IMAT Maths Preparation Book

Chapter 1: Numbers

🔍 Theory & Explanations:

In this chapter, you'll learn the foundational concepts necessary for quick mental arithmetic and number
manipulation, which are critical in the IMAT exam where calculator use is prohibited.

📌 Key Concepts:

1. Types of Numbers:

Natural numbers (N): 1, 2, 3, ...

Whole numbers: 0, 1, 2, ...
Integers (Z): ..., -3, -2, -1, 0, 1, 2, ...
Rational numbers (Q): Fractions like 1/2, -5/3, etc.
Irrational numbers: Cannot be expressed as fractions, e.g., π, √2.
Real numbers (R): All rational and irrational numbers.
Complex numbers (C): Includes imaginary numbers.

2. Divisibility Rules:

Divisible by 2: Even last digit

Divisible by 3: Sum of digits divisible by 3
Divisible by 5: Ends in 0 or 5
Divisible by 11: Alternating sum of digits is divisible by 11

3. Prime and Composite Numbers:

Prime: Only 2 factors (e.g., 2, 3, 5, 7)

Composite: More than 2 factors (e.g., 4, 6, 8)

4. HCF and LCM:

HCF (Highest Common Factor): Greatest number dividing all

LCM (Least Common Multiple): Smallest number divisible by all

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5. Exponents and Roots:

Laws of exponents: a^m × a^n = a^(m+n), etc.

Roots: √9 = 3, ∛8 = 2

6. Fractions and Decimals:

Conversion and operations

Simplifying and comparing

7. Percentages, Ratios & Proportions:

Percentage = (Part/Whole) × 100

Ratio: Comparison of two quantities
Proportion: Two ratios are equal

8. Scientific Notation:

Expressing very large/small numbers: 4,500 = 4.5 × 10^3

9. Absolute Value and Number Line:

|x| = x if x ≥ 0, −x if x < 0

🔢 50+ IMAT-Style MCQs:

1. Which of the following is a prime number less than 100 but not ending in 1, 3, 7, or 9?

a. 61

b. 89

c. 97

d. 2

3. What is the LCM of 45 and 75?

a. 225

b. 675

c. 135

d. 90

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4. Which of the following values is closest to 1/3 but not exactly equal to it?

a. 0.33

b. 0.34

c. 0.333...

d. 0.3

5. If (5/8)x = 75, then x = ?

a. 100

b. 110

c. 120

d. 125

6. What is the remainder when 2345 is divided by 9?

a. 2

b. 0

c. 5

d. 8

7. The product of two numbers is 108 and their HCF is 6. What is their LCM?

a. 18

b. 36

c. 72

d. 108

8. Which of the following is both a perfect square and a perfect cube?

a. 36

b. 64

c. 144

d. 216

9. Simplify: (0.2)^-2

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a. 0.04

b. 4

c. 25

d. 0.25

10. Which of these is a terminating decimal?

a. 1/6

b. 3/7

c. 5/8

d. 4/9

11. Which pair of numbers is in the ratio 3:5 and adds up to 64?

a. 24, 40

b. 18, 30

c. 28, 36

d. 20, 44

12. Which number is divisible by 4 but not by 8?

a. 64

b. 48

c. 20

d. 16

13. Simplify: \[(4/5)^2 ÷ (2/3)^2]

a. 81/100

b. 25/16

c. 16/25

d. 100/81

14. Convert 3.45 × 10^4 into standard form.

a. 34500

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b. 3450

c. 0.0345

d. 345000

15. The sum of digits of which number is divisible by 3?

a. 172

b. 213

c. 415

d. 761

16. What is the absolute value of -3.5?

a. -3.5

b. 3.5

c. 0

d. -7

17. A number divided by 5 gives the same result as subtracting 6 from it. What is the number?

a. 7.5

b. 10

c. 12.5

d. 15

18. Which number lies between √5 and √6?

a. 2.2

b. 2.4

c. 2.6

d. 2.8

19. If x is an irrational number, which of the following is always irrational?

a. x^2

b. x + 1

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c. x – x

d. x × 0

20. Which of these numbers is closest to π?

a. 3.1

b. 3.14

c. 3.1428

d. 3.4

21. Find the smallest 3-digit number divisible by both 3 and 4.

a. 100

b. 102

c. 108

d. 120

21. What is the HCF of 84 and 98?

a. 7
b. 14
c. 28
d. 21

22. Which of the following numbers is not divisible by 9?

a. 729
b. 1008
c. 513
d. 1182

23. What is the decimal expansion of 7/20?

a. 0.35
b. 0.375
c. 0.345
d. 0.7

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24. A number is increased by 25% and the result is 500. What was the
original number?

