Year 7 - Formulas

Please complete in the back of your book and show all working.

I have given you examples of excellent answers for 1)a and 2)a

Title: Formulas

1)
a What is  5 + 6w equal to when w = 2?

 Excellent answer :

5 + 6w = 5 + (6 x 2) = 5 + 12 = 17  (use the same method for the other questions)

bWhat is 6 + 3t equal to when t = 3?
c What is 2w + 5 equal to when w = 2?
d What is 2 + 15d equal to when d = 3?
e What is 17 + 3r equal to when r = 6?

2)
A window cleaner uses the following formula:

C = £5 + 2w

where

C = cost in £
w = number of windows

Calculate how much the window cleaner charges to wash the following number of windows:

a 3 windows
 Excellent answer:
C = £5 + 2w  and w = 3 (as we have 3 windows)

C = 5 + (2 x 3) = 5 + 6 = £11  (use the same method for the other questions)

b 6 windows
c 9 windows

3)
A dentist uses the following formula:

C = £15 + 20t

where

C = cost in £
t = number of teeth removed

Calculate how much the dentist charges to remove the following number of teeth:

a 1 tooth
b 3 teeth
c 4 teeth

4)
A formula for renting a car is  :

C = £46 + 24d

where

C = cost in £
d = number of days

Calculate how much it costs to rent a car for the following number of days:

a 2 days
b 4 days
c How much more expensive is it to rent a car for 6 days compared to 4 days?

Year 8 - Percentages

Complete in the back of your excercise book.  Do not use a calculator and show all of your working.

Example
What is 15% of 95

Answer:
10% of 95 = 9.5
5% of 95 = 4.75
15% of 95 = 9.5 + 4.75 =  14.25

1.
a What is 25% of 56
b What is 75% of 60
c  What is 40% of 70
d What is 60% of 85
e What is 37% of 25
f What is 18% of 120

2.
a What is 75 increased by 10%
b What is 85 decreased by 10%
c What is 110 increased by 50%
d What is 60 decreased by 25%
e What is 35 increased by 11%
f What is 150 decreased by 17%

Year 7 Algebra Homework

Complete the following questions in the back of your book.

Write the title: Algebra Homework

If you're not sure of the method look back through your book, you
have completed similiar questions in your books.

1
a How do you write n multiplied by 8 in algebra
b How do you write x divided by 9 in algebra
c How do you write y minus 7 in algebra
d How do you write n multiplied by 3 then add 6 in algebra

2
a What is 4n when n = 6
b What is 3y when y = 7
c What is 11n when n = 5
d What is 4b -3 when b = 2
e What is n + 7 when n = 2
f  What is 5q - 7 when q = 2
g What is n - 7 when n= 14
h What is n²+ 5 when n = 3
i What is n²- 6 when n = 6
j What is n/7 (n over 7) when n=14
k what is n/3 (n over 3) when n=27

3
Simplify these expressions:
a 3n + 11n
b 15n + 2n
c 4n + 7n + 2b
d 11b + n + 2b + 4n            

Converting between Fractions and Decimals

Complete the homework in the back of your exercise book.  Do not complete on the sheet if you choose to print it out.

1. Convert the following decimals to fractions and then cancel to their simplest form.

a 0.3
b 0.35
c 0.78
d 0.375
e 0.984

2. Covert the following fractions to decimals, do not use a calculator and show full working.  Use an appropriate method.

a 4/5
b 19/20
c 7/25
d 2/11
e 1/6

3. Covert the following recurring decimals into fractions showing a clear method.
a 0.2222222...
b 0.5555555...
c Can you see a pattern in your results? What is the pattern and can you predict what 0.8888888888.. will be equal to?


Extension Questions
a 0.1414141414...
b 0.4545454545...
c 0.125125125125...
d 0.833333333333....

Year 7 - Mean, Mode, Median and Range Homework - 7Q2

Please complete in the back of your books.  Thank you all those students who contributed questions.

Homework is due 22nd November.

The title is Mean, Mode, Median and Range


1) How do you work out the mean?

2) Work out the mean and median of these values:

2, 9, 10, 21, 28

3) Work out the range and median of these values:

2, 9, 3, 7, 11, 10, 15, 22

4) Work out the mean of these values:

6, 5, 7, 4, 8, 6

5) What is the mode of these values:

6, 3, 4, 3, 2

6) What is mode, median and range of these values:

3, 5, 6, 7, 1, 5, 7, 9 , 11

7) How do you know which is the modal choice for a bar chart?

Adding and subtracting fractions - 8R1

Please complete the following questions in the back of your book, not on the sheet if you print it out.  Show your working out.  CLICK ON THE QUESTIONS TO ENLARGE THEM.

