3.2 Homework due 17.3.15 ANSWERS

1. Solve \[ \begin{align*} 3&x+2y=13 \\ -5&x+6y=81 \\ &\text{__________} \\ 15&x+10y=65 \\ -15&x+18y=243 \\ 28&y = 308 \\ \therefore &y=11 \\ &x=-3 \end{align*} \]

   [3 marks]

2. For the sequence $-3,2,7,12...$, find $u_n$ and $u_{50}$ \[ u_n=5n-8\\u_{50}=250-8=242 \]

   [3 marks]

3. For the sequence $24,21,18,15...$, find $u_n$ and $u_{50}$ \[ u_n=27-3n\\u_{50}=27-150=-123 \]

   [3 marks]

4. True or false, $-134$ is in the sequence $36,32,28,....$. Give a reason for your answer. \[ u_n=40-4n\\ 40-4n=-134 \\ -4n=-174 \\ n=43.5\] NOT in the sequence as n is not a whole number

   [2 marks]

5. Write down the first five terms of the sequence $u_n=12-5n$ \[ 7,2,-3,-8,-13 \]

   [2 marks]

6. How many green tiles would there be in pattern 120?
   \[ u_n=2n+1\\u_{120}=240+1=241 \]

   [2 marks]

7. Expand $(3x+2)(5x-4)$ \[15x^2-2x-8\]

   [2 marks]

8. Factorise $x^2-3x+28$ \[(x-7)(x+4)\]

   [2 marks]

9. Find $u_n$ for $-1,2,7,14,23,....$ \[u_n=n^2-2 \]

   [2 marks]

10. Find $u_n$ for $2,16,54,128,250....$ \[u_n = 2n^3 \]

    [2 marks]

3.2 Homework Due Tue 17th March

To be done in front of books neatly. Show all working out. Marks: 23

Sequence notes

1. Solve \[ \begin{align*} 3&x+2y=13 \\ -5&x+6y=81 \end{align*} \]

   [3 marks]

2. For the sequence $-3,2,7,12...$, find $u_n$ and $u_{50}$

   [3 marks]

3. For the sequence $24,21,18,15...$, find $u_n$ and $u_{50}$

   [3 marks]

4. True or false, $-134$ is in the sequence $36,32,28,....$. Give a reason for your answer.

   [2 marks]

5. Write down the first five terms of the sequence $u_n=12-5n$

   [2 marks]

6. How many green tiles would there be in pattern 120?
   

   [2 marks]

7. Expand $(3x+2)(5x-4)$

   [2 marks]

8. Factorise $x^2-3x-28$

   [2 marks]

9. Find $u_n$ for $-1,2,7,14,23,....$

   [2 marks]

10. Find $u_n$ for $2,16,54,128,250....$

    [2 marks]

3rd Year Hwk Due Tue 10th Feb 15

To be done in front of books neatly. Show all working out. Marks: 21

ANSWERS

1. Solve \[ \begin{align*} 3&x+4y=19 \\ -5&x+6y=59 \end{align*} \]

   [3 marks]

2. A jacket is reduced by £45 in a 15% OFF sale. What was the price of the jacket in the sale?

   [3 marks]

3. A ball bounces to 90% of the previous height. If it was dropped from 5m, how high will it reach after the third bounce?

   [3 marks]

4. Give a quick explanation of why the sine ratio is never more than 1.

   [2 marks]

5. In a test there are 50 questions. For each correct answer I score 7 points and for each incorrect answer I lose 3 points. If my total score for the test was 260 points, set up simultaneous equations to find x (the number of questions I got correct) and y (the number of questions I got wrong).

   [4 marks]

6. Find x to 2decimal places
   

   [3 marks]

7. Find the angle x to 1 decimal place.
   

   [3 marks]