a. 375
b. 400
c. 425
d. 450

25. Which of the following cannot be expressed as a fraction?

a. 0.123
b. 0.666...
c. √5
d. 3.25

26. If the average of four consecutive odd numbers is 27, what is the
smallest of them?

a. 23
b. 25
c. 27
d. 29

27. What is the product of the LCM and HCF of two numbers 15 and 20?

a. 300
b. 30
c. 100
d. 75

28. If 2^x = 32, what is the value of x?

a. 4
b. 5
c. 6
d. 3

29. What is the reciprocal of 0.25?

a. 2
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 b. 4
c. 0.4
d. 1/4

30. Which of the following is not a rational number?

a. 7/8
b. 0.25
c. √2
d. -1

31. Which number is both even and a prime?

a. 2
b. 4
c. 6
d. 8

32. Convert 0.6 (recurring) into a fraction.

a. 3/5
b. 2/3
c. 5/8
d. 4/7

33. If a number is 25% more than 160, what is the number?

a. 190
b. 180
c. 200
d. 210

34. The sum of three consecutive natural numbers is 96. What is the
smallest number?

a. 30
b. 31
c. 32
d. 33

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35. Which of these is not a perfect cube?

a. 8
b. 27
c. 125
d. 36

36. How many digits are there in 2^10?

a. 2
b. 3
c. 4
d. 5

37. Which of the following is equal to 100%?

a. 1
b. 0.1
c. 10
d. 0.01

38. Which number has exactly 3 distinct prime factors?

a. 30
b. 36
c. 42
d. 60

39. What is the square root of 196?

a. 13
b. 14
c. 15
d. 16

40. Which of the following is closest to √10?

a. 3.0
b. 3.1
c. 3.2

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 d. 3.3

41. The smallest number divisible by 2, 3, and 5 is:

a. 10
b. 15
c. 30
d. 60

42. Which of the following numbers is a multiple of 11?

a. 242
b. 333
c. 500
d. 901

43. 15% of a number is 45. What is the number?

a. 200
b. 250
c. 300
d. 350

44. If x = 5 and y = 2, what is x^2 + y^2?

a. 25
b. 29
c. 30
d. 35

45. What is the value of (1/2)^-3?

a. 1/8
b. 8
c. 2
d. 4

46. What is 1.6 × 10^3?

a. 160

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 b. 1600
c. 16000
d. 16

47. Which of the following numbers lies between 2/5 and 3/5?

a. 0.3
b. 0.5
c. 0.7
d. 0.8

48. Which of the following has the smallest value?

a. 1/2
b. 0.49
c. 5/9
d. 0.51

49. What is the least common multiple of 6, 8, and 12?

a. 24
b. 48
c. 36
d. 60

50. Which number is irrational?

a. √3
b. 22/7
c. 3.14
d. √4

Chapter 2: Algebra

🔍 Theory & Explanations:

This chapter focuses on algebraic expressions, equations, inequalities, and manipulation of symbols—
core skills for IMAT.

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📌 Key Concepts:

1. Algebraic Expressions

An algebraic expression consists of variables, constants, and mathematical operators (+, −, ×, ÷). For
example: 3x + 2 , 2a^2 - 5a + 4 .

Term: Each part of the expression separated by + or − (e.g., 3x and 2 in 3x + 2)

Coefficient: The number multiplied by the variable (e.g., 3 in 3x)
Like terms: Have the same variable and exponent (e.g., 2x and -5x)

👉 Example: Simplify 3x + 4 - 2x + 6 = (3x - 2x) + (4 + 6) = x + 10

2. Equations and Identities

Equations: Statements of equality that are true for specific values (e.g., x + 2 = 5 is true for x
= 3)
Identities: Equations that are true for all values of variables (e.g., (a + b)^2 = a^2 + 2ab +
b^2 )
Solving equations: Apply inverse operations to isolate the variable

👉 Example: Solve 2x - 3 = 7 → 2x = 10 → x = 5

3. Inequalities

Inequalities involve symbols like < , > , ≤ , ≥ . Their solution is usually represented as a range.

Apply same rules as equations when solving

But flip the inequality symbol when multiplying/dividing by a negative

👉 Example: Solve -2x + 3 < 7 → -2x < 4 → x > -2

4. Polynomials

Polynomials are expressions with one or more terms involving variables with non-negative integer
exponents.