Year 7 - Area and Perimeter Homework

Sorry I couldn't put more of your rectangles up, some were very hard!


Complete the homework in the BACK of you book and draw the shapes before you work out the area and perimeter.


Work out the area and perimeter of the next four shapes.



1)

2)

3)

4)

Extension Homework

Work out the area and perimeter of the next two compound shapes.

Remember to split the compound shape up into small rectangles or squares, work out the areas of these shapes and then add them together at the end. 

Have a look at THIS if you need help.

1)

2)

Year 7 - Diet Homework

Remember the calories need to add up to a certain amount depending on your athlete.

 You won't be able to get them add up exactly but try and get them as close as possible.

Use the table below to finish the diet plan you started in class

Click on table below to enlarge

Percentages - Decimal Multipliers

Use DECIMAL MULTIPLIER and SHOW WORKING


Method
Percentage increase using Decimal Multipliers
For the explanation I will assume it's a 20% increase of a quantity 50
step 1 -  add increase to 100%: 100% + 20% = 120%
step 2 - divide this by 100: 120%÷ 100 = 1.2
step 3 - times quantity 50 by 1.2: 50 x 1.2 = 60


So 50 increased by 20% is 60


Percentage decrease using Decimal Multipliers
For the explanation I will assume it's a 20% decrease of a quantity 50
step 1 -  subtract decrease from 100%: 100% - 20% = 80%
step 2 - divide this by 100: 80% ÷ 100 = 0.8
step 3 - times quantity 50 by 0.8: 50 x 0.8 = 40 


So 50 decreased by 20% is 40


Also see BBC website below for more explanation and examples


http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/percentages/percentincrease/factsheet5.shtml



Questions


1.My salary was £230 per week before I got a 7% pay rise. What is my new salary?
£230 x 1.07 =


2.The price of a TV is reduced by 15%. If it cost £500 before the reduction, what was it after?
£500 x 0.85 =


3.The price of an England shirt dropped by 20% after the World Cup, it was £35 before. How much was it after?


4.A house’s price increased 20% in 4 years, it was £230 000 4 years ago, how much is it now?


5.The number of boys in a school increased by 5% from 670 last year.
How many boys are there in the school this year?


6.VAT is 17.5%, add VAT to the following items giving your answers to 2 d.p..


Prices before VAT
a.  TV - £400
b.  Ipod - £70
c.  Laptop - £356


7. After an increase of 37% a house cost Richard £137 000. He wants to know how much it would have cost if it hadn’t been increased?(Different method to other question)

Year 7 - Decimal Homework

1. Work out the following:
a) 96 x 100   b) 5.2 x 10   c) 37.4 x 100   d) 4.8 ÷ 100

2. Work out the following:

a) 4.6 x 100   b) 0.042 x 10   c) 1.7 x 100   d) 4.8 ÷ 100

3. Work out the following:

a) 46.5809 x 100   b) 0.0968 ÷ 1000   c) 159.7 x 1000   d) 0.08015 ÷ 100000

2. Fill in the blanks:

a) 0.4 x …. = 40         b) 6 ÷ …. = 0.06          c) …. X 100 = 0.3




Extension Task


1.
Work out what weighs more given the information below, an elephant or 10000 pints of water?!


Weight of elephant : 4.5 Tonnes (1 tonne = 1000kg , 1kg=1000g)
Weight of a pint of water 568.2 grams


2.
Some ants can carry ten times their own weight, how much could one carry in milligrams? 
Try and convert you answer to grams
An ant weighs 3 milligrams (1 gram = 1000milligrams)


How many ants would it take to carry a dragon fly that weighed 0.03 grams?

Year 10 - Reverse Percentages Homework

Please show ALL WORKING for ALL questions

Question 1
To find 20% of 40 we can multiply it by 0.40

What decimal would we need to multiply 56 by find:
A 15% of 56
B 55% of 56
C 90% of 56
D 12.5% of 56
E 150% of 56

Question 2
A
If a car's price was increased by 20% and is now £6000, how much was it before the increase in price?

B
If a house price dropped by 15% and is now £85000, how much did it cost orginally?

C
The population of an island has risen 8% since last year.  The population is now 280 000.
What was it a year ago?  Give your answer to 2 significant figures.

D
A store reduces all its prices by 30% in a sale.
The reduced price of a television is £875.  How much was it before the sale?

E
Dave buys a car for £3150.  The price was reduced by 10% for paying cash.
Dave says 'I saved £315 by paaying in cash.'
i) Explain why Dave is wrong.
ii) Work out how much Dave saved.

