Transcript Standard Grade - Bell Baxter High School

Paper 1 Questions
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Paper 1 Questions
Credit Level
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Two yachts leave from harbour H.
N
Bearing 072°
Yacht A sails on a bearing of 072°
for 30 kilometres and stops.
72°
Yacht B sails on a bearing of 140°
for 50 kilometres and stops.
68°
How far apart are the two
yachts when
they have both stopped?
Do not use a scale drawing.
h
Bearing
140°
140°
SAS
Cosine Rule
h = a +b -2× abcos(h)°
2
2
2
h = 30 +50 -2×30×50cos68° = 47.7km
2
2
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A mug is in the shape of a cylinder with
diameter 10 cms and height 14 cms.
a) Calculate the volume of the mug.
b) 600 mls of coffee are poured in.
Calculate the depth of the coffee in the cup.
Volume   r 2 h
Volume    52 14
 1100 mls
Let height be h cms
600    5  h
2
600
h
  52
h  7.64 cms
Paper 1 Questions
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The number of diagonals, d, in a polygon
with n sides is given by the formula:
n(n -3)
d=
2
A polygon has 20 diagonals. How many sides does it have?
What are we trying to find ?
n
n(n -3)
20 =
2
40 =n(n -3)
n2 -3n - 40 = 0
n -8n +5 = 0
Polygon has 8 sides
40 =n2 -3n
n = 8 or n = -5
Paper 1 Questions
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In the diagram
Angle STV = 34°
Angle VSW = 25°
Angle SVT = Angle SWV = 90°
ST = 13.1 centimetres
Calculate the length of SW
SV
sin34° =
13.1
SV =13.1 × sin34° = 7.33 cm
SW
cos25° =
SV
SW = 7.33×cos25° = 6.64 cm
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The area of triangle ABC
is 38 square centimeters.
AB is 9 centimetres and
BC is 14 centimetres.
Calculate the size of the acute angle ABC
SAS
Use Area = ½ a b sin C
need to transpose letters !!!
1
38 = 63sinB
38 = × 9 ×14 × sinB
2
sinB =
38
63
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Find points where curve cuts the axes
and co-ordinates of minimum turning point.
x2 +2x -8 = 0
y =0
 x-2x + 4 = 0
x -2 = 0  x =2
x + 4 = 0  x = -4
Axis of symmetry is between the roots
-1
-4
y = x2 +2x -8
2
(-1, -9)
x = -1
when x = -1
y =(-1)2 +2(-1) -8  y = -9
min t.p. = (-1, -9)
when x = 0
y = 02 +2(0)-8  y = -8
y-intercept = (0, -8)
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The diagram shows part of the graph of a
quadratic function, with equation of the form
y =k(x - a)(x -b)
1
The graph cuts the y-axis at (0, -6) and
the x-axis at (-1, 0) and (3, 0)
a) Write down the values of a and b.
b) Calculate the value of k.
c) Find the coordinates of the minimum
turning point of the function
a = -1 and b = 3
1,  8
y =k  x +1 x-3
Choose a point on the curve (0, -6) -6 =k  0 +1 0-3
y =2 x +1 x-3
y =21+11-3
y = -8
-6 = -3k
1, -8
k =2
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Two perfume bottles are mathematically similar in shape.
The smaller one is 6 centimetres high
and holds 30 millilitres of perfume.
The larger one is 9 centimetres high.
What volume of perfume will the larger one hold.
Find the linear scale factor
9
3

6
2
Since we are finding volume – scale factor is cubed
3 3 3
30 ×27
30 × × × =
= 101.25
2 2 2
8
Volume = 101.25 mls
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A sheep shelter is part of a cylinder as shown
figure 1. It is 6 metres wide and 2 metres high.
The cross-section of the shelter is a segment of
a circle with centre O, as shown in Figure 2.
OB is the radius of the circle.
Calculate the length of OB.
Pythagoras
M
r- 2
O
r2 = 32 +  r -2 
2
3
B
r
r2 =32 +r2 - 4r + 4
r
r
4r =13
r =3.25 metres
Paper 1 Questions
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a) A driver travels from A to B, a distance of x miles at a constant
speed of 75 kilometres per hour. Find the time taken for the
journey in terms of x.
x
b) The time for the journey from B to A is 50 hours. Calculate the
driver’s average speed for the whole journey.
D
S
D
S=
T
T
D
T=
S
x
T=
75
hours
x
5x
x
x
3x
2x
=
=
=
+
Distance = 2 x Total time = +
50 75 150 150
30
150
x
30
2
x
÷
= 60 mph
= 2x 
Speed = Distance  Time Speed
30
x
=
Paper 1 Questions
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Fiona checks out the price of a litre of milk in several shops.
The prices in pence are:
49
44
41
52
47
43
x
(x - x)
a) Find the mean price of a litre of milk.
b) Find the standard deviation of the prices.
c) Fiona also checks out the price of
a kilogram of sugar in the same shops
and finds that the standard deviation
of the prices is 2.6.
Make one valid comparison between
the two sets of prices.
276
 x - x 
2
s=
n -1
Mean = 6
84
= 4.1
5
= 46
x - x 
2
49
3
9
44
-2
4
41
-5
25
52
6
36
47
1
1
43
-3
9
276
84
Price of milk varies more than price of sugar
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A microwave oven is sold for £150.
This price includes VAT at 17.5%
Calculate the price of the microwave oven without VAT.
Price without VAT  1.175 = £ 150
150
Price without VAT =
1.175
= £ 127.66
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Solve the equation
2
2x -3x -7 = 0
Give your answers correct to 1 decimal place.
Use the quadratic formula
a = 2, b = -3, c = -7
x=
3 ± 65
4
x=
-b ± b2 - 4ac
x=
2a
-(-3) ± (-3)2 - 4(2)(-7)
x=
2(2)
3+ 65
3- 65
or x =
4
4
x =2.8 or x = -1.3