2.4 Homework 18th March Answers

Complete neatly in the front of your books. Calculator allowed but working must be shown.

1. A postman has a 12% pay increase from £18,000. What is his new salary? \[£18000\times 1.12 = £20160\]

   [3 marks]

2. The number of insects on a corpse increases by 25% every hour. At 9am there were 1000 insects on the corpse.
   1. How many insects were there at 10am? \[1000 \times 1.25 = 1250 \text{ insects}\]
   2. How many insects were there at 11am? \[1250 \times 1.25 = 1562.5 \mbox{ i.e. 1563 insects}\]
   3. Roughly how many insects will there be by midday? \[1562.5 \times 1.25 = 1953.125 \text{ i.e. 1953 insects}\]

   [6 marks]

3. A pair of trainers costs £35 AFTER a discount of 45%. How much were they before the discount? \[? \times 0.55 = 35 \\ ? = 35 \div 0.55 = £63.64 \]

   [3 marks]

4. A paperboy has his wage increased by 15% to £6.65 per hour. What was his wage before it was increased? \[? \times 1.15 = 6.65 \\ ? = 6.65 \div 1.15 = £5.78 \]
5. Express 490 as a product of its prime factors \[ 490 = 2 \times 5 \times 7^2\]

   [2 marks]

6. How many millimetres are there in 150m? \[150m \times 100 = 15000cm \times 10 = 150,000mm\]

   [2 marks]

7. £1 is worth $1.75
   1. How many dollars is £5.85? \[5.85 \times 1.75 = \$10.24\]
   2. How many pounds is 228? \[228 \div 1.75 = £130.29\]

      [3 marks]

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]

2.4 Homework Due Wed 18 March. Total 21

Complete neatly in the front of your books. Calculator allowed but working must be shown.

1. A postman has a 12% pay increase from £18,000. What is his new salary?

   [3 marks]

2. The number of insects on a corpse increases by 25% every hour. At 9am there were 1000 insects on the corpse.
   1. How many insects were there at 10am?
   2. How many insects were there at 11am?
   3. Roughly how many insects will there be by midday?

   [6 marks]

3. A pair of trainers costs £35 AFTER a discount of 45%. How much were they before the discount?

   [3 marks]

4. A paperboy has his wage increased by 15% to £6.65 per hour. What was his wage before it was increased??

   [3 marks]

5. Express 490 as a product of its prime factors

   [2 marks]

6. How many millimetres are there in 150m?

   [2 marks]

7. £1 is worth $1.75
   1. How many dollars is £5.85?
   2. How many pounds is $228?

      [3 marks]

Any thoughts?

2.4 Homework Due Mon 9 March Total 21

Complete neatly in the front of your books. Calculator allowed but working must be shown.

1. A car is reduced by 15% from £9,200. What is the new price of the car?

   [3 marks]

2. The number of birds in a nature reserve increases by 15% every year. There were 1800 birds in 2013.
   1. How many birds were there in 2014?
   2. How many birds were there in 2015?
   3. Roughly how many birds will there be in 2018?

   [6 marks]

3. An iPhone costs £435 with 15% discount. How much is the phone without the discount?

   [3 marks]

4. The price of a house is reduced by 5% to £275,000. What was the house price before the reduction?

   [3 marks]

5. Express 78 as a product of its prime factors

   [2 marks]

6. How many centimetres are there in 3.5km?

   [2 marks]

7. £1 is worth € 1.35
   1. How many euros is £3.45?
   2. How many pounds is € 17.22?

      [3 marks]

Answers

5th Homework 5.3 Due Mon 9th March Total 22

1. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{Height in cm} & \text{Freq.} & \text{Cum. Freq.} & \text{Freq. Den.} \\ \hline \text{100 $\leq$ h < 115} & 5 & & \\ \hline \text{115 $\leq$ h < 120} & 11 & & \\ \hline \text{120 $\leq$ h < 150} & 39 & & \\ \hline \text{150 $\leq$ h < 200} & 25 & & \\ \hline \end{array}

   [3]

   1. Using axes: $100 \leq x \leq 200$ and $0 \leq y \leq 80$, plot a LARGE, CLEAR cumulative frequency curve
   2. From your curve, estimate the median
   3. From your curve, estimate the Inter Quartile Range (IQR) by finding the UQ and LQ
   4. Complete: 15% of pupils were more than _____cm tall

      [8]

2. By constructing an appropriate table, find an estimate of the mean spent:

   

   [4]

3. Simplify $3\sqrt{50} - 4\sqrt{18}$

   [3]

4. Expand and simplify $(3\sqrt{50} - 4)(5\sqrt{18}-2)$

   [4]