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    Category III

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    Мөнхтулга Б
    This document contains 25 multiple choice questions testing math and problem solving skills for grades 7-8. The questions cover a range of topics including number properties, probability, geometry, averages, patterns, and algebraic expressions.

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    © All Rights Reserved
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    Category III

    Uploaded by

    Мөнхтулга Б
    122 views5 pages
    This document contains 25 multiple choice questions testing math and problem solving skills for grades 7-8. The questions cover a range of topics including number properties, probability, geometry, averages, patterns, and algebraic expressions.

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    This document contains 25 multiple choice questions testing math and problem solving skills for grades 7-8. The questions cover a range of topics including number properties, probability, geometry, averages, patterns, and algebraic expressions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    122 views5 pages

    Category III

    Uploaded by

    Мөнхтулга Б
    This document contains 25 multiple choice questions testing math and problem solving skills for grades 7-8. The questions cover a range of topics including number properties, probability, geometry, averages, patterns, and algebraic expressions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 5

    Category III - Grades 7 & 8

    1. Seven-digit number 62ab427 is divisible by 99. Find the value of A+B.

    A) 7 B) 5 C) 6 D) 4

    2. There are 37 numbers on a roulette wheel: 0 and the whole numbers from 1
    to 36. What is the chance of getting a perfect square number?

    A) 1/6 B) 7/37 C) 6/37 D) 5/37

    3. The square in the figure has side length equal to 2. What is the radius of the
    small circle? (circles are touching

    A) √2 - 1
    2
    B)
    2+1
    C) √2
    D) 3 − 2√2

    4. The average of five weights is 13 grams. If a 7-gram weight is added, what is


    the average of the six weights?

    A) 11 B) 12 C) 13 D) 14

    5. The sum of 10 consecutive natural numbers are 195. Find the value of the
    first one.

    A) 13 B) 14 C) 15 D) 16

    6. Every day at school, Alex climbs a flight of 6 stairs. Alex can climb using 1, 2
    or 3 steps or a combination of any of them. How many ways can Alex climb
    the flight of 6 stairs?

    A) 18 B) 20 C) 22 D) 24
    2

    7. Fine the simplest form of ( 10−1) −3


    10+ 3−1

    A) 10 − 3 − 1 B) 10 + 3 − 1 C) 7 − 1 D) 3 + 1

    8. Inside two parallel lines there are two squares


    ABCD and AKLM. Find the angle <TLK, if
    < 𝐵𝐶𝐸 = 66° and < 𝐷𝐴𝑀 = 118° .

    A) 42°
    B) 48°
    C) 52°
    D) 58°

    9. If 𝑎1 + 𝑎2 = 1, 𝑎2 + 𝑎3 = 2, 𝑎3 + 𝑎4 = 3, … 𝑎50 + 𝑎51 = 50 and 𝑎51 + 𝑎1 = 51, then


    what is the sum of 𝑎1, 𝑎2, 𝑎3, … , 𝑎51?

    A) 538 B) 1075 C) 663 D) 754

    2 2 𝑎+𝑏
    10.If 𝑎 + 𝑏 = 117 and 𝑎𝑏 = 54, then find the value of 𝑎−𝑏

    A) 3/5 B) 3 C) 5 D) 5/3

    11. In the given figure, ABCD is a


    quadrilateral. <ADB = 60°, <BAC = 70°,
    <DBC = 30° and <ACB = 60°. Find <DAC.

    A) 20°
    B) 30°
    C) 40°
    D) 50°
    1 3 1
    12.If 𝑥 + 𝑥
    = 4, find the value of 𝑥 + 3
    𝑥

    A) 8 B) 16 C) 8.5 D) 52

    13. In ABCD quadrilateral AB:BC:CD:DA=2:3:4:5. The perimeter of ABC is


    equal to 15cm and the perimeter of ACD is equal to 27cm. What is the
    length of CD?

    A) 10 B) 27/5 C) 15 D) 12

    3 2𝑎
    14.Solve equation (𝑥∇5) − 3(𝑥∇7) + 3𝑥 = 3 35
    if (𝑎∇𝑏) = 𝑏
    +1

    A) x=12/5 B) x=3 C) x=2 D) x=2.5

    2
    15.If 𝑓(𝑥) =− 𝑥 and 𝑔(𝑥) =− 4𝑥 − 5 , for what positive value of 𝑥 will be
    𝑓(𝑥 + 2) equal to 𝑔(𝑥 + 2)

    A) 4.5 B) 2 C) 3 D) 4

    16.If a, b are positive natural numbers and


    2022 − 𝑎𝑏 = 2𝑎(1 + 𝑏) + 𝑎 + 3𝑏 + 3
    Find the value of 𝑎 + 𝑏

    A) 2022 B) 341 C) 337 D) 2021

    17. Calculate:
    ( ( 1
    )
    4.5: 47.375− 26 3 −18*0.75 *2.4:0.88 )
    2 5
    17.81:1.37−23 :1
    3 6

    A)3 B) 4 C) 3.5 D) 3.6

    18.If 𝑓(𝑡) = 3 − |2𝑡 + 1| find the value of


    𝑓(− 2) + 𝑓(− 1) + 𝑓(0) + 𝑓(1) + 𝑓(2)

    A) 2 B) 3 C) 1 D) 0
    4 3 2
    19.How many divisors does 2 * 3 * 4 have?

    A) 12 B) 24 C) 25 D) 36

    20.Find the length of 𝐶𝐷, if AB is a diameter,


    < 𝐶𝑀𝑂 = 60° , 𝑀𝐹 = 12 and 𝑀𝐸 = 18.

    A) 30
    B) 60
    C) 6
    D) 40

    2022
    21.What is the last digit of 2022 ?

    A) 2 B) 4 C) 6 D) 8

    22. ABCD is a square, and MNPQ is a rectangle.


    Find the sum of Perimeters of the colored
    rectangles, if AB=8, MN=2, NP=14.

    A) 48 B) 52 C) 60 D) 64

    4 4
    2022 −2021
    23. Which one of the following numbers is equal to 2 2
    2022 +2021
    2 2
    A) 2043 B) 4043 (
    C) 2021.5 D) 2 * 2022 − 2021 )
    24.Three points A, B, and C have coordinates (0, 4), (6, 2), and (10, 4),
    respectively. What is an angle ∠ABC ?

    A) 105° B) 120° C) 135° D) 145°

    25. Fine the simplest form of 5 − 2 6.

    A) 0.5 B) 3 − √2 C) 5 − √3 D) 5 − √2
    ANSWERS

    1. C) 6
    2. B) 7/37
    3. D) 3 − 2√2
    4. B) 12
    5. C) 15
    6. D) 24
    7. A) 10 − 3 − 1
    8. C) 52°
    9. C) 663
    10. D) 5/3
    11. B) 30°
    12. D) 52
    13. D) 12
    14. C) x=2
    15. C) 3
    16. C) 337
    17. B) 4
    18. A) 2
    19.D) 36
    20. B) 60
    21. B) 4
    22. C) 60
    23. B) 4043
    24. C) 135°
    25.B) 3 − √2

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