City and Guilds Level 3 Aeronautical Engineering: Unit 215 Exam Questions And Answers Verified 100% Correct

City and Guilds Level 3 Aeronautical Engineering: Unit 215 Exam Questions And Answers Verified 100% Correct Why is unit consistency essential in aeronautical formulae? - ANSWER -To avoid catastrophic miscalculations (e.g., Mars Climate Orbiter crash due to unit error). Velocity equation: - ANSWER -v = d/t Density equation: - ANSWER -p = m/V Pressure equation: - ANSWER -P = F/A Relative error equation: - ANSWER -(Error / True value) x 100 Absolute error equation: - ANSWER -|Measured - true| Rearrange v = u + at to make 'a' the subject. - ANSWER -a = (v-u)/t Solve x^2 - 9x + 20 = 0. - ANSWER -x = 4 or x = 5 Simplify (2x^2)(-3x^3). - ANSWER --6x^5 Define the difference between an equation and an identity. - ANSWER -An equation is true for some values; an identity is true for all values. Factorise x^2 - 7x + 12. - ANSWER -(x - 3)(x - 4) Define 'identity' in algebra. - ANSWER -An equality true for all values of the variable (e.g., (x + 1)^2 = x^2 + 2x + 1). How are nested brackets simplified? - ANSWER -Work from the innermost bracket outward, apply BODMAS. Evaluate: (2x^2)^3 - ANSWER -8x^6 Use a formula to calculate centre of gravity. - ANSWER -CG = ∑(mx)/∑m Give an example of an aeronautical formula with square roots. - ANSWER -Mach number: M = v/sqrt(γRTv) Quadratic equation: - ANSWER -ax^2 + bx + c = 0 Quadratic formula: - ANSWER -x = (-b ± sqrt(b^2 - 4ac))/2a Standard law for a^m x a^n: - ANSWER -a^(m+n) Standard law for (a^m)/(a^n): - ANSWER -a^(m-n) Standard law for (a^m)^n: - ANSWER -a^(m x n) Standard law for a^-n: - ANSWER -1/(a^n) Standard law for nth-root(a): - ANSWER -a^(1/n) What is the volume of a cylinder with radius 4 cm and height 10 cm? - ANSWER -pi x r^2 x h = pi x 16 x 10 = 160pi cm = 502.655 cm Define 'chord' in a circle. - ANSWER -A straight line connecting two points on the circumference. Calculate the area of a triangle with base 6 m and height 3 m. - ANSWER -1/2 x 6 x 3 = 9 m^2 Name a 3D shape used to model aircraft fuel tanks. - ANSWER -Cylinder or ellipsoid What is the surface area of a sphere with a radius 5 m? - ANSWER -4 x pi x r^2 = 4pi x 25 = 100pi = 314.159 Define 'chord' of a circle. - ANSWER -A straight line connecting two points on the circumference. What is the segment of a circle? - ANSWER -The area between a chord and the corresponding arc. Circle circumference equation: - ANSWER -C = 2 x pi x r Circle area equation: - ANSWER -A = pi x r^2 Arc length equation: - ANSWER -L = theta x r (when theta in radians) Sector area equation: - ANSWER -A = 1/2 x r^2 x theta Cube volume equation: - ANSWER -V = s^3 Cylinder volume equation: - ANSWER -V = pi x r^2 x h Cone volume equation: - ANSWER -V = 1/3 x pi x r^2 x h Sphere volume equation: - ANSWER -V = 4/3 x pi x r^3 sin(0): - ANSWER -0 sin(30): - ANSWER -0.5 sin(90): - ANSWER -1 cos(0): - ANSWER -1 cos(60): - ANSWER -0.5