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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 ModeMedianMean
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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.
A belt fits tightly around the rollers. Find the length of the belt.
47
6
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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 pq, where p and q are integers.
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8. There are four pairs of positive integers (x,y), such that
x2 - y2 = 105Find 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 and E, so that each letter appears just once in each row, column and diagonal. Fill up the empty squares.
D
E D CB
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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 sub-divided similarly. The process goes on indefinitely. What is the sum of the areas of all the circles?
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13. ab = ab . ab = ab . . a+b a-b
and ab = a+b . a-b
Find the value of
(ab) (ab),
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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15. How many triangles with vertices at the marked points A1, A2,….,A10 can be drawn?Note that the order of the vertices does not change the triangle.
A1
A2 A3
A4
A10
A6
A5
A9 A8 A7
