SZF IOM 2022 previous year paper practice · PYQ-pattern set

SZF IOM 2022 PYQ-pattern questions

Showing 10 of the 18 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Quadratic Equations

   If α and β are the roots of the equation 2x² - 5x + 3 = 0, then the value of (1/α + 1/β) is:

   • A. 3/5
   • B. 5/3
   • C. 2/3
   • D. 3/2
   Answer and solution

   Answer: B

   1/α + 1/β = (α + β)/(αβ). From the equation, sum of roots α + β = 5/2 and product αβ = 3/2. Therefore, (5/2)/(3/2) = 5/3.

2. Q2 · Number System

   The HCF and LCM of two numbers are 18 and 1260 respectively. If one of the numbers is 126, then the other number is:

   • A. 162
   • B. 176
   • C. 180
   • D. 198
   Answer and solution

   Answer: C

   Using the property: Product of two numbers = HCF × LCM. So 126 × other number = 18 × 1260 = 22680. Therefore, other number = 22680/126 = 180.

3. Q3 · Area of Triangles, Parallelograms and Circles

   A parallelogram has a base of 12 cm and a height of 7 cm. What is its area?

   • A. 84 cm²
   • B. 42 cm²
   • C. 19 cm²
   • D. 38 cm²
   Answer and solution

   Answer: A

   Area of a parallelogram = base × height = 12 × 7 = 84 cm².

4. Q4 · Triangles

   In a triangle, two sides are 9 cm and 5 cm. Which of the following CANNOT be the length of the third side?

   • A. 6 cm
   • B. 13 cm
   • C. 15 cm
   • D. 12 cm
   Answer and solution

   Answer: C

   By triangle inequality, the third side must be less than 9 + 5 = 14 cm and greater than 9 - 5 = 4 cm. 15 cm exceeds this range.

5. Q5 · Non-Verbal Reasoning

   A figure is given which is rotated 90° clockwise. Which of the following represents the rotated figure? (Assume a square with a triangle on top becomes a square with triangle on right side)

   • A. Triangle on left side of square
   • B. Triangle on right side of square
   • C. Triangle on bottom of square
   • D. Triangle on top of square
   Answer and solution

   Answer: B

   Rotating 90° clockwise moves the top position to the right position, so the triangle moves from top to right side of the square.

6. Q6 · Logarithms

   If log₁₀ 2 = 0.3010, what is the value of log₁₀ 50?

   • A. 1.3010
   • B. 1.6990
   • C. 1.4771
   • D. 1.5441
   Answer and solution

   Answer: B

   log₁₀ 50 = log₁₀ (100/2) = log₁₀ 100 - log₁₀ 2 = 2 - 0.3010 = 1.6990.

7. Q7 · Advanced Geometry

   A cone and a cylinder have equal base radii and equal heights. If the volume of the cylinder is 450 cm³, what is the volume of the cone?

   • A. 100 cm³
   • B. 125 cm³
   • C. 150 cm³
   • D. 200 cm³
   Answer and solution

   Answer: C

   Volume of cone = (1/3) × volume of cylinder when they have equal base and height. Volume of cone = 450/3 = 150 cm³.

8. Q8 · Advanced Algebra

   The sum of three consecutive terms of a geometric progression is 42, and their product is 512. What is the common ratio if it is greater than 1?

   • A. 2
   • B. 3
   • C. 4
   • D. 1/2
   Answer and solution

   Answer: C

   Terms a/r, a, ar: product a³=512 gives a=8. Sum equation 8/r+8+8r=42 leads to 4r²-17r+4=0, roots r=4 or 1/4. Since ratio>1, r=4.

9. Q9 · Coordinate Geometry

   The midpoint of the line segment joining points P(-4, 6) and Q(8, -2) is:

   • A. (2, 2)
   • B. (4, 4)
   • C. (6, 1)
   • D. (2, 4)
   Answer and solution

   Answer: A

   Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) = ((-4+8)/2, (6-2)/2) = (4/2, 4/2) = (2, 2).

10. Q10 · Logarithms

    If log₂(x) + log₄(x) + log₈(x) = 11, then what is the value of x?

    • A. 32
    • B. 64
    • C. 128
    • D. 256
    Answer and solution

    Answer: B

    Converting to base 2: log₂(x) + log₂(x)/2 + log₂(x)/3 = 11. This gives log₂(x)(1 + 1/2 + 1/3) = 11, so log₂(x)(11/6) = 11, therefore log₂(x) = 6, giving x = 2⁶ = 64.