5th Homeowrk Due 2nd Feb, 20 Marks

1. Expand and simplify: $(x+3)(x-2)(x-5)$

   [3]

2. Factorise the denoimnators and simplify: \[ \frac{5}{6x+9} - \frac{4}{2x^2-11x-21} \]

   [5]

3. A car travels at 70mph for 3 hours and 41 minutes, how many miles has it travelled?

   [2]

4. If a=5cm, b=4cm and c=3cm, find
   
   1. the length d
   2. The surface area of the cuboid

   [5]

5. In the previous question, find the angle between AG and the face ABCD.

   [5]

Fourth Year Homework due Tue 20 Jan, SHOW ALL WORKING OUT. Click pics to enlarge. MARKS: 21.

1. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{No. of petals} & \text{Frequency} & \text{... } \\ \hline \text{3} & 4 & \\ \hline \text{4} & 15 & \\ \hline \text{5} & 22 & \\ \hline \text{6} & 14 & \\ \hline \end{array} Use it to:
   a. Find the mean
   b. Find the median

   [4 marks]

2. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{Height in cm} & \text{Freq-Girls} & \text{M.P. $\times$ F} & \text{Freq-Boys} & \text{M.P. $\times$ F} \\ \hline \text{110 $\leq$ h < 115} & 5 & & 11 \\ \hline \text{115 $\leq$ h < 120} & 21 & & 29\\ \hline \text{120 $\leq$ h < 125} & 29 & & 14\\ \hline \text{125 $\leq$ h < 130} & 15 & & 16\\ \hline \end{array} Use it to:
   a. Find separate estimates of the mean for the boys and girls to 4 significant figures
   b. Make a comment comparing boys height to girls using this data.

   [5 marks]

3. HARD: Boat A sails 5 miles on a bearing of $099^\circ$ from Dover. Boat B sails 7 miles on a bearing of $200^\circ$ from Dover. Draw a clear diagram and use it to find the distance between Boat A and Boat B. HINT: you might want to look up the Cosine Rule.

   [4 marks]

4. In triangle XYZ, XY=7cm and YZ=13cm. Angle Y is $54^\circ$, find angle X

   [3 marks]

5. Find angle X to 3 significant figures
   

   [5 marks]

5th Year Post Mock Workout

Due Monday 19th Jan in front of books. Click pics to enlarge. SHOW ALL working. Marks: 23

1. A car travels 120km in 2 hours and 17 minutes. Calculate its average speed. Give the units.

   [2 marks]

2. An iPad is reduced by £54 in a sale which is offering 22% off. What was it's price before the sale?

   [3 marks]

3. Find n(AuBuC')
   

   [2 marks]

4. $ \epsilon$ = {set of odd numbers}, A = {factors of 15}, B = {factors of 75} List all the items in AnB

   [3 marks]

5. M is the midpoint of the side AD. Find the angle between the face ABCD and the line MF to 3 significant figures.
   

   [5 marks]

6. Find angle X (O is the centre of the circle - I know it doesn't really look like a circle!)
   

   [3 marks]

7. By factorising the denominators, simplify: \[ \frac{4}{2x+2} - \frac{3}{x^2 -x -2} \]

   [5 marks]