Download S4 Test yourself at Credit 9

Mathematics
Department
Clyde Valley High School
1.
Find the equation of the straight
line shown in the diagram.
y
(6,2)
0
x
(0,-2)
2.
Write
6
in its simplest form as a surd with a rational
18
denominator.
3.
The diagram shows a set of stacked circles. The circles are all
identical and have a diameter of 2cm. Find the height of the
point P above the ground. P
●
Ground
Mathematics
Department
Clyde Valley High School
4.
Solve the equation
2x + 5 1 − x 2
=
−
3
2
5
5. The number of eagles breeding in
Scotland is estimated at 5600. The numbers
are expected to rise by 5% in each of the next
3 years. Find the number of eagles expected
to be breeding in each of the next three
years.
6.
Simplify the expression 6x(x – 2) – 6(x - 1)2.
7.
Solve the trigonometric equation 12cosx – 7 = 0,
where, 0 ≤ x ≤ 360°.
8.
Write as a single fraction
9.
Calculate the area of the
shape ABCD.
x − 2 1− x
−
.
5
6
C
D
A
4cm
8cm
10. Solve the simultaneous equations
4x – 3y = 11
y=x-2
B
Mathematics
Department
Clyde Valley High School
11. The diagram shows a washer with
an internal radius r and a width w.
a) Prove that the area of the washer is
A = πw(2r + w)
b)
w
A new washer with the same
internal radius but with double the
width is to be made.
Find the area of the new washer.
c)
Prove that the increase in the area
over the original washer is
h r
πw(2r + 3w)
12. A ship leaves Dundee and sails 60km east. It then turns and
sails 96km on a bearing of 046°. Find the distance and the
bearing of the ship from Dundee.
N
N
●Ship
Dundee
13. The diagram shows two similar urns. The volume of the
larger urn is 400cm3. Find the volume of the smaller urn.
9cm
12cm
Mathematics
Department
Clyde Valley High School
14. Solve the inequation 5(1 – x) -2x > 5
15. The annual profit (₤) of a company was 3.8 × 108 for the year
2006. What profit did the company make per minute?
Give your answer in scientific notation correct to 3
significant figures.
16. Calculate the shaded area.
12cm
17. In the triangle shown, x and y are whole
numbers and x > y.
Use the converse of Pythagoras to
Prove that the triangle is right angled.
x2 + y2
x2 - y2
2xy
18. Solve the quadratic equation 2x2 – x – 2 = 0 , giving your
answers correct to 2 decimal places.
Mathematics
Department
Clyde Valley High School
19. The diagram shows a lake.
Two towers A and B are on
opposite sides of the lake.
Lake
A●
The distances from an
observation point to
each of the towers is shown.
The angle made by the towers
143m
at the observation point is 34°.
How far apart are the towers?
●B
154m
34°
● Observation
Point
20. The triangular array shown is called Pascal’s Triangle.
Row 1
Row 2
Row 3
Row 4
Row 5
1
1
1
1
1
1
2
3
4
1
3
6
1
4
1
a) Write down the next two rows.
b) Pascal’s Triangle can be used to expand expressions
like (1 + x)n where n is a whole number.
Eg. (1+x)0 = 1
(1+x)1 = 1 + x
(1+x)2 = 1 + 2x + x2
(1+x)3 = 1 + 3x + 3x2 + x3
etc.
Use Pascal’s Triangle to expand
(i) (1+x)4
(ii) (1+x)5
(iii) (1+x)6