Degree: Highest exponent (e.g., in 4x^3 - 2x + 1 , degree is 3)

Factor Theorem: If f(a) = 0 , then (x - a) is a factor of f(x)
Remainder Theorem: Remainder of dividing f(x) by (x - a) is f(a)

👉 Example: Factor x^2 + 5x + 6 = (x + 2)(x + 3)

5. Functions and Graphs

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A function relates an input (x) to exactly one output (y). Common types: linear, quadratic, rational.

Linear function: y = mx + c → straight line

Quadratic function: y = ax^2 + bx + c → parabola
Domain: Set of valid x-values
Range: Set of resulting y-values

👉 Example: If f(x) = x^2 , then f(2) = 4 , f(-2) = 4 . Graph is a parabola opening upwards.

🔢 IMAT-Style MCQs:

1. Which of the following is an identity?

a. (x + 3)^2 = x^2 + 6x + 9
b. x + 2 = 5
c. x^2 - 4 = 0
d. 2x + 3 = 7

2. Solve for x: 2x - 5 = 9

a. 7
b. 6
c. 5
d. 4

3. Which of the following is not a polynomial?

a. x^2 + 2x + 1
b. x^3 - x + 5
c. 3x^(-1) + 2x
d. 2x^4 + 1

4. Factorize: x^2 + 5x + 6

a. (x + 2)(x + 3)
b. (x - 2)(x - 3)
c. (x + 1)(x + 6)
d. (x - 1)(x - 6)

5. What is the solution to the inequality: 3x - 2 < 10?

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 a. x < 4
b. x > 4
c. x < 5
d. x > 5

6. What is the degree of the polynomial: 4x^3 - x^2 + 6x - 5?

a. 2
b. 3
c. 4
d. 1

7. If x = -1 is a root of the polynomial x^3 + x^2 - x - 1, then:

a. It satisfies the equation

b. It is not a root
c. The polynomial is reducible
d. None of the above

8. What is the factorized form of x^2 - 9?

a. (x + 3)(x + 3)
b. (x - 3)(x - 3)
c. (x + 3)(x - 3)
d. (x + 9)(x - 1)

9. Which of the following is the correct expansion of (2x - 3)^2?

a. 4x^2 - 12x + 9
b. 4x^2 - 6x + 9
c. 4x^2 + 9
d. 4x^2 + 12x + 9

10. Solve: x^2 - 5x + 6 = 0

a. x = 3, x = 2
b. x = -3, x = -2
c. x = 1, x = 6
d. x = 4, x = 1

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11. What is the value of x in the equation 3(x - 2) = 2(x + 1)?

a. x = 4
b. x = 5
c. x = 3
d. x = 2

12. The graph of y = x^2 is:

a. A straight line
b. A parabola opening upward
c. A parabola opening downward
d. A circle

13. If f(x) = x^2 + 2x + 1, then f(-1) = ?

a. 0
b. 1
c. -1
d. 2

14. Which of the following is the solution of the inequality x - 4 > 2?

a. x > 6
b. x < 6
c. x = 2
d. x > 2

15. What is the result of (x + 2)^2?

a. x^2 + 4x + 4
b. x^2 + 2x + 4
c. x^2 - 4x + 4
d. x^2 + 4x - 4

16. If a polynomial has a root at x = 2, which of the following is a factor?

a. (x + 2)
b. (x - 2)
c. (x^2 - 4)

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 d. (x^2 + 4)

17. What is the value of (x + y)^2 - (x - y)^2?

a. 2xy
b. 4xy
c. x^2 - y^2
d. x^2 + y^2

18. Which function represents a straight line?

a. f(x) = x^2
b. f(x) = x + 2
c. f(x) = √x
d. f(x) = 1/x

19. What is the domain of the function f(x) = 1/(x - 3)?

a. x ≠ 0
b. x ≠ 3
c. x > 3
d. x < 3

20. If f(x) = x^2 - 4x + 4, what is the minimum value of f(x)?

a. 0
b. 2
c. 4
d. -4

21. Solve: x^2 = 25

a. x = ±5
b. x = 5
c. x = -5
d. x = 0

22. What are the roots of the quadratic equation x^2 - 7x + 10 = 0?

a. x = 2, x = 5

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 b. x = -2, x = -5
c. x = 1, x = 10
d. x = 3, x = 4

