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SASMO 2022 Grade 6

Question 1

Platform scoring: start at 0; Q1–15: 2 points each; Q16–25: 4 each; wrong or blank: 0; maximum 70. Official SASMO reference: start at 15; Section A correct/wrong/blank +2/−1/0, Section B +4/0/0; maximum 85.

Calculate $(37+75\times92)\div(93\times75-38)$.
  1. 0
  2. 1
  3. 1.5
  4. 2
  5. None of the above

Question 2

Mason built a pyramid using identical cubes. It is shown below from different angles. Mason paints the whole pyramid green. How many cubes have exactly 3 faces painted green?

Question illustration

Question illustration

Interpretation of the dark source diagrams: use four centered, solid square layers of side lengths 7, 5, 3 and 1 cubes from bottom to top. Paint every exposed face, including the underside. The clear plan-view schematic is editorial and makes this intended model explicit; it does not recover hidden grid lines from the scan.
  1. 12
  2. 24
  3. 28
  4. 36
  5. None of the above

Question 3

In square $ABCD$, points $E$ and $F$ lie on $AB$ and $CD$, respectively, with $AE=FC=2$ cm. The square has area $196\text{ cm}^2$. What is the area of the shaded region?

Question illustration
  1. $84\text{ cm}^2$
  2. $112\text{ cm}^2$
  3. $28\text{ cm}^2$
  4. $14\text{ cm}^2$
  5. None of the above

Question 4

What is the next number in the sequence 1, 2, 5, 14, 41, …?

Use the intended elementary rule suggested by the successive differences. A finite list can fit other artificial rules.
  1. 122
  2. 121
  3. 68
  4. 50
  5. None of the above

Question 5

Tom spent 225 dollars on clothes and 38% of his original money on school stationery. He had 17% of his original money left. How much money did he have at first?
  1. 45 dollars
  2. 100 dollars
  3. 275 dollars
  4. 500 dollars
  5. None of the above

Question 6

The number in each unshaded square is the sum of the two numbers connected to it in the row above. What number belongs in the square with the question mark?

Question illustration
  1. 4
  2. 5
  3. 6
  4. 7
  5. None of the above

Question 7

Ten classrooms have equal numbers of students. If 10 students leave each classroom, the total remaining in all 10 classrooms equals the initial total in 9 classrooms. How many students were there altogether initially?
  1. 1000
  2. 900
  3. 100
  4. 90
  5. None of the above

Question 8

The difference between two whole numbers is 2022. Their quotient is 7. Find their sum.
  1. 2969
  2. 2696
  3. 2359
  4. 337
  5. None of the above

Question 9

What is the sum of the digits of $2007\times\underbrace{111\ldots111}_{12\text{ ones}}$?
  1. 108
  2. 99
  3. 90
  4. 81
  5. None of the above

Question 10

Study the picture. Arrange the animals in ascending order of their represented values.

Question illustration

Each animal represents a fixed positive number. The same animal always represents the same value.
  1. Rhino, crocodile, hippo, bear. Question illustration
  2. Rhino, crocodile, bear, hippo. Question illustration
  3. Crocodile, rhino, bear, hippo. Question illustration
  4. Rhino, bear, crocodile, hippo. Question illustration
  5. None of the above

Question 11

The product of three consecutive whole numbers is 226920. What is their sum?
  1. 180
  2. 183
  3. 186
  4. 60
  5. None of the above

Question 12

The digit sum of a four-digit number is 24. How many such numbers are less than 2000?
  1. 3
  2. 9
  3. 12
  4. 15
  5. None of the above

Question 13

In how many ways can 30 be expressed as the sum of two or more consecutive whole numbers?
  1. 3
  2. 2
  3. 1
  4. 0
  5. None of the above

Question 14

For whole numbers $a,b,c$, it is given that $\displaystyle\frac{25}{17}=a+\frac{1}{b+\frac1c}$. What is $a+b+c$?

All denominators must be nonzero. Read the nesting exactly as displayed.
  1. 8
  2. 9
  3. 10
  4. 11
  5. None of the above

Question 15

Five girls each prepared one gift for a party. In how many ways can the five gifts be distributed among the five girls so that no girl receives her own gift?

The gifts are distinguishable by their owners, and each girl receives exactly one gift.
  1. 120
  2. 45
  3. 44
  4. 24
  5. None of the above

Question 16

How many triangles are there in the figure?

Question illustration

Input: enter the requested whole-number answer without units. Leading zeroes from the paper grid may be omitted.

Question 17

The graph shows the numbers of toys Mr Tan sold in the first six days of a week. All horizontal lines are equally spaced. Monday’s sales were 40% of Sunday’s sales. The average for the whole week was 210 toys per day. How many toys did he sell on Sunday?

Question illustration

The bars start at the shared zero baseline. Labels run Monday, Tuesday, Wednesday, Thursday, Friday, Saturday from left to right.

Input: enter the requested whole-number answer without units. Leading zeroes from the paper grid may be omitted.

Question 18

A game starts with four piles containing 10, 12, 15 and 17 marbles. On each turn, a player takes 3 marbles from the largest pile and gives one to each of the other three piles. How many marbles are in the smallest pile after the 2022nd turn?

Input: enter the requested whole-number answer without units. Leading zeroes from the paper grid may be omitted.

Question 19

Derrick spent $4/9$ of his money on a toy, then $3/7$ of his remaining money on a book. He spent the rest on 5 cakes costing 7 dollars each. How much money, in dollars, did he pay for the toy?

Input: enter the requested whole-number answer without units. Leading zeroes from the paper grid may be omitted.

Question 20

Towns A and B are 3.3 km apart. At 9:00 a.m., Aaron cycles from A toward B at 132 m/min, while Jeremy cycles from B toward A at 143 m/min. How many metres has Aaron cycled when they meet?

Assume both cyclists maintain their stated speeds along the same route without stopping.

Input: enter the requested whole-number answer without units. Leading zeroes from the paper grid may be omitted.