IMAS 2013 Junior Division First Round

What is the value of the expression $|-2013|+2^0+1^3$?

Which of the following real numbers has the greatest absolute value?

Which of the following five numbers is divisible by 6?

In the diagram, $AD$ is parallel to $BC$. A point $P$ moves from $C$ to $D$ along the side $CD$. Which of the following is the accurate description of the change in the area of triangle $ABP$ during the motion?

If $x$ is a real number, which of the following is an accurate description of the expression $|x|-x$?

In a promotional sale, a store reduces the price of all merchandise by 40%. If payment is made on a membership card, there is a further reduction of 10%. What is the combined reduction in using a membership card?

The length of each side of a triangle is a different odd positive integer. What is the minimum perimeter of this triangle?

The coordinates of a point in the plane are $(w,1-w)$, where $w$ is a real number. Which of the following is an accurate description of the position of this point?

Mickey accidentally drops a triangular sheet of glass into four pieces as shown in the diagram. He wishes to take only one of the pieces to a repair shop so that they can reproduce the triangular sheet of glass. How many different choices for this piece does he have?

In the diagram, $ABCD$ is a square. The common part of $ABCD$ and triangle $EFG$ is shaded. Its area is $\frac45$ of that of $EFG$ and $\frac12$ of that of $ABCD$. If the area of triangle $EFG$ is $40\text{ cm}^2$, what is the length of a side of $ABCD$, in cm?

What is the value of the expression $\frac{3^{2013}-3^{2011}}{3^{2013}+3^{2012}}$?

Linda cuts out a shape as shown in the diagram. $AB$ is parallel to $CD$ and the measure of angle $AFE$ is $40^\circ$. What, in degrees, is the total measure of angles $BAF$, $FED$ and $EDC$?

May and Cherry bought the same kind of coloured pens from a stationery store. Such a pen costs more than 10 dollars. May’s total bill comes to 182 dollars while Cherry’s total bill comes to 221 dollars. What is the total number of pens the two of them have bought?

The diagram shows the result of folding a piece of triangular paper so that the vertex $C$ becomes the point $C^{\prime}$ on the side $AB$. If $AB=AC$ and $C^{\prime}A=C^{\prime}D$, what is the measure, in degrees, of angle $A$?

Mickey is asked to multiply four positive integers, but he adds them instead. Amazingly, his correct answer is equal to the correct answer for the multiplication problem. What is the sum of these four numbers?

Mickey starts working on his report at 7:30 am. By 10:10, he has finished $\frac23$ of it. He takes a one-hour break and then continues to work at the same rate. When will he finish the report?

$P$ is a point inside a triangle which has side lengths of 7 cm, 24 cm and 25 cm. If $P$ is at the same distance from all three sides of the triangle, what is this distance, in cm?

The diagram shows how each of the digits 0 to 9 can be made from matchsticks. In this representation, the number 609 reads the same way upside down as right side up. How many such numbers are there with three digits, the first of which is not 0?

The alien clock divides an earth day into 10 of their hours, each of which is divided into 100 of their minutes. If they plan to attack earth at 6:36 am our time, what is the time indicated on their clock?

Fanny, Lily and Sherry all shop at regular intervals, Fanny once every 3 days, Lily once every 4 days and Sherry once every 5 days. Yesterday, all three shopped. On how many of the next 100 days, starting from today (today is the first day), will at least two of them be shopping?