DJY Mathematics Blog

Wednesday, 25 March 2015

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

A postman has a 12% pay increase from £18,000. What is his new salary? \[£18000\times 1.12 = £20160\]
[3 marks]
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]
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]
A paperboy has his wage increased by 15% to £6.65 per hour. What was his wage before it was increased? \[? \times 1.15 = 6.65 \\ ? = 6.65 \div 1.15 = £5.78 \]
Express 490 as a product of its prime factors \[ 490 = 2 \times 5 \times 7^2\]
[2 marks]
How many millimetres are there in 150m? \[150m \times 100 = 15000cm \times 10 = 150,000mm\]
[2 marks]
£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]

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]
For the sequence $-3,2,7,12...$, find $u_n$ and $u_{50}$ \[ u_n=5n-8\\u_{50}=250-8=242 \]
[3 marks]
For the sequence $24,21,18,15...$, find $u_n$ and $u_{50}$ \[ u_n=27-3n\\u_{50}=27-150=-123 \]
[3 marks]
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]
Write down the first five terms of the sequence $u_n=12-5n$ \[ 7,2,-3,-8,-13 \]
[2 marks]
How many green tiles would there be in pattern 120?
\[ u_n=2n+1\\u_{120}=240+1=241 \]
[2 marks]
Expand $(3x+2)(5x-4)$ \[15x^2-2x-8\]
[2 marks]
Factorise $x^2-3x+28$ \[(x-7)(x+4)\]
[2 marks]
Find $u_n$ for $-1,2,7,14,23,....$ \[u_n=n^2-2 \]
[2 marks]
Find $u_n$ for $2,16,54,128,250....$ \[u_n = 2n^3 \]
[2 marks]

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

Solve \[ \begin{align*} 3&x+2y=13 \\ -5&x+6y=81 \end{align*} \]
[3 marks]
For the sequence $-3,2,7,12...$, find $u_n$ and $u_{50}$
[3 marks]
For the sequence $24,21,18,15...$, find $u_n$ and $u_{50}$
[3 marks]
True or false, $-134$ is in the sequence $36,32,28,....$. Give a reason for your answer.
[2 marks]
Write down the first five terms of the sequence $u_n=12-5n$
[2 marks]
How many green tiles would there be in pattern 120?

[2 marks]
Expand $(3x+2)(5x-4)$
[2 marks]
Factorise $x^2-3x-28$
[2 marks]
Find $u_n$ for $-1,2,7,14,23,....$
[2 marks]
Find $u_n$ for $2,16,54,128,250....$
[2 marks]

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

A postman has a 12% pay increase from £18,000. What is his new salary?
[3 marks]
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]
A pair of trainers costs £35 AFTER a discount of 45%. How much were they before the discount?
[3 marks]
A paperboy has his wage increased by 15% to £6.65 per hour. What was his wage before it was increased??
[3 marks]
Express 490 as a product of its prime factors
[2 marks]
How many millimetres are there in 150m?
[2 marks]
£1 is worth $1.75
1. How many dollars is £5.85?
2. How many pounds is $228?
  [3 marks]