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IKMC 2018 - Grades 7-8 - Set 2 - Self-study

Question 1

The rectangle ABCD with perimeter 4 m is divided into 4 parts by 4 horizontal and 5 vertical segments. If the sum of the lengths of the vertical segments is equal to 44 cm, find the sum of the lengths of the horizontal ones.

Question illustration
  1. 88 cm
  2. 102 cm
  3. 124 cm
  4. 156 cm
  5. 180 cm

Question 2

When the letters of the word MAMA are written vertically above one another, the word has a vertical line of symmetry, as shown. Which of these words also has a vertical line of symmetry when written in the same way?

Question illustration
  1. ROOT
  2. BOOM
  3. BOOT
  4. LOOT
  5. TOOT

Question 3

Koko the kangaroo is preparing for the Olympics. In the first training series, he jumped 225 jumps in a row. Because he was tired, he jumped 196 in the second and 169 in the third series. In the fourth he jumped 144, in the fifth 121, and in the sixth 100 jumps. How many times in a row did Koko jump in the last, eighth series?
  1. 81
  2. 79
  3. 64
  4. 58
  5. 49

Question 4

A tank of water was $1/2$ full. Then 200 litres were used for watering the flowers. Now the tank is $1/3$ full. What is the full capacity of the tank?
  1. 1000 litres
  2. 1200 litres
  3. 1400 litres
  4. 1600 litres
  5. 1800 litres

Question 5

The panels of Fergus’ 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 approached his fence?

Question illustration
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 6

Two figures, a right-angled triangle and a square, are shown below. Which of the following statements is true?

Question illustration
  1. Area of the triangle is 6 cm² more than the area of the square.
  2. Perimeter of the triangle is 12 cm less than the perimeter of the square.
  3. Area of the triangle is 10 cm² less than the perimeter of the square.
  4. Perimeter of the triangle is equal to the area of the square.
  5. Area of the triangle is equal to the perimeter of the square.

Question 7

Kate said: “Exactly a month ago was the same day of the week as two days ago.” What is a month when this could happen?
  1. January
  2. February
  3. March
  4. April
  5. May

Question 8

A large rectangle is made up of nine identical rectangles whose longest sides are 10 cm long. What is the perimeter of the large rectangle?

Question illustration
  1. 40 cm
  2. 48 cm
  3. 76 cm
  4. 81 cm
  5. 90 cm

Question 9

Inside a rectangle of dimensions $a\times b$, with $a<b$, there are two circles, each touching three sides of the rectangle as shown. What is the distance between the centres of the circles?

Question illustration
  1. $(b-a)\pi$
  2. $\frac14(a+b)$
  3. $\frac18(b^2-a^2)$
  4. $b-a$
  5. None of the previous

Question 10

Square ABCD has sides of length 3 cm. 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?

Question illustration
  1. 0.5 cm
  2. 1 cm
  3. 1.5 cm
  4. 2 cm
  5. 2.5 cm

Question 11

Martha multiplied two 2-digit numbers correctly on a piece of paper. Then she scribbled out three digits as shown. What is the sum of the three digits she scribbled out?

Question illustration
  1. 5
  2. 6
  3. 9
  4. 12
  5. 14

Question 12

A rectangle is divided into 40 identical squares. The rectangle contains more than one row of squares. Andrew found the middle row of squares and coloured it. How many squares did he not colour?
  1. 20
  2. 30
  3. 32
  4. 35
  5. 39

Question 13

Philip wants to know the weight of a book within an error margin of half a gram. His weighing scale can only weigh within an error margin of 10 grams. What is the smallest number of identical copies of this book that Philip should weigh together to be able to do what he wants?
  1. 5
  2. 10
  3. 15
  4. 20
  5. 50

Question 14

A lion is hidden in one of three rooms. A note on room 1 reads “The lion is here”. Room 2 reads “The lion is not here”. Room 3 reads “2 + 3 = 2 × 3”. Only one of these sentences is true. In which room is the lion hidden?
  1. In room 1.
  2. In room 2.
  3. In room 3.
  4. It may be in any room.
  5. It may be in either room 1 or room 2.

Question 15

Valeria draws a zig-zag line inside a rectangle, creating angles of 10°, 14°, 33° and 26° as shown. What is the size of angle θ?

Question illustration
  1. 11°
  2. 12°
  3. 16°
  4. 17°
  5. 33°

Question 16

Alice wants to write down a list of prime numbers less than 100, using each of the digits 1,2,3,4 and 5 exactly once and no other digits. Which prime number must be in her list?
  1. 2
  2. 5
  3. 31
  4. 41
  5. 53

Question 17

A hotel on an island in the Caribbean advertises “350 days of sun every year!” According to the advert, what is the smallest number of days Willi Burn has to stay at the hotel in 2018 to be certain of having two consecutive days of sun?
  1. 17
  2. 21
  3. 31
  4. 32
  5. 35

Question 18

The diagram shows a rectangle and a line X parallel to its base. Two points A and B lie on X inside the rectangle. The sum of the areas of the two shaded triangles is 10 cm². What is the area of the rectangle?

Question illustration
  1. 18 cm²
  2. 20 cm²
  3. 22 cm²
  4. 24 cm²
  5. It depends on the positions of A and B.

Question 19

James wrote a different integer from 1 to 9 in each cell of a 3×3 table. He calculated the sum of the integers in each row and each column. Five of his answers are 12,13,15,16 and 17, in some order. What is his sixth answer?

Question illustration
  1. 17
  2. 16
  3. 15
  4. 14
  5. 13

Question 20

Eleven points are marked from left to right on a straight line. The sum of all distances between the first point and the other points is 2018. The sum of all distances between the second point and the other points, including the first, is 2000. What is the distance between the first and second points?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5