23. The value of (a + b)^2 - (a - b)^2 is:

a. 0
b. 2ab
c. 4ab
d. a^2 - b^2

24. What is the slope of the line y = 3x + 7?

a. 3
b. 7
c. -3
d. 0

25. If the roots of a quadratic equation are real and equal, then the
discriminant is:

a. Greater than zero

b. Less than zero
c. Equal to zero
d. Non-real

26. What is the y-intercept of the line y = -2x + 5?

a. 5
b. -2
c. -5
d. 2

27. Which of the following expressions is always positive for all real x?

a. (x + 1)^2
b. x^2 - 1
c. x^2 - 2x + 1
d. x^2 + x + 1

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28. The value of x if x^2 - 3x = 0 is:

a. x = 0, 3
b. x = -3, 0
c. x = 1, 3
d. x = 0, -3

29. Solve: (x - 1)(x + 3) = 0

a. x = -3, 1
b. x = 3, -1
c. x = -3, -1
d. x = 3, 1

30. If x + y = 10 and x - y = 2, what is the value of x?

a. 6
b. 4
c. 8
d. 10

31. Which of the following is a quadratic equation?

a. x^2 + 3x + 2 = 0
b. x + 3 = 0
c. x^3 - 4 = 0
d. x/2 + 1 = 0

32. Solve: 4x^2 - 9 = 0

a. x = ±3/2
b. x = ±2/3
c. x = ±4/3
d. x = ±9/2

33. Which expression represents the difference of squares?

a. x^2 - 4
b. x^2 + 4
c. x^2 - 2x + 1

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 d. x^2 + 2x + 1

34. The vertex of y = x^2 - 4x + 3 is:

a. (2, -1)
b. (1, -2)
c. (2, 1)
d. (4, 3)

35. Which of these is not a valid function?

a. f(x) = √x
b. f(x) = 1/x
c. f(x) = ±√x
d. f(x) = x^2

36. Which graph represents an increasing function?

a. y = x
b. y = -x
c. y = -x^2
d. y = -1/x

37. What is the product of the roots of x^2 - 6x + 9 = 0?

a. 9
b. -9
c. 6
d. -6

38. If f(x) = 2x + 3, find f(4)

a. 11
b. 10
c. 9
d. 12

39. Which of the following is not a linear equation?

a. y = 3x + 2

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 b. x + y = 5
c. y = x^2 + 1
d. y = -x

40. Solve: x^2 + 6x + 9 = 0

a. x = -3
b. x = 3
c. x = ±3
d. x = -6, x = 9

41. Which of the following is a binomial?

a. x + y
b. x
c. x^2 + 2x + 1
d. x^2

42. A linear equation always graphs as:

a. A straight line
b. A parabola
c. A circle
d. A hyperbola

43. Solve: 5x - 2 = 3x + 4

a. x = 3
b. x = 2
c. x = 1
d. x = -1

44. Find the remainder when x^3 + 2x^2 - x + 1 is divided by x + 1

a. 3
b. 1
c. 0
d. 2

45. What is the standard form of a quadratic equation?

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 a. ax^2 + bx + c = 0
b. ax + b = 0
c. ax^3 + bx^2 + c = 0
d. ax^2 + bx = 0

46. Which of the following expressions is a perfect square trinomial?

a. x^2 + 4x + 4
b. x^2 - 9
c. x^2 - 4x + 4
d. Both a and c

47. Solve: x^2 = -1

a. x = ±i
b. x = ±1
c. x = 0
d. x = i

48. If (x + 1)^2 = 0, then x = ?

a. -1
b. 1
c. 0
d. 2

49. What is the value of (2x)^2?

a. 4x^2
b. 2x^2
c. x^2
d. 2x

50. The graph of y = -x^2 + 4x - 3 opens:

a. Downward
b. Upward
c. Rightward
d. Leftward

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IMAT Maths Preparation Book

Chapter 1: Numbers
(...existing content remains unchanged...)

Chapter 2: Algebra
(...existing content remains unchanged...)

50. The graph of y = -x^2 + 4x - 3 opens:

a. Downward
b. Upward
c. Rightward
d. Leftward

Chapter 3: Geometry

🔍 Theory & Explanations:

Geometry in IMAT includes properties of shapes, angles, coordinate geometry, and measurement of
areas, perimeters, and volumes. It requires both visual understanding and algebraic manipulation.

📌 Key Concepts:

1. Lines and Angles

Types of angles: acute (< 90°), right (90°), obtuse (> 90°), straight (180°)
Pairs of angles: complementary (sum = 90°), supplementary (sum = 180°), vertically opposite,
adjacent
Parallel lines and transversals: corresponding, alternate interior, and co-interior angles

👉 Example: If two parallel lines are cut by a transversal and one angle is 120°, alternate interior angle is
also 120°.

