Question bank IMAS 2011

Exam papers

80 questions

Question 1

What is $2011+1102\times(1-3)$?

$193$
$4215$
$6226$
$-193$
$-6226$

Question 2

Which number is the largest?

$3.14$
$\pi$
$\frac{22}{7}$
$3.135$
$304\%$

The temperature on the shady side of a certain planet is $-253^\circ\mathrm{C}$. The temperature on its sunny side is only $-223^\circ\mathrm{C}$. Which of the following statement is an accurate description of the relation between the temperatures on the shady side and on the sunny side?

Question illustration

The temperature of its sunny side is $30^\circ\mathrm{C}$ higher than its shady side;
The temperature of its sunny side is $30^\circ\mathrm{C}$ lower than its shady side;
The temperature of its sunny side is $476^\circ\mathrm{C}$ higher than its shady side;
The temperature of its sunny side is $476^\circ\mathrm{C}$ lower than its shady side;
The temperature of its sunny side is the same as its shady side.

Question 4

The given diagram shows a rectangular piece of paper folded in quarters along two perpendicular folds. If a cut is made around the corner marked 1, which of the following cannot possibly be the shape of the resulting hole in the piece of paper?

Question illustration

Octagon
Quadrilateral
Hexagon
Triangle
Circle

Question 5

Around 550 BC, the Greek mathematician Pythagoras discovered and proved a theorem which now bears his name. To celebrate this achievement, he had 100 cows killed for a feast. Thus the result is also known as the One Hundred Cows Theorem. What is the anniversary of this result in 2011? (There is no Year 0.)

$2562$
$2560$
$2561$
$1460$
$1461$

Question 6

A rectangle is 6 cm by 8 cm. It is revolved about an axis on the rectangle itself. What is the number of different cylinders that may be obtained in this way?

$2$
$4$
$6$
$8$
Infinity

Question 7

There is a pattern to the given sequence of figures:

Question illustration

Which of the following will be the 2011-th figure of the sequence?

Question 8

The given diagram shows two overlapping right triangles having a common vertex $O$. If $\angle AOD=123^\circ$, what is the measure, in degrees, of $\angle BOC$?

Question illustration

$33$
$53$
$57$
$60$
$66$

Question 9

A greengrocer is having an apple sale. The price is 6 dollars per kilogram. If the total purchase exceeds 3 kilograms, a $20\%$ discount is applied to the portion over 3 kilograms. There is no discount if the total purchase does not exceed 3 kilograms. If Leith buys 8 kilograms of apples from this greengrocer, how much does he pay?

32 dollars
36 dollars
42 dollars
44 dollars
21 dollars

Question 10

The given diagram shows a pocket knife. The shaded part is a rectangle with a small semicircular indentation. The two edges of the blade are parallel, forming angles 1 and 2 with the shaft as shown. What is the measure, in degrees, of $\angle1+\angle2$?

Question illustration

$30$
$45$
$60$
$90$
could not be determined

Question 11

The given diagram shows the projected sale and actual sale of a certain toy company for the fourth quarter of the year. The achievement percentage is equal to $\frac{\text{actual sale}}{\text{projected sale}}\times100\%$. What is this achievement percentage?

Question illustration

$86\%$
$88.3\%$
$88\%$
$86.3\%$
$90.3\%$

Question 12

Leon is given five wooden blocks:

Question illustration

Which of the following blocks should be added so that he can make a $4\times4\times4$ cube? (None of the blocks can be dissected)

Question 13

The given diagram shows how a square $ABCD$ with side length 40 may be dissected into six pieces by three straight cuts $AC$, $BD$ and $EF$, where $E$ and $F$ are the respective midpoints of $AB$ and $BC$. The pieces are then rearranged to form the given shape. What is the total area, in square centimetres, of the shaded part of the given shape?

Question illustration

$200$
$400$
$600$
$800$
$1000$

Question 14

The given diagram shows the calendar for the month of November, 2011. Three numbers from the same column are chosen. Of the following number, which can be the sum of three such numbers?

Question illustration

$21$
$37$
$38$
$40$
$54$

Question 15

The given diagram shows a large cube formed of eight identical small cubes. The surface area of the large cube is 216 square centimetres less than the total surface areas of the eight small cubes. What is the length, in centimetres, of a side of a small cube?

Question illustration

Question 16

In an NBA basketball game, a player scores 44 points, 5 of which come from 5 foul shots (each shot scores 1 point). He makes more 2-point shots than 3-point shots. Of the following number, which cannot possibly be the total number of 2-point and 3-point shots made by this player?

$15$
$16$
$17$
$18$
$19$

Question 17

The given diagram shows a rectangle $ABCD$ being folded along a straight segment $AE$ with $E$ on $CD$, so that the new position of $D$ is on $AB$. Triangle $ADE$ is then folded along $DE$ so that the new position of $A$ is on the extension of $DB$. The new position of $AE$ intersects $BC$ at $F$. If $AB=10$ centimetres and $AD=6$ centimetres, what is the area, in square centimetres, of triangle $ABF$?

Question illustration

$2$
$4$
$6$
$8$
$10$

Question 18

A child is operating a remote-controlled car on a flat surface. Starting from the child’s feet, the car moves forward 1 metre, makes a $30^\circ$ turn counterclockwise, moves forward 1 metre, makes a $30^\circ$ turn counterclockwise, and so on. When the car first time returns to its starting point for the first time, what is the total distance, in metres, that it has covered?

$4$
$8$
$12$
$16$
$24$

Question 19

Each interior angle of a regular convex polygon is greater than $100^\circ$ and less than $140^\circ$. Of the following numbers, which cannot possibly be the number of sides of this polygon?

Question 20

In the given diagram, each vertex of the hexagon $PQRSTU$ is labeled with 0 or 1. Starting counterclockwise from a vertex, he multiplies the labels by 3, 7, 15, 31, 63 and 127 respectively and add the six products. If the starting point is $P$, the final sum is $1\times3+1\times7+0\times15+1\times31+0\times63+1\times127=168$. What is the starting point if the final sum is 180?

Question illustration