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Mathematical Test Dec 2011
Name................................
The solutions are on the next page.
1) Find the total cost of the following:
Cost of item
Number of items
Tin of beans 65c
1tin
Tin of Carrots 80c
2 tins
Sausages @ €8 per kg
¼ kg
2) Find the value of 4x + 3 when
x = 1,
x = 2,
x= 10
3) A gable wall with no windows is the shape of a square with a triangle on the
top. The square side is 5m, and the perpendicular height of the triangle is 2m.
a) What is the area of the gable wall?
b) If a tin of paint covers 10 m2 and costs €7 how much does it cost for paint for
the gable wall?
Hint:
Area of square = (length of side) * (length of side)
Area of triangle = ½ * base * perpendicular height.
4) A shop buys a table for €120 without VAT.
a) the shop adds 21% VAT what does it cost now?
b) after January the shop will add 23% VAT what will it cost then?
5) A triangle has sides of length 12, 5 and 13.
a) Verify that it’s a right angle triangle. Which side is the hypotenuse?
(Hint: Pythagoras’ Theorem a2 = b2 + c2)
b) Calculate its area.
( Hint: Area of Triangle = ½ * base * perpendicular height)
6) The probability of an event = (number of ways event can happen)/(number of
possible events) e.g. getting a head when tossing a fair coin is= 1/2 = 0.5.
a) what’s the probability of getting a 3 when tossing a die (dice).
b) What’s the probability of getting a club or a 5 when picking a card from a
full pack?
1) Find the total cost of the following:
Cost of item
Number of items
Tin of beans 65c
1tin
Tin of Carrots 80c
2 tins
Sausages @ €8 per kg
¼ kg
1*65 =
65c
2&80 = €1.60
¼ * 8 = 8/2 = €2.00
Multiplying by ¼ is the same as dividing by 4.
2) Find the value of 4x + 3 when
x = 1, 4*1 + 3 = 7
x = 2, 4*2 + 3 = 11
x= 10, 4*10 + 3 = 43
3) A gable wall with no windows is the shape of a square with a triangle on the
top. The square side is 5m, and the perpendicular height of the triangle is 2m.
a) What is the area of the gable wall?
The square part is 5 * 5
= 25m2
The triangular part is ½ * 2 * 5 = 5m2
Total is 30m2
b) If a tin of paint covers 10 m2 and costs €7 how much does it cost for paint for
the gable wall?
30 / 10 = 3 so we need 3 tins of paint, costing 3*7 = €21.
Note that if your question had an area of 45m2 then you need 5 tins of paint, not
four and a half.
Hint:
Area of square = (length of side) * (length of side)
Area of triangle = ½ * base * perpendicular height.
4) A shop buys a table for €120 without VAT.
a) the shop adds 21% VAT what does it cost now?
1% = €1.20
(move the decimal point two places to the left, which makes the number
smaller)
21% = 1.20 * 21 = 25.20
Price including 21% VAT = 120 + 25.20 = €145.20
b) after January the shop will add 23% VAT what will it cost then?
1% = 1.20
23% = 1.2 * 23 = €27.60
Price Including 23% VAT = 120 + 27.60 = €147.60
5) A triangle has sides of length 12, 5 and 13.
a) Verify that it’s a right angle triangle. Which side is the hypotenuse?
The hypotenuse is always the longest side of the right angled triangle.
12,5,13 is a right angled triangle if (and only if)
132 = 122 + 52
To check this we calculate these three numbers
169 = 144 + 25 which is true, therefore 12,5,13 was a right angled triangle.
(Hint: Pythagoras’ Theorem a2 = b2 + c2)
b) Calculate its area.
Since 13 is the hypotenuse the other two are perpendicular
Hence area = ½ * 12 * 5 = 30
( Hint: Area of Triangle = ½ * base * perpendicular height)
6) The probability of an event = (number of ways event can happen)/(number of
possible events) e.g. getting a head when tossing a fair coin is= 1/2 = 0.5.
a) what’s the probability of getting a 3 when tossing a die (dice).
There is only one way to get a 3, there are six possible results so the probability
of getting a 3 is 1/6 = 0.166666666........
b) What’s the probability of getting a club or a 5 when picking a card from a
full pack?
The first thing is to count how many cards qualify as either a club or a 5.
There are Thirteen clubs, there are four 5s. However there is only one 5 of
Clubs which is in both sets. So there are 13+4-1 = 16
There are a total of fifty two cards.
The probability of getting a club or a 5 is 16/52 = 4/13 = 0.30769