2. Triangles
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 Types: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (no equal sides)
Angle Sum Property: Sum of interior angles = 180°
Pythagoras Theorem: a² + b² = c² (right-angled triangle)
Area: (1/2) × base × height; Heron’s Formula: √[s(s-a)(s-b)(s-c)] where s = semi-perimeter

👉 Example: A triangle with sides 3, 4, 5 has area = (1/2) × 3 × 4 = 6

3. Quadrilaterals

Types: Square, Rectangle, Parallelogram, Trapezium, Rhombus

Properties: Opposite angles/sides, diagonals, symmetry

Area formulas:

Square: side²
Rectangle: length × breadth
Trapezium: (1/2) × (a + b) × height

4. Circles

Radius, diameter, chord, tangent

Circumference: 2πr; Area: πr²
Angle in a semicircle = 90°
Inscribed angle = ½ central angle

👉 Example: If radius = 7 cm, area = 22/7 × 7 × 7 = 154 cm²

5. Polygons

Sum of interior angles: (n − 2) × 180°

Regular polygon: all angles and sides equal
Each angle: [(n − 2) × 180°] / n

6. Coordinate Geometry

Distance formula: √[(x₂ − x₁)² + (y₂ − y₁)²]

Midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2)
Slope (m): (y₂ − y₁) / (x₂ − x₁)
Equation of line: y = mx + c

7. Mensuration (3D Geometry)

Surface area and volume of cube, cuboid, cylinder, cone, sphere

Cube: SA = 6a², V = a³

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 Sphere: SA = 4πr², V = (4/3)πr³
Cylinder: SA = 2πr(h + r), V = πr²h

🔢 IMAT-Style MCQs:

1. What is the sum of the interior angles of a hexagon?

a. 540°
b. 720°
c. 900°
d. 1080°

2. The area of a triangle with base 10 cm and height 6 cm is:

a. 30 cm²
b. 60 cm²
c. 16 cm²
d. 26 cm²

3. In a right-angled triangle, if the two shorter sides are 6 cm and 8 cm,

the hypotenuse is:

a. 10 cm
b. 12 cm
c. 14 cm
d. 9 cm

4. What is the length of the diagonal of a rectangle with sides 3 cm and 4

cm?

a. 5 cm
b. 6 cm
c. 7 cm
d. 8 cm

5. The area of a circle with radius 5 cm is:

a. 25π cm²
b. 10π cm²

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 c. 20π cm²
d. 100π cm²

6. What is the measure of each interior angle of a regular octagon?

a. 135°
b. 140°
c. 145°
d. 160°

7. What is the perimeter of a square with side length 7 cm?

a. 14 cm
b. 28 cm
c. 21 cm
d. 35 cm

8. Which of the following shapes has only one pair of parallel sides?

a. Square
b. Rectangle
c. Rhombus
d. Trapezium

9. The coordinates of the midpoint of the segment joining (2, 3) and (6,
7) are:

a. (4, 5)
b. (3, 5)
c. (2, 6)
d. (5, 4)

10. What is the slope of the line passing through (1, 2) and (3, 6)?

a. 2
b. 4
c. 1
d. 3

11. The volume of a sphere of radius 3 cm is:

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 a. 36π cm³
b. 81π cm³
c. 113.1 cm³
d. 108π cm³

12. A cone has a height of 12 cm and radius of 5 cm. What is its volume?

a. 100π cm³
b. 200π cm³
c. 300π cm³
d. 250π cm³

13. Which triangle cannot exist?

a. 2 cm, 2 cm, 3 cm
b. 4 cm, 5 cm, 9 cm
c. 3 cm, 4 cm, 5 cm
d. 5 cm, 6 cm, 7 cm

14. Which formula gives the area of a trapezium?

a. (1/2) × base × height

b. (1/2) × (a + b) × height
c. length × breadth
d. πr²

15. What is the area of a parallelogram with base 10 cm and height 4 cm?

a. 40 cm²
b. 20 cm²
c. 30 cm²
d. 50 cm²

16. The total surface area of a cube with edge 4 cm is:

a. 64 cm²
b. 96 cm²
c. 48 cm²
d. 100 cm²

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17. If the coordinates of point A are (2, -1) and B are (6, 3), what is the
length AB?