7Q2 - Ordering decimals - 22/09/2010

Put the following decimals in order from SMALLEST to LARGEST


1.    1.4, 1.9, 1.8, 2.1, 1.97
2.    1.23, 1.2, 1.234, 1.203
3.    0.9987, 0.9999, 0.9897, 0.9862
4.    2.35, 2.34, 2.356, 2.346

5.   Copy and complete table below in your book, add  4 extra rows and put in the following numbers:

4.57, 45, 4.057, 0.045

Extension Question 

5.   One meter is 100 cm.  Change all the lengths below and put the in order from SMALLEST to LARGEST

        

         6.25 m, 269 cm, 32 cm, 2.7 m, 0.34 m

6.   One kilogram is 1000 grams.  Change all the weights below and put the in order from SMALLEST to LARGEST

         467 g, 1.260 kg, 56 g, 0.5 kg, 0.055 kg

10B2 - Percentage homework - 22/09/2010

Question 1 - Use spider percentage method to work out the following percentages
a.  Find 25% of 36
b.  Find 16% of 22
c.  Find 75% of 84
d.  Find 66% of 53

Question 2 - Write down method used
To answer this type of question it is helpful to know what the different numbers mean.  In part b, we have
Find 16 as a percentage of 64.
In this case 64 is the quantity that is equal to 100%, we need to work out, if 64
is equal to 100%, was is 16 equal to.

To do this
STEP 1
We divide 16 by 64, which will give us the decimal 0.25 or a fraction of 16 over 64 which can be cancelled to a quarter.
STEP 2
We then times it by 100 to turn the decimal or fraction in to a percentage. 0.25 or a quarter times 100 gives 25%

a.  Find 40 as a percentage of 100

b.  Find 16 as a percentage of 64

c.  Find 12 as a percentage of 20

d.  Find 33 as a percentage of 44

Question 3

 - Write down method used

Out of 52 people who take a driving test, 34 people pass.

    What percentage of people:

a.  pass?

b.  fail?

Year 7 - Function Machines Homework

Question 1 - Fill in blanks where the question marks are, like we did in class.

Introduction to Algebra - Independent Learning Task


Read then complete the questions below, only the first three questions are compulsory.

In mathematics letters can be used to represent a  number that we don’t know, or when it can vary (it could be lots of different numbers )
Here is some algebra shorthand:

• 2x means 2 multiplied by x, where x can be any number

x can be any number, so let's say x = 5 then 2x = 2 × 5 = 10!

• 2g means 2 multiplied by g
• 6y means 6 multiplied by y
• 6x + 2 means 6 multiplied by x then add 2

2x, 2g, 6y and 6x + 2 are all called expressions.
x, g and y are called variables because they are unknown or could be lots of different numbers, they can vary.

Example
Write down what the expression  6x is equal to when
A. x=2 B. x=3 C. x=10
Answers:
When x=2 , 6x = 6 × 2   = 12
When x=3 , 6x = 6 × 3 = 18
When x=10 , 6x = 6 × 10 = 60

Questions
1. Write down what the expression  10x is equal to when
A. x=2 B. x=3 C. x=10

2. Write down what the expression  x + 5 is equal to when
A. x=41 B. x=52 C. x=10

3. Write down what the expression  x—5 is equal to when
A. x=8 B. x=15 C. x=25

Extension Questions
4. Write down what the expression  5x - 54 is equal to when
A. x=9 B. x=25 C. x=105

5. Write down what the expression  ½(2x  - 5) is equal to when (HINT— you do the calculation in the brackets first then half it)
A. x=12 B. x=9 C. C. x=10

6. Write down what the expression  ¼n(n + 5) is equal to when ( HINT—you do the calculation in the brackets first then multiply  it by ¼n)
A. n=4 B. n=16 C. n=10

Link to BBC page if you're having trouble understanding or want to find out more about algebra. Click HERE!

Year 7 – Sequence Homework

Year 7 – Sequence Homework 

1.
Give the next two terms in the following sequences.
Describe the term to term rule you have used. Hint: Think how you get from one number (TERM) to the next

Example:
 0,7,14,...
Answer: 0,7,14, 21, 28 Term to term rule : add seven.

a.  3,6,9,... b. 4,8,12,.. c. 4,9,14, … d. 23,20,17…
e. 101,108,115,… f. 9,18,27,.. g. 32, 28, 22, … h  301, 310, 319, …
i. 2,10,50,... j. 2,6,18, ... k. 1,4,9,16,… l. 240,120,60,…
m. 10, 7, 4, 1, -2, … n. 1000,100,10,1,0.1,..

2.
For each pair of numbers find two different sequences, writing the next two terms. Describe the term to term rule you have used
Hint :one rule may be addition based the other rule may be multiplication based

Example:
4,8,...
Answer: Sequence 1: 4,8,12,16 Term to term rule : add four
 Sequence 2: 4,8,16,32 Term to term rule double/multiply by 2

a.  1,4,... b.2,6, … c. 5,15, …