.
What is $20
60 + 40 + 30 = 130 → leftover = $20
In a right-angled triangle, θ = 30° and the adjacent side is 8 cm. The hypotenuse is this length.
What is 9.24 cm
cos 30° = adj/hyp → 0.866 = 8/h → h = 9.24 cm
In a right-angled triangle, the hypotenuse is 13 cm and one leg is 5 cm. The missing side is this length
What is 12 cm
132−52=169−25=144→12
A cylinder has a radius of 3 cm and height 8 cm. Its curved (lateral) surface area is this amount
What is 150.72 cm²
CSA = 2πrh = 2 × 3.14 × 3 × 8 = 150.72 cm²
This is the surface area of a shape made from two cubes each with edge length 4 cm, joined on one face.
What is 160 cm²
2 cubes = 2 × 6 × 4² = 192 cm².
Subtract the 2 hidden faces = 192 – 2×16 = 160 cm²
A pair of shoes originally priced at $120 is discounted by 25%. The sale price is this amount.
What is $90
25% of 120 = 30 → 120 – 30 = $90
A right-angled triangle has opposite = 5 cm and adjacent = 12 cm. The size of angle θ is this many degrees.
What is 22.6°
tan θ = 5/12 → θ = arctan(0.4167) = ≈ 22.6°
A TV measures 55 inches diagonally and is 48 inches wide. The height of the screen is this many inches
What is approximately 26.9 inches
552−482=3025−2304=721
→721=26.85
A right-angled triangle has a hypotenuse of 20 cm and an adjacent side of 12 cm
What is 0.6
cos θ = 12/20 = 0.6
This is the surface area of a square-pyramid with base side 12 cm and slant height 10 cm.
What is 384 cm²
Base area = 12² = 144 cm²
4 triangular faces = 4 × ½ × 12 × 10 = 240 cm²
Total = 384 cm²
The value of an investment of $2000 compounded annually at 4% for 3 years
What is $2249.73
A = P(1 + r)³ = 2000(1.04)³ = $2249.73
A ladder 4 m long leans against a wall. The base is 1.2 m from the wall. The angle the ladder makes with the ground is this many degrees.
What is 72.5°
cos θ = 1.2/4 = 0.3 → θ = arccos(0.3) = ≈ 72.5°
A 10 m ladder reaches a window 8 m above the ground. Its base is this far from the wall.
What is 6 metres
102−82=100−64=36→36=6
A laptop measures 40 cm in width and 25 cm in height. The diagonal length of the screen is this many centimetres
What is approximately 47.2 cm
402+252=1600+625=2225
→2225≈47.2