a. 4
b. 5
c. √32
d. √16

18. A triangle has angles in the ratio 2:3:4. The largest angle is:

a. 80°
b. 90°
c. 100°
d. 120°

19. The equation of a line with slope 3 and y-intercept -2 is:

a. y = 3x - 2
b. y = 2x - 3
c. y = -2x + 3
d. y = 3x + 2

20. The volume of a cuboid is 240 cm³. If the base area is 30 cm², what is
the height?

a. 6 cm
b. 8 cm
c. 4 cm
d. 12 cm

21. What is the length of the side of a square whose area is 121 cm²?

a. 10 cm
b. 11 cm
c. 12 cm
d. 13 cm

22. What is the volume of a cylinder with radius 3 cm and height 7 cm?

a. 63π cm³
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 b. 66π cm³
c. 72π cm³
d. 49π cm³

23. Which of the following has all sides and all angles equal?

a. Rectangle
b. Rhombus
c. Parallelogram
d. Square

24. What is the distance between the points (5, 1) and (1, 1)?

a. 4
b. 5
c. 6
d. 3

25. A triangle has two sides measuring 6 cm and 8 cm, and an included
angle of 90°. What is the area?

a. 24 cm²
b. 48 cm²
c. 36 cm²
d. 18 cm²

26. In a circle, a chord that passes through the center is called:

a. Tangent
b. Radius
c. Diameter
d. Arc

27. The height of a cylinder is 10 cm, and the base area is 25 cm². What is
its volume?

a. 250 cm³
b. 500 cm³
c. 200 cm³
d. 225 cm³

Page 28 of 73
28. What is the exterior angle of a regular polygon with 10 sides?

a. 30°
b. 36°
c. 40°
d. 45°

29. What is the area of a rhombus with diagonals 10 cm and 8 cm?

a. 40 cm²
b. 45 cm²
c. 35 cm²
d. 50 cm²

30. Which figure has only rotational symmetry and no line symmetry?

a. Square
b. Circle
c. Scalene triangle
d. Parallelogram

31. If the diameter of a semicircle is 14 cm, its perimeter is:

a. 22 cm
b. 36 cm
c. 29 cm
d. 35 cm

32. How many sides does a polygon have if the sum of interior angles is
900°?

a. 5
b. 6
c. 7
d. 8

33. What is the surface area of a sphere with radius 5 cm?

a. 25π cm²
b. 100π cm²

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 c. 50π cm²
d. 75π cm²

34. Which pair of angles are always equal when two lines intersect?

a. Adjacent angles
b. Vertically opposite angles
c. Supplementary angles
d. Complementary angles

35. What is the sum of exterior angles of any polygon?

a. 180°
b. 360°
c. Depends on number of sides
d. 90°

36. If a circle has a radius of 4 cm, what is its area?

a. 8π cm²
b. 16π cm²
c. 12π cm²
d. 4π cm²

37. Which quadrilateral has diagonals that bisect each other at right
angles but are not equal?

a. Square
b. Rhombus
c. Rectangle
d. Trapezium

38. A triangle has angles 40°, 60°, and ____?

a. 60°
b. 80°
c. 100°
d. 70°

Page 30 of 73
39. What is the total surface area of a cylinder with radius 3 cm and
height 5 cm?

a. 48π cm²
b. 72π cm²
c. 96π cm²
d. 120π cm²

40. What is the volume of a cone with base radius 3 cm and height 9 cm?

a. 27π cm³
b. 81π cm³
c. 36π cm³
d. 90π cm³

41. If the slope of a line is -2, and it passes through (1, 2), the equation is:

a. y = -2x + 4
b. y = -2x + 2
c. y = 2x - 2
d. y = 2x + 4

42. What is the side length of a cube whose volume is 64 cm³?

a. 2 cm
b. 4 cm
c. 8 cm
d. 6 cm

43. The diagonal of a square divides it into:

a. Two rectangles
b. Two triangles
c. Two trapeziums
d. Two circles

44. Which of the following figures has no diagonals?

a. Triangle
b. Square

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 c. Pentagon
d. Hexagon

45. If the height of a parallelogram doubles and base remains same,

area becomes:

a. Half
b. Same
c. Double
d. Four times

46. A rectangle has length 12 cm and diagonal 13 cm. What is its width?

a. 5 cm
b. 6 cm
c. 7 cm
d. 9 cm

47. What is the area of a sector with angle 60° and radius 6 cm?

a. 6π cm²
b. 12π cm²
c. 4π cm²
d. 8π cm²

48. What is the base length of a triangle with area 30 cm² and height 5
cm?

a. 12 cm
b. 10 cm
c. 8 cm
d. 6 cm

49. Which quadrilateral has both pairs of opposite sides equal and
diagonals equal?

a. Rhombus
b. Parallelogram
c. Rectangle

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 d. Trapezium

50. If the radius of a circle doubles, its area:

a. Remains same
b. Doubles
c. Triples
d. Quadruples

Chapter 4: Functions and Graphs

🔍 Theory & Explanations:

Understanding functions is crucial for mastering a wide range of mathematical problems in IMAT. This
chapter dives deep into different types of functions, their properties, and how to visualize them using
graphs.

