Willow Park School
1st Year Christmas Exam
2012
300 Marks in Total
Answer all questions
Part A = 10 marks
Part B = 20 marks
Part c = 20 marks
Q1.
A) S = {w, x, y, z}
I) Write down a proper subset of S.
II) Write down an improper subset of S.
B)
U is the universal set. U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
P = {2, 3, 4, 7, 6, 9}
Q = {1, 3, 5, 6}
I)
Represent the following set using a Venn diagram.
II)
Find P
III)
IV)
Find (P u Q)
Find (P n Q)
V)
Find (P u Q)’
’
C)
U is the universal set.
U = {x ǀ x is a natural number between 1 and 30 inclusive}
A = {x ǀ x is a multiple of 2 between 1 and 30 inclusive}
B = {x ǀ x is a multiple of 3 between 1 and 30 inclusive}
I)
Find the #(A u B)
II)
Find the #(A u B)’
III)
How many divisors does each of the numbers in (A u B)’ have.
IV)
What name is given to numbers that have this many divisors?
Q2
A)
(I)
(III)
7 x (12 − 8)
2 x √25 + 4
(II)
2
5 x 4 + 3 x (10 − 4)
22 x √100
(IV)
4 x (6−1)
B)
(I)
Divide the LCM of 6, 9 and 12 by their HCF
(II)
Multiply the LCM of 8, 16 and 24 by their HCF
(III)
The bell at Church A rings every 6 minutes. At church B, the bell rings every 9
minutes. Both bells ring together at 9 a.m. What is the next time both bells ring
together?
(IV)
There is a piece of rope 48m long. It must be cut into 3 different sizes. The first
size is 6m. What are the other two sizes?
C)
(i)
(ii)
A cinema has 13 rows of seats. The rows are numbered from 1 to 13.
Odd-numbered rows have 18 seats.
Even-numbered rows have 20 seats.
How many seats are in the cinema?
A large box of chocolates and a small box of chocolates cost €18.
If the large box costs €4 more than the small box, then what is the price of the
small box of chocolates.
Q3
A)
(I)
Describe what an integer is and give an example of when you would use
integers in your daily lives.
Find the value of each of the following
(II)
-14 -5 -23 -87
(III)
2 x (10 -2)
(IV)
(16 – 4)2 + 3 x 2
(V)
48 ÷ 6 ÷ √4
B)
(I)
The number in the square is the product of two integers on either side of it.
Complete the triangles below.
-12
-24
18
(II)
Complete the multiplication grid below
x
1
-3
-2
12
6
-18
-5
-8
64
(c)
(III)
Evaluate the following sums
(I)
74 x − 4 − (−11) x − 12 ÷ 22 ÷ −3
(II)
−213 ÷ −(−114) x 9 ÷ −27
(i) There are 10 questions on a multiple choice test. A correct mark is worth 5 marks.
An incorrect answer incurs a penalty of − 2 marks, and an unanswered question is worth 1
mark.
Johnny, Hugh and Aoife take the test.
(a) Johnny answers five questions correctly, leaves two unanswered and gets the
rest wrong. How many marks did he get on the test?
(b) Hugh answers six questions correctly and answers one incorrectly. He leaves the
rest unanswered. How many marks does he get in the test?
(c) Aoife answers 4 questions incorrectly and leaves one unanswered. She gets the
rest correct. How many marks does she get on the test?
(ii) Emily is climbing Mt Blanc. For every 100m she climbs, the temperature goes
down by 4 degrees. She started from base camp and the temperature was
degrees.
−3
(a) She climbs 900m and takes a break, what is the temperature now?
(b) She climbs 700m back down the mountain , what is the temperature now?
Q4
A)
(I)
Express each of the following mixed fractions as improper fractions
33 469 13 126 17
,
, ,
,
19 8 4 24 9
(II)
Write each of the following fractions in order starting with the smallest.
5 9 3 5 7
, , , ,
12 16 4 6 24
B)
Evaluate the following sums.
1
1
4
3
6
2
7
3
1
1
4
3
(I)
( +
)÷(1 −1 )
(II)
( ×
(I)
Mrs McFee has 10 meters of material. She cuts 6 pieces, each 1 ¼ meters
long. How much material does she have left?
(II)
Mr Smith gives some money to his four children. Paul receives 1/3 of the
money, Gail receives ¼ and Mike receives 3/8 of it. Sarah receives €90.
How much money did Mr Smith give to his children in total?
(I)
Anne receives €5 in pocket money each week. She saves 4 of this and spends
÷
9
14
) ÷[1
1
3
1
3
2
4
×(4 −1 )]
C)
1
the rest. How many weeks does it take Anne to save €15 exactly?
Q5
(a)
(i)
(ii)
Write each of the following as a decimal:
(a) 6/10 (b) 3/10 (c) 6/100 (d) 27/1000 (e) 7/8
Express each of the following decimals as a fraction in its lowest terms:
(a) 0.75 (b) 0.4 (c) 2.6 (d) 0.825 (e) 0.375
(b) (i)
Insert a decimal point into each of the following numbers:
(a)
(b)
(c)
(d)
(e)
(ii)
274 so that the 7 represents seventy
328 so that the 4 represents two units
7956 so that 6 represents six hundredths
6749 so that the 9 represents nine thousandths
78 so that the 8 represents eight thousandths
In each of the following questions round off each number to its nearest whole
number and give an approximate answer:
(a)
(b)
2.8 x 5.7 + 2.04
3.95 x 8.42 + 2.948
1.8 x 4.3 − 1.2
(iii)
(c) (i)
Correct 3.67765 to two significant figures:
Simplify the following and give your answer correct to two decimal places
1.48 x 6.34
11.25
(ii)
On his birthday, Daniel is given a big jar of small sweets. He wants to find
how many sweets are in the jar but it would take too long to count them.
A label on the jar tells him that the total mass of the sweets is 600g.
He weighs 5 sweets and their mass is 3.75g.
Mass of Jar = 600g
How many sweets are in the jar?
Q6
A)
(I)
A boy has 60 marbles some of which are red, some are blue. If there are 15
red marbles what is the ratio of red to blue marbles.
(II)
Divide 144 in the ratio of 7:2
B)
(I) A man plans to travel 1273km. Petrol costs €1.60. His car travels 19km on 1 litre
of petrol. How much will he spend on petrol for is trip?
(II) The recipe to the left makes 20 scones.


How much dried fruit is needed to make 50 scones?
How much butter is needed to make 12 scones?
500g
250g
100g
50ml
Flour
Butter
Dried Fruit
Water
C)
(I)
A boy is 18 years old and his father is 54. Calculate the ratio of the boy’s age
to his fathers.
(a) Now
(b) When they were both 6 years younger
(c) When they are both 6 years older
(II) A machine prints 720 labels in two minutes.
How many labels will it print in 40 seconds?