Station Plaza Campus t. 044 44 Hastings f. 044 7649 East Sussex www.sussexcoast.ac.uk TN34 BA Clive Cooke Principal HNC / HND Engineering & HNC Construction Interview Task Name.. Date... This test is intended to help us ascertain your basic mathematical skills such as manipulation of formulae and data. It should take about - 3 hours maximum to complete. Please answer on separate sheets ensure that your name is on each sheet and that your answers are clearly highlighted and any working clearly shown. PLEASE BRING YOUR COMPLETED WORK TO YOUR INTERVIEW Assessment Grading Criteria Achieved Comments Transposition of formulae Yes / No Basic graphs (ymx+c) Yes / No 3 Trigonometry right angled triangles Yes / No 4 Trigonometry practical example Yes / No 5 & 6 Volumes and surface areas Yes / No 7 Areas of circles Yes / No 8 Handling data Yes / No 9 Using formulae Yes / No 0 Using formulae Yes / No Assessors name Assessors signature Keith Wood Student Declaration to be completed before submission I declare that this is all my own original work Student signature: Date:
. Transposition of formulae:. Transpose the following simple formulae, making the required variable the subject. (a) Make I the subject of V IR (b) Make p the subject of pv c (c) Make h the subject of p ρgh (d) Make ω the subject of T π ω (e) Make A the subject of F p (f) Make C the subject of A x πfc. Transpose the following complex formulae, making the required variable the subject. (a) Make I the subject of P I R (b) Make t the subject of v u + at (c) Make V the subject of V P (d) Make h the subject of v gh R L (e) Make L the subject of T π (f) Make s the subject of T π g m s (g) Make u the subject of s ut + ½at (h) Make u the subject of v u + as (i) Make L the subject of f (j) Make a the subject of π LC c a + b.3 Transpose the following combined formulae, making the required variable the subject. (a) Make v the subject of mv mgh (b) Make V the subject of LI CV (c) Make s the subject of v u v u t s m v v Sx (d) Make v the subject of ( ) π 64 (e) Make D the subject of Ak ( D 4 d 4 ) (f) Make v the subject of p p 4f v ρg gd
. Using the graph paper supplied, plot a graph using the data shown below. Determine the gradient and intercept and clearly mark these on your graph. Based on this information state the equation that the graph represents. W (N) 500 000 500 000 500 3000 3500 E (N) 55 70 00 0 35 50 80 3. For the right-angled triangle in Figure.3 calculate: (a) The sine of angle X. (b) The value of angle X in degrees. (c) The value of angle Y in degrees. (d) The length of side y using either the SINE, COSINE or TANGENT ratio. Y 0 cm 6 cm X Z y
4. A surveyor stands on level ground to look up at a tall building and measures the angle of elevation to the top of the building as 5 as shown in Figure.4. If he is standing 000 metres away from base of the building, calculate the height of the building? 5. A sphere has a radius of 0. m (a) Find the volume of the sphere (b) Find the total surface area of the sphere 6. A cylinder has a volume of 60.8 x 0 3 mm 3 and a height of 40 mm (a) Find the diameter of the cylinder (b) Find the total surface area of the cylinder 7. Determine the area of the following circles. Give your answers in metres. a) Radius m b) Radius 00 mm c) Diameter 50 mm
8. The table below shows the diameter of a sample of small manufactured wheels. Diameter (mm) Frequency 5 3 6 7 7 8 0 9 5 0 8 Calculate: a) The mean b) The median c) The mode 9. The extension of a piece of material subjected to a change in temperature is given by the following formula: Where: L αl θ ΔL is the change in length α is the coefficient of linear expansion L is the original material length Δθ is the change in temperature What is the change in length of an aluminium bar m long when subjected to a temperature change of 50 O c? The coefficient of linear expansion for aluminium is 5x0-6.
0. The relationship between Volume and Temperature of a gas at constant pressure is given by the formula: V T V T Where V is volume in m 3 /s and T is temperature in K. NOTE: to convert from o C to K you must add 73. A balloon has a volume of 0 m 3 at 0 o C. What is the new volume if the temperature is increased to 00 o C? If you have any questions please contact me on 044 458396 / kwood@sussexcoast.ac.uk