📌 Key Concepts:

1. Definition of a Function

A function is a rule that assigns to each input exactly one output. It is often written as f(x) =
expression .

Domain: set of all possible inputs (x-values)

Range: set of all possible outputs (y-values)
Notation: If f(x) = x² , then f(2) = 4 , f(−3) = 9

👉 Example: f(x) = 2x + 1 means for every x, the output is double x plus one.

2. Types of Functions

Linear functions: f(x) = mx + c → straight line

Quadratic functions: f(x) = ax² + bx + c → parabola
Cubic functions: f(x) = ax³ + bx² + cx + d
Absolute value functions: f(x) = |x| → V-shaped graph
Step functions: Piecewise constant values, like the floor function

3. Graphs of Functions

Intercepts:

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 x-intercept: where the graph crosses the x-axis (f(x) = 0)
y-intercept: value when x = 0 (f(0))

Slope (m): Measures the steepness of a line

Vertex: Highest or lowest point of a parabola

👉 Tip: For f(x) = ax² + bx + c , vertex is at x = -b/(2a)

4. Transformations

Vertical shift: f(x) + k → shifts up/down

Horizontal shift: f(x + k) → shifts left/right

Reflections: −f(x) reflects over x-axis, f(−x) over y-axis

Stretching/Shrinking:

Multiply by constant >1 → stretches

Multiply by constant <1 → compresses

👉 Example: f(x) = x² , f(x) + 3 shifts the parabola 3 units up.

5. Composite Functions and Inverses

Composite: (f ∘ g)(x) = f(g(x))

Inverse: Reverses the function rule. If f(x) = 2x + 3 , then f⁻¹(x) = (x − 3)/2

👉 Test: If f(f⁻¹(x)) = x , the inverse is correct.

6. Inequalities in Graphs

Shading above/below the graph for inequalities

Dashed lines (excluded) or solid lines (included)

7. Common IMAT Tricks

Plug values smartly to test domains or rule out options

Know common graph shapes to match equations to graphs
Sketch rough graphs to visualize changes

🔢 IMAT-Style MCQs:

Page 34 of 73
1. Which of the following represents a linear function?

a. y = 2x + 3
b. y = x² − 5x
c. y = √x
d. y = |x|

2. The graph of y = x² is a:

a. Straight line
b. Parabola opening downward
c. Parabola opening upward
d. Circle

3. If f(x) = 2x + 1 and g(x) = x², then (f ∘ g)(2) = ?

a. 9
b. 11
c. 13
d. 17

4. The domain of f(x) = √(x − 4) is:

a. x ≥ 4
b. x > 4
c. x ≤ 4
d. x < 4

5. What is the vertex of y = x² − 6x + 5?

a. (3, −4)
b. (3, 5)
c. (−3, −4)
d. (6, 0)

6. What is the inverse of the function f(x) = 3x − 5?

a. f⁻¹(x) = (x − 5)/3
b. f⁻¹(x) = 3x + 5
c. f⁻¹(x) = (x + 5)/3

Page 35 of 73
 d. f⁻¹(x) = x/3 − 5

7. If f(x) = x² + 4x + 4, then the vertex is at:

a. (−2, 0)
b. (2, 8)
c. (−4, 4)
d. (−2, −4)

8. The graph of y = |x − 3| is:

a. Shifted 3 units left

b. Shifted 3 units right
c. Reflected over x-axis
d. Narrower than y = |x|

9. If f(x) = √(9 − x²), what is the domain?

a. −3 ≤ x ≤ 3
b. x > 3
c. x < −3
d. x ≥ 0

10. A quadratic function has a maximum point if:

a. a > 0
b. a = 0
c. a < 0
d. b > 0

11. Which of the following is NOT a function?

a. f(x) = x²
b. f(x) = √x
c. f(x) = ±√x
d. f(x) = x³

12. The range of y = x² is:

a. All real numbers

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 b. x ≥ 0
c. y ≥ 0
d. y > 0

13. Which point lies on the graph of y = 2x + 1?

a. (2, 5)
b. (1, 4)
c. (0, 0)
d. (−1, −3)

