This is the Math Kangaroo Solutions video library, presenting solution suggestions for levels 7 to 8 from the year 2018. These solutions are presented by Lucas Nelskowski. The purpose of the Math Kangaroo Solutions video library is to help you learn how to solve math problems such as those presented in the Math Kangaroo competition. It is important that you make sure to read the problem as well as listen as I read the problem. After reading or listening to the question, pause the video. Try to solve the problem on your own. Question 1. What is the value of 20 plus 18 divided by 20 minus 18? Look at the problem more closely, and we have to recognize the fact that we have parentheses, so we must do what's inside the parentheses first. We do 20 plus 18, which gives us 38, and 20 minus 18, which gives us 2. We are left with 38 divided by 2, which gives us 19. So the correct answer is B, 19. Question 2. When the letters of the word mama are written vertically above one another, the word has a vertical line of symmetry. Each of these words also has a vertical line of symmetry when written in the same way. We look at each of the words, and we write them out just like the mama was. We get roo, boom, boot, loot, and toot. If we make a vertical line of symmetry for all of them, we notice that only one of them will have symmetry on both sides, and that is 2, since if it is flipped over vertically, it will remain the same. Therefore, the correct answer is E, 2. Question 3. A triangle has sides of length 6, 10, and 11. An equilateral triangle has the same perimeter. What is the length of each side of the equilateral triangle? Draw our initial triangle with sides 6, 10, and 11, and you get something like this. To get the perimeter, we add together all three sides, like so, 6 plus 10 plus 11, and we get the answer of 27. Since the triangle has three sides, and an equilateral triangle is characterized by each equal length, then we just have to take the perimeter and divide it by 3, and 27 divided by 3 gives us an answer of 9, so the correct answer is B, 9. Question 4. Which number should replace the star in the equation 2 times 18 times 14 equals 6 times star times 7 to make it correct? First let us write out the equation once more. If we look closely, we know that we can simplify the 18 to be a 3 times a 6, and the 6 to be 2 times 3. With this, we get the equation 2 times 3 times 6 times 14 equals 2 times 3 times star times 7. We can divide both sides by 3 to eliminate the 3s. 7 we will transfer over, and also multiply the 2 by the 7. We get 2 times 6 times 14 equals 14 times star. We can divide both sides by 14 and get 2 times 6 equals star, therefore the star equals 12. The answer is D, 12. Question 5. The panels of Fergus's fence are full of holes. One morning, one of the panels fell flat on the floor. Which of the following could Fergus see as he approaches his fence? Look closely at the fence. We notice it has a series of triangles that go up and down, and a series of circles that are in the center. If we outline the distinctive features of the fence, we get something like this. And since it will fall flat on the floor, if we rotate it, we see that the triangles will be pointing down, up, down, up, and then down. The only answers that are like this are B and C. However, in B, the circles are far too high, since the circles in the initial fence are in the center. The correct answer is C. Question 6. Bertie the Builder is assembling stairs. Each step is 15 centimeters tall and 15 centimeters deep, as shown in the diagram. How many steps does he need in the stairs in order to reach the second floor, which is 3 meters above the first floor in the building? It's first recognized that 3 meters is equal to 300 centimeters. Then we divide 300 centimeters by 15 centimeters, which is the height of every stair, we get 20. Therefore, the correct answer is D, 20. Question 7. A game consists of dropping a ball from the top of the board with rows of pins, as shown in the picture. The ball bounces either to the right or to the left each time it hits a pin. The possible route for the ball to take is shown below. How many different routes can the ball take to reach bin B? We start analyzing each possible way that the balls can fall. The first way we notice it goes here, bounces, bounces, and then bounces into bin B. We follow the purple path, the yellow path, and the green path. These are all the possible ways that the ball can bounce into bin B. All other paths will result in landing in bin A, C, D, or E. Therefore, the correct answer is C, 4. Question 8. A large rectangle is made up of nine identical rectangles whose longest sides are each 10 centimeters long. What is the perimeter of the large rectangle? Look at the rectangle. We notice that one of its sides is made up of two smaller rectangles with their longer sides. Therefore, one side of the large rectangle is 20 centimeters, since it is made up of two 10-centimeter segments. Also look at this. We notice that five short sides make up for the same length, 20 centimeters. So if we do 20 divided by 5, we get a length of 4 centimeters. We know that one short length of the rectangle is 4 centimeters. With this, we can calculate the length of the larger rectangle, 10 plus 4 plus 4, 18 centimeters. To calculate the perimeter, we can add together all sides. So we do 20 plus 20 plus 18 plus 18, giving us 76. Therefore, the correct answer is C, 76 centimeters. Question 9. The diagram shows a rectangle with dimensions 11 by 7, containing two circles. Each circle touches three of the sides of the rectangle. What is the distance between the centers of the two circles? If we look more closely at the picture, and we know that three sides of the rectangle are touched by each circle, we notice that the length of the shorter side of the rectangle is equal to 7. Therefore, we know that the diameter of the circles is 7. Therefore, the radius is half of that, so 3.5. We look at the radius and turn it 90 degrees on both sides. We know that this distance is 3.5. So to find our solution, we must take the distance of the longer side of the rectangle, 11, and subtract it by two radii of the circles. So we get 11 minus 3.5 minus 3.5, giving us the answer of 4. Therefore, the correct answer is D, 4. Question 10. Square ABCD has sides with lengths equal to 3 centimeters. The points M and N lie on AD and AB so that CM and CN split the square into three pieces of the same area. What is the length of DM? Take a closer look at triangle CDM. We can notice that it has an area of 3. Since the square is a 3 by 3 square, its total area will be 9. And if it is split into three equal pieces, 9 divided by 3 gives us an area of 3. We know that one of the sides is equal to 3 centimeters. Now, if we take the formula for finding the area of a triangle, which is base times height divided by 2, is equal to the area of the triangle, we can solve our problem. We put in that the base is unknown, since that is DM. We know that the height is 3 centimeters, and we know that the area is also 3. So going by this, we can figure out that the base will be 2, since 2 times 3 divided by 2 will give us 3. Therefore, the correct answer is D, 2.

Math Kangaroo 2018

Lucas Nelskowski

mathematical solutions

geometry problems

probability paths