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SASMO 2022 Grade 7

Question 1

Grading: platform starts at 0; Q1–15: 2 points each, Q16–25: 4 each; wrong/blank: 0; maximum 70. Official reference starts at 15; Section A +2/−1/0 and Section B +4/0/0 for correct/wrong/blank; maximum 85. Time: 90 minutes (official-reference default).

Find the value of $2022-1876+1979+4876$.
  1. 7000
  2. 7001
  3. 7010
  4. 7100
  5. None of the above

Question 2

If $a$ is an odd integer and $b,c$ are even integers, which statement is NOT true?
  1. $(c-a)a$ is odd
  2. $(b-a)c$ is even
  3. $(b-a)c^2$ is odd
  4. $(b-a)^2c$ is even
  5. None of the above

Question 3

What is the next number in $13,20,29,40,53,68,\ldots$?

Pattern convention: continue the consecutive odd increases shown by the listed terms.
  1. 81
  2. 83
  3. 85
  4. 87
  5. None of the above

Question 4

Emma earns $a$ dollars per hour for the first 6 hours of her shift and $b$ dollars per hour for each hour after that. If she works 12 hours in one shift, what is her average hourly wage?
  1. $\frac{a+b}{3}$
  2. $\frac{a+2b}{2}$
  3. $6a+6b$
  4. $\frac{a+b}{2}$
  5. None of the above

Question 5

Find the last digit of $4^{2022}\times9^{2024}$.
  1. 2
  2. 4
  3. 6
  4. 8
  5. None of the above

Question 6

Tom spent 450 dollars on clothes and 40% of his remaining money on school stationery. He then had 26.25% of his original money left. How much did he have at first?
  1. 250 dollars
  2. 275 dollars
  3. 800 dollars
  4. 1000 dollars
  5. None of the above

Question 7

How many numbers appear in both arithmetic sequences below? $$28,34,40,46,\ldots,1000$$ $$54,65,76,87,\ldots,1000$$
  1. 14
  2. 15
  3. 16
  4. 22
  5. None of the above

Question 8

A square has side length 84 cm. Three semicircles are drawn inside it, with three sides of the square as diameters, as shown. Find the shaded area in $\mathrm{cm}^2$. Use $\pi=\frac{22}{7}$.

Question illustration
  1. $2772\ \mathrm{cm}^2$
  2. $5544\ \mathrm{cm}^2$
  3. $11088\ \mathrm{cm}^2$
  4. $22176\ \mathrm{cm}^2$
  5. None of the above

Question 9

The six-digit number $75A2B8$ is a multiple of 36. If it is as large as possible, find $A-B$. Here $A,B$ are digits.
  1. −1
  2. 2
  3. 3
  4. 6
  5. None of the above

Question 10

Which cube is formed when the net below is folded? Choose the labelled option shown in the figure.

Question illustration
  1. Cube A
  2. Cube B
  3. Cube C
  4. Cube D
  5. Cube E

Question 11

The operator $\otimes$ gives $3\otimes8=817$, $1\otimes6=615$, $4\otimes9=918$, and $15\otimes13=2022$.

Find $20\otimes22$.

Pattern convention: use the intended rule of separately adding fixed constants to the two inputs and concatenating the resulting decimal strings.
  1. 2531
  2. 2520
  3. 2031
  4. 2025
  5. None of the above

Question 12

How many three-digit positive integers contain at least one digit equal to 4?
  1. 900
  2. 648
  3. 252
  4. 225
  5. None of the above

Question 13

The least common multiple (LCM) of two positive integers is 1000. Their ratio is $2:25$. Find their highest common factor (HCF).
  1. 4
  2. 5
  3. 10
  4. 20
  5. None of the above

Question 14

The product of 24 integers is 3. Which value cannot be their sum?
  1. 22
  2. 14
  3. −4
  4. −10
  5. None of the above

Question 15

In square $ABCD$, $E$ and $F$ lie on $AD$ and $CD$ respectively, with $3DE=3FC=AB$. Segments $BF$ and $CE$ meet at $G$. The square has area $140\ \mathrm{cm}^2$. Find the area of quadrilateral $EDFG$.

Question illustration
  1. $7\ \mathrm{cm}^2$
  2. $14\ \mathrm{cm}^2$
  3. $21\ \mathrm{cm}^2$
  4. $28\ \mathrm{cm}^2$
  5. None of the above

Question 16

How many triangles are in the figure below? Count triangles of every size whose sides lie entirely on drawn straight segments.

Question illustration

Answer format: enter one whole number without units. The source answer sheet uses four digits with leading zeros if needed; ordinary numeric entry is used here.

Question 17

A four-digit number has four different digits whose product is 810. What is the greatest such number?

Answer format: enter one whole number without units. The source answer sheet uses four digits with leading zeros if needed; ordinary numeric entry is used here.

Question 18

The four-digit number 1120 is divisible by the sum of its digits, $1+1+2+0=4$. What is the greatest four-digit number divisible by the sum of its digits?

Answer format: enter one whole number without units. The source answer sheet uses four digits with leading zeros if needed; ordinary numeric entry is used here.

Question 19

The operation $\triangle$ is illustrated by $3\triangle3=2+3+4$, $5\triangle2=4+5$, and $9\triangle6=8+9+10+11+12+13$. If $x\triangle12=2022$, find $x$.

Convention: the second input is the number of consecutive terms, beginning one below the first input.

Answer format: enter one whole number without units. The source answer sheet uses four digits with leading zeros if needed; ordinary numeric entry is used here.

Question 20

The 2022nd term of the sequence below, reduced to lowest terms, is $a/b$ with $\operatorname{HCF}(a,b)=1$. Find $a+b$.

Question illustration

Pattern convention: for each denominator $n=2,3,4,\ldots$, list numerators $1,2,\ldots,\lfloor n/2\rfloor$ in order. Keep every displayed position even when two fractions have the same value.

Answer format: enter one whole number without units. The source answer sheet uses four digits with leading zeros if needed; ordinary numeric entry is used here.