14. What is the slope of the line y = −4x + 7?

a. 7
b. 4
c. −4
d. −7

15. The graph of y = −x² opens:

a. Upward
b. Downward
c. To the right
d. To the left

16. For which function is the range y ≤ 0?

a. f(x) = −x²
b. f(x) = x²
c. f(x) = |x|
d. f(x) = √x

17. The equation y = x² − 2x + 1 is equivalent to:

a. (x + 1)²
b. x(x − 1)
c. (x − 1)²
d. (x − 2)²

18. What is the graph of y = −|x| + 2?

Page 37 of 73
 a. V shape opening upward
b. V shape opening downward
c. Parabola opening upward
d. Line with positive slope

19. The function f(x) = x³ is:

a. Even
b. Odd
c. Neither
d. Constant

20. A function f is defined as f(x) = 1/x. The domain is:

a. All real numbers

b. x ≠ 0
c. x ≥ 0
d. x < 0

21. The graph of y = x³ + 2 is shifted:

a. 2 units up
b. 2 units down
c. 2 units left
d. 2 units right

22. If f(x) = 2x + 3 and g(x) = x − 1, what is (f ∘ g)(x)?

a. 2x + 1
b. 2x − 1
c. 2x − 2
d. x + 2

23. Which transformation results in a vertical stretch of y = f(x)?

a. y = 2f(x)
b. y = f(2x)
c. y = f(x) + 2
d. y = f(x − 2)

Page 38 of 73
24. The graph of y = 1/x is:

a. Linear
b. Quadratic
c. Hyperbola
d. Exponential

25. The graph of y = x² − 4x + 3 intersects the x-axis at:

a. x = 1 and x = 3
b. x = −1 and x = −3
c. x = 2 only
d. x = −1 only

26. What is the y-intercept of y = −2x + 5?

a. −2
b. 5
c. 2
d. −5

27. If f(x) = |x − 1|, what is f(−3)?

a. 2
b. 4
c. −4
d. −2

28. Which of the following functions has no real x-intercepts?

a. f(x) = x² + 4
b. f(x) = x² − 4
c. f(x) = x² − 9
d. f(x) = x² − 1

29. The range of the function f(x) = √x is:

a. All real numbers

b. x ≥ 0
c. y ≥ 0

Page 39 of 73
 d. y > 0

30. The function f(x) = −x² + 6x − 8 opens:

a. Upward
b. Downward
c. Sideways
d. Horizontally

31. Which of the following functions is even?

a. f(x) = x³
b. f(x) = x⁵ − x
c. f(x) = x²
d. f(x) = x³ + x

32. What is the slope of a line perpendicular to y = −3x + 1?

a. −3
b. 1/3
c. 3
d. −1/3

33. If f(x) = x² − 6x + 9, then f(x) is equal to:

a. (x − 3)²
b. (x + 3)²
c. x(x − 6)
d. x(x + 3)

34. The function f(x) = 4 − x² is decreasing in which interval?

a. (−∞, 0)
b. (−∞, −2)
c. (0, ∞)
d. (−∞, 2)

35. If f(x) = 2x − 5, what is f⁻¹(3)?

a. 1

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 b. 4
c. −1
d. 5

36. The domain of f(x) = 1/(x − 2) is:

a. All x ≠ 0
b. All x ≠ 2
c. All real numbers
d. x > 0

37. What is the vertex of f(x) = −(x − 1)² + 4?

a. (−1, 4)
b. (1, 4)
c. (0, 4)
d. (1, −4)

38. Which of the following is a cubic function?

a. f(x) = x³ − x
b. f(x) = x² + 2x + 1
c. f(x) = √x
d. f(x) = |x|

39. The graph of a quadratic function is symmetric about:

a. The x-axis
b. The y-axis
c. A vertical line (axis of symmetry)
d. A horizontal line

40. What is the range of f(x) = −x² + 1?

a. y ≥ 1
b. y ≤ 1
c. y > 1
d. y < 1

Page 41 of 73
41. Which transformation reflects the graph of f(x) = x² across the x-
axis?

a. f(x + 2)
b. −f(x)
c. f(x) − 2
d. f(−x)

42. What is the composite function (g ∘ f)(x) if f(x) = x + 1 and g(x) = x²?

a. x² + 2x + 1
b. x² + 1
c. x² + x + 1
d. x + 2

43. What is the graph of y = √x + 2 shifted from y = √x?

a. 2 units up
b. 2 units down
c. 2 units left
d. 2 units right

44. What is the solution of f(x) = 0 if f(x) = x² − 5x + 6