Mahajana Mathematics Competition Sample Grade 11 & 12 _____________________________________________________________________

Mahajana Mathematics Competition Sample Grade 11 & 12 _____________________________________________________________________

Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
Part A (10 Questions, Each Question Is Worth 2 Marks)
1.
2. In the diagram below, the five smaller rectangles are identical in
size and shape. The ratio of DC: AD is
(A) 3:2
(B) 3:5
(C) 5:3
(D) 2:3
3. In 2011 Mahajanan Contest Grade 9+10, 30 students wrote a test.
If 20 students scored 80, 8 students scored 90, and 2 students scored
100, then the average on this Grade 9+10 test was
(A) 90
(B) 84
(C) 82
(D) 86
4. If the expression 256 x 286 x 557 was evaluated, it would end with a
string of consecutive zeros. The numbers of consecutive zeros in this
string when evaluated are:
(A) 10
(B) 12
(C) 8
(D) 14
5. In the diagram, OP = 3, PQ = 4 and OQ = 5. The slope of OP is?
(A) 3/4
(B) 4/3
(C) 5/3
(D) 3/5
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
6.
If a + b = 12, b + c = 15 and c + d = 19. Then the value of a + d
is?
(A)
17
(B)
16
(C)
18
(D)
14
7. A square floor is tiled, as partially shown, with a large number of
regular hexagonal tiles. The tiles are coloured blue or white. Each blue
tile is surrounded by 6 white tiles and each white tile is surrounded by
3 white and 3 blue tiles. Ignoring part tiles, the ratio of the number of
blue tiles to the number of white tiles is closest to
(A) 1:6
(B) 2:3
(C) 1:2
(D) 1:4
8. The equation of a circle is x2 + y2 = 16. The length of the longest
possible cord passing through the points (1, -2) is?
(A)
2√7
(B)
2π
(C)
8
(D)
16
9. The graph y = 10 (x + 1) (x - 3) intersects the x-axis at two points A
and B. The length of AB is?
(A)
2
(B)
6
(C)
4
(D)
8
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
10. A rectangular wooden prism is made up of
three pieces, each consisting of four cubes of
wood glued together.
Which of the pieces below has the same shape as
the black piece?
Part B (10 Questions, Each Question Is Worth 4 Marks)
11. A cube measures 20 cm ×20 cm ×20 cm. Three cuts are made
parallel to the faces of the cube as shown creating eight separate
solids which are then separated. What is the increase in the total
surface area?
(A) 300 cm2
(B) 2400 cm2
(C) 1200 cm2
(D) 600 cm2
12. The median of a set of five positive integers is the middle integer
when the set is arranged in increasing order. A set of 5 positive
integers has all of the following properties:
• its median is 9,
• its average (mean) is 10 and
• the only integer in the list that occurs more than once is 8
The largest possible integer the above set could appear in the list
(A) 15
(B) 16
(C) 17
(D) 24
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
13. A regular pentagon is placed in the line PQ as shown and
then reflected on line PQ and rotated clockwise 216°
about the centre of the pentagon,
Its new position is
14. When x2 – kx2- 10kx + 25 is divided by (x - 2), the remainder is 5.
The value of k is?
(A) 25
(B) 1
(C)
(D)
15. In the square ABCD, two pairs of identical
isosceles triangles are cut off, leaving
rectangle PQRS. The total area cut off
is 400 m2. The length of PR, in metres, is
A) 40√2
B) 20
C) 20√3
D) 40√3
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
16. If W= 2129 x381 x 5131,
Z=2125 x 382 x 5132
X=2127 x381x5131,
Y=2126x382 x5131,
Then the order from the smallest to largest is
(A) w, x, y, z
(B) x, w, y, z
(C) x, y, z, w
(D) z, y, x, w
17. In the diagram below, all triangles are equilateral. If AB = 32, then
the total area of all the white triangles is
(A) 37√ 3
(B) 108√ 3
(C) 148√ 3
(D) 74/3
18. In the triangular pattern of numbers shown on
the right side, every row begins with a 1 and ends
with a 2. Each of the numbers, not on the end of a
row, is the sum of the two numbers located
immediately above and to the right, and immediately
above and to the left. For example, in the fourth
row the 9 is the sum of the 4 and the 5 in the third
row.
If this pattern continues, the sum of all of the numbers in the 14th row
is
A) 12,288
B) 24,576
C)
12 294
D) 18,984
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
19. Two 3-digit numbers, p, q, r and x, y, z, have the following
property:
None of the value of p, q, r, x, y and z is zero. The sum of p+q+r+x+y+z
is
(A) 10
(B) 19
(C) 21
(D) 28
20. In the figure below, the four circles have a common centre, and
have radii of 1 cm, 2 cm, 3 cm, and 4 cm.
The ratio of the area of the shaded regions to the area of the largest
circle with radius 4 cm is
A) 5: 8
(B) 3: 8
(C) 7: 16
(D) 1: 2
Part C (5 Questions, Each Question Is Worth 6 Marks)
21. In the diagram, the tangents to the two circles intersect at 90° as
shown. If the radius of the smaller circle is 2, and the radius of the
larger circle is 5, what is the distance between the centers of the two
circles?
(A) 5
(B) 72
(C) 7√2
(D) 7
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
22. Sunday morning Banu and Shirley have to move 10 large bags
and 16 small bags. Look at the chart below which indicates the time
that each person takes to move each type of box.
BANU
6min
SHIRLY
5min
LARGE BAG
2min
3min
SMALL BAG
Banu and Shirley start moving the boxes at 10:00 a.m. The earliest
time at which they can be finished moving all of the boxes is
(A) 10:41 AM.
(B) 10:42 AM.
(C) 10:43 AM.
(D) 10:44 AM.
23. There are five circles in the diagram below and they are tangent at
points B, C, D and E. An ant wants to move from point A to point F
entirely on the circumferences of the circles so that no portion of any
circumference is covered more than once. The number of possible
paths is
(A) 2
(B) 8
(C) 16
(D) 32
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
24. A square spiral of numbers is created, as shown, starting with the
number 1. If the pattern of the square spiral continues, in what
configuration will the numbers 483, 484 and 485 appear?
(A) 483 484 485
(B) 483 400399
(C)
(D)
25. In the diagram, each of the three identical circles touches the
other two. The circumference of each circle is 72. What is the
perimeter of the shaded region?
(A) 18
(B) 6
(C) 36
(D) 12
Mahajana Mathematics Competition Sample
Grade 11 & 12
_____________________________________________________________________
BONUS QUESTION: (10 Marks )
A pattern of regular pentagon family with a fixed top vertex T is shown
below in Figure 1, Figure 2 and Figure 3.
Figure 1 is a regular pentagon with side length 1 cm.
Figure 2 is a regular pentagon of side length 2cm drawn around
Figure 1 sothat the two shapes share the fixed top vertex, T, and the
sides on either side of T overlap.
Figure 3 is a regular pentagon of side length 3cm drawn around
Figure 2 so that the two shapes share the fixed top vertex, T, and the
sides on either side of T overlap.
The tracing length along the sides of Figure 1 is 5cm.The tracing
length along the sides of Figure 2 is 13cm. The tracing length along
the sides of Figure 3 is 24cm.The pattern continues so that for each n
> 1, Figure n is a regular pentagon of side length n cm drawn around
the previous Figure so that the two shapes share the fixed top vertex,
T, and the sides on either side of T overlap. The tracing length of each
Figure is the sum of the lengths of all of the line segments in the
respective Figure.
a) Determine the tracing length of Figure 4.
b) Determine the tracing length of Figure 100
Good Luck!