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IKMC 2021 - Grades 7-8 - Self-study

Question 1

Which of these Zodiac symbols has an axis of symmetry? A: Sagittarius; B: Scorpio; C: Leo; D: Cancer; E: Capricorn.
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Question 2

Three concentric circles are crossed by four lines through their common centre. What percentage of the figure is shaded?

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  1. 30%
  2. 35%
  3. 40%
  4. 45%
  5. 50%

Question 3

What is $\frac{20\cdot21}{2+0+2+1}$?
  1. 42
  2. 64
  3. 80
  4. 84
  5. 105

Question 4

How many four-digit numbers have consecutive digits in ascending order from left to right?
  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Question 5

When the five pieces are fitted together correctly, they form a rectangle with a calculation on it. What is its value?

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  1. −100
  2. −8
  3. −1
  4. 199
  5. 208

Question 6

Each vase has the same height and volume 1 litre. Half a litre of water is poured into each. In which vase is the water level highest?
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Question 7

A student correctly adds the two two-digit numbers at the left of the board and gets 137. What is the sum of the two four-digit numbers at the right?

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  1. 13737
  2. 13837
  3. 14747
  4. 23737
  5. 137137

Question 8

A 3×3×3 cube consists of white, grey and black unit cubes. The diagrams show the whole cube and its white and black parts. Which option shows the grey part?

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Question 9

A bike lock has four wheels, each numbered 0 to 9 in order. Each wheel is turned 180° from the displayed code to obtain the correct code. Which is correct?

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Question 10

Byron is 5 cm taller than Aaron and 10 cm shorter than Caron. Darren is 10 cm taller than Caron and 5 cm shorter than Erin. Which statement is true?
  1. Aaron and Erin are equally tall
  2. Aaron is 10 cm taller than Erin
  3. Aaron is 10 cm shorter than Erin
  4. Aaron is 30 cm taller than Erin
  5. Aaron is 30 cm shorter than Erin

Question 11

A rectangular chocolate bar is made of equal squares. Neil breaks off two complete strips and eats their 12 squares. Later Jack breaks off one complete strip and eats its 9 squares. How many squares remain?

Source note: the source does not specify that Neil’s strips are parallel. Use that intended reading for the listed choices.
  1. 72
  2. 63
  3. 54
  4. 45
  5. 36

Question 12

A jar one fifth full of water weighs 560 g. The same jar four fifths full weighs 740 g. What does the empty jar weigh?
  1. 60 g
  2. 112 g
  3. 180 g
  4. 300 g
  5. 500 g

Question 13

The large square has area 16 cm², and each small square has area 1 cm². What is the total area of the central flower, in cm²?

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  1. $3$
  2. $\frac72$
  3. $4$
  4. $\frac{11}2$
  5. $6$

Question 14

Costa builds a fence using 25 planks, each 30 cm long, with the same slight overlap between adjacent planks. The total fence length is 6.9 m. How many centimetres is each overlap?

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  1. 2.4
  2. 2.5
  3. 3
  4. 4.8
  5. 5

Question 15

Five identical right triangles form the shown star with their larger acute angles meeting at the centre. Another star is formed with their smaller acute angles meeting. How many triangles are needed?

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  1. 10
  2. 12
  3. 18
  4. 20
  5. 24

Question 16

Five squares are positioned as shown. The indicated small square has area 1. What is h?

Source note: the area unit is omitted, although choices are in metres. The intended unit is 1 m².

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  1. 3 m
  2. 3.5 m
  3. 4 m
  4. 4.2 m
  5. 4.5 m

Question 17

A quiz has 20 questions: correct answers score 7, wrong answers −4, and blanks 0. Eric scores 100. How many questions did he leave blank?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

Question 18

A 4 cm×13 cm strip is folded as shown. The two rectangles have areas P and Q, with P=2 Q. What is x?

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  1. 5 cm
  2. 5.5 cm
  3. 6 cm
  4. 6.5 cm
  5. $4\sqrt2$ cm

Question 19

A box has twice as many apples as pears. Christy and Lily divide all the fruit so that Christy has twice as many pieces as Lily. Which statement is always true?
  1. Christy took at least one pear
  2. Christy took twice as many apples as pears
  3. Christy took twice as many apples as Lily
  4. Christy took as many apples as Lily took pears
  5. Christy took as many pears as Lily took apples

Question 20

Three villages are connected as shown. Downend to Uphill via Middleton is 1 km longer than direct; Downend to Middleton via Uphill is 5 km longer; Uphill to Middleton via Downend is 7 km longer. How long is the shortest direct path?

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  1. 1 km
  2. 2 km
  3. 3 km
  4. 4 km
  5. 5 km