Transcript C(-2,3) - Shambles

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each problem.
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Trial Question 1
Find the area of the region
formed by the solution of this
system of inequalities.
x + 3y > 2
x+y<4
x - 3y > - 4
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Trial Question 2
Given the following data:
16, 14, 30, 14, 18, 19, 24, 13, 14
Find
Mean  Median  Mode
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1. What is the Highest
Common Factor of:
215280, 290472 & 6683040 ?
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2. The two circles
are identical, and
have radius x.
The quadrilaterals
are squares.
What is the sum of
the purple shaded
areas in terms of x ?
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3. A thick cylindrical pipe fits
exactly in a box. The radius of the
hole in the pipe is 2cm. The width
and height of the box are both
8cm.The box is 5 times as long as it
is wide.
Find in terms of  the volume of
water that could be contained in the
box (inside and outside the pipe).
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4. Three rollers,
each of radius 1,
are mounted from
their centres to
the vertices of a
triangular frame
with sides 4, 6 & 7.
7
4
6
A belt fits tightly around the rollers.
Find the length of the belt.
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5. A box 9cm by 5cm by 4cm
is covered by 6 plastic sheets,
each covering completely one
face.
What are the dimensions of the
smallest rectangle from which all
6 sheets can be cut?
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6. The digits 1, 1, 2, 2, 3 and 3 can
be arranged as a six digit number
in which the 1’s are separated by
one digit, the 2’s are separated by
two digits, and the 3’s are
separated by 3 digits.
Find the sum of all such six-digit
numbers.
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7. Consider the graphs of the
two equations:
a) xy = 12
b) y = 2x - 10
Which graph comes closer to
the origin, and what is its
distance from the origin?
Give the distance in the form
pq, where p and q are integers.
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8. There are four pairs of
positive integers (x,y), such that
2
x
-
2
y
= 105
Find them.
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9. Given that the coordinates of
the triangle ABC are
A(3,1)
B(1,1)
C(-2,3),
find the coordinates of the
triangle A’B’C’ which is the
image of ABC after rotating it
about (0,0) through an angle of
90º anti-clockwise.
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10. The grid can be
filled up using only
the letters A, B, C, D
D and E, so that
each letter appears
just once in each
row, column and
E
diagonal. Fill up
the empty squares.
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B
D C
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11. Three fair six-sided dice A, B
and C are numbered
A: 1,1,2,2,3,3
B: 4,4,5,5,6,6
C: 7,7,8,8,9,9
The three dice are rolled once.
Find the probability of obtaining a
total which is an odd number.
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12. In a circle of
radius 1 unit, two
congruent circles
are drawn tangent
to the large circle
and passing
through its centre.
Then each smaller circle is subdivided similarly. The process goes on
indefinitely. What is the sum of the
areas of all the circles?
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13. ab = ab
a+b
.
.
and
.
ab = ab
a-b
.
ab = a+b
a-b
Find the value of
(ab)  (ab),
if a = 10 and b = -2.
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14. All the angles except one in
a convex polygon add up to
3315º.
How many sides does the
polygon have?
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A2
A3
15. How many
triangles with
vertices at the A
1
marked points
A1, A2,….,A10
A10 A9 A8 A7
can be drawn?
A4
A5
A6
Note that the order of the vertices
does not change the triangle.
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