Download 1st Year Revision Worksheet workings

Revision Worksheet
First Year Maths
Question 1
List all of the factors of 18 and 24.
What are the factors that are common to 18 and 24?
What is the highest common factor of 18 and 24?
Question 2
John has 24 packets of crisps and 20 chocolate bars. How many friends could he share with so that
everybody has the same amount of each and there are none left over?
Question 3
Write down the Prime Factors of (i) 30 and (ii) 108.
Question 4
Find the lowest common multiple of 3, 5 and 10.
Question 5
True or false (tick the box):
a
b
c
d
e
f
Statement
1 is the smallest prime number
The letter N is used to denote the set of “Natural Numbers”
11 is a factor of 34
98 is a multiple of 7
Any multiple of 6 is also a multiple of 3
The LCM of 6 and 8 is 48
T
F
Question 6
HINT: Remember BIRDMAS!
Express each of the following as a single integer:
a) 3 × 4
b) 3 + 5
c)
d) 7 × 8 − 3 − (72 ÷ 8)
e) (14 − 3) ÷ 2
f) (16 + 4) ÷ 5 + 14 × 2
g) −7 + 2
h) −3 × −7
i) 6 − (−5)
j)
2
2
100
52
−7×8
−10+6
3
Question 7
True or false (tick the box):
a
b
c
d
e
f
Statement
A negative number plus a positive number is always positive
The letter I is used to denote the set of “Integers”
3 squared equals 6
A minus multiplied by a minus is a minus
Squaring a negative number gives a negative number
The square root of a number is always a Natural Number
Question 8
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F
Question 9
Question 10
Question 11
Question 12
Question 13
Multiply out and simplify the following expressions
a) 2(𝑥 + 4)
b) 3(2𝑥 − 5)
c) 4𝑥(2𝑥 − 𝑦)
d) 5𝑥(2𝑥 + 6)
Question 14
Solve the following equations for 𝑥
a) 3𝑥 − 5 = 16
b) 3𝑥 + 7 = 32 − 2𝑥
c) 4(2𝑥 − 3) = 2(3𝑥 − 5)
d) 2(𝑥 + 2) − 3(𝑥 − 3) = 𝑥 + 7
Question 15
Question 16
U is the universal set of Natural Numbers between 1 and 20 inclusive.
Let A = the set of numbers that are multiples of 3.
Let B = the set of numbers that are multiples of 4.
Fill in the information on the above diagram and answer the following questions:
a)
b)
c)
d)
What is #A?
List the elements of: A∩ B
List the elements of: (A∪ B)’
What is #A∪ B?