Homework 1 - Fractions 1
Show all necessary working:
1.Write the following fractions as percentages:
a)b)c)
d)e)f)
2.Add or subtract the following fractions, expressing your answer in its simplest form:
a)b)
c)d)
3.Add or subtract the following fractions, expressing your answer in its simplest form:
a)b)
c)d)
Exercise 2 - Fractions 2
Show all necessary working:
1.Write the following percentages as fractions in their simplest form:
a)10%b)80%c)35%
d)12%e)44%f)
2.Multiply or divide the following fractions, expressing your answer in its simplest form:
a)b)
c)d)
3.Multiply or divide the following fractions, expressing your answer in its simplest form:
a)b)
c)d)
Algebra History
While the word algebra comes from the Arabic language (al-jabr, الجبر literally, restoration) and much of its methods from Arabic/Islamic mathematics, its roots can be traced to earlier traditions, most notably ancient Indian mathematics, which had a direct influence on Muhammad ibnMūsā al-Khwārizmī (c. 780-850). He learned Indian mathematics and introduced it to the Muslim world through his famous arithmetic text, Book on Addition and Subtraction after the Method of the Indians. He later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is independent of geometry and arithmetic.
Exercise 3 - Algebra 1
1. Given that , find when .
2. Evaluate , when .
3. Evaluate , when and .
4. Evaluate , when and .
5. Given that , find when and .
Exercise 4 - Algebra 2
Solve the following equations for x:
1.3x + 2 = x – 82.4x - 2 = 5x + 16
3.3(x + 4) + 7x = 44.5x – 2(x + 1) = 9
5.7x+ 2 = 3x + 36.
Exercise 5 - Algebra 3
Factorise the following expressions by taking out a common factor:
1.3m + 62.2b – 143.9s - 12
4.6a + 9b5.18 – 12y6.9b + 15y
7.8.3a + 6b9.
10.
Exercise 6- Probability and Statistics 1
1. / Last month a dealer sold 10 red cars, 7 silver cars and 13 black cars.Jill bought one of these cars.
What is the probability that the car she bought was red?
Give your answer as a fraction in its simplest form.
2. / Sixty people took part in a shopping survey.
They were asked whether or not they bought organic food.
The following table summarises the responses.
Buys Organic / Doesn’t buy Organic
Male / 10 / 18
Female / 25 / 7
What is the probability that a person chosen at random from this group:
(a) / Is female
(b) / Doesn’t buy organic food
(c) / Is a male who buys organic food?
3. / A company manufactures boxes of jelly beans.
It claims that there are “on average” 60 jelly beans per box.
The contents of 100 boxes are checked in a random sample.
The results are shown in the table below.
Number of Jelly Beans
x / Frequency
f / f × x
57 / 7
58 / 13
59 / 21
60 / 24
61 / 19
62 / 12
63 / 4
Total / 100
(a) / Copy and complete the above frequency table.
Find the mean number of jelly beans per box.
(b) / Is the company claim reasonable?
You must give a reason for you answer.
Exercise 7- Probability and Statistics 2
1. / Laura has a bag of sweets which she is sharing with her friends. It contains 5 chocolate sweets, three candy sweets, and seven liquorice sweets. Stephen chooses a sweet at random from the bag:(a) / What is the probability that Stephen chooses a candy?
(b) / If Stephen did chose a candy, what is the probability that the next sweet chosen will be a chocolate?
2. / The number of passengers travelling by bus from Glasgow to
Edinburgh was recorded on 21 journeys.
29 / 45 / 36 / 27 / 41 / 38 / 14
48 / 31 / 39 / 24 / 17 / 23 / 34
29 / 38 / 42 / 12 / 32 / 36 / 33
(a) / Display this information in an ordered stem and leaf diagram.
(b) / Find the median number of passengers.
(c) / Find the range of passengers.
3. / Two fair dice are rolled simultaneously.
Calculate the probability that the sum of the outcomes is less than 5.
4. / The ages of a group of teenagers attending a birthday party are shown below
Age / Frequency / Cumulative Frequency
15 / 3
16 / 4
17 / 2
18 / 6
19 / 7
Total
(a) / Copy and complete the frequency table.
(b) / State the modal age.
(c) / Use the frequency table to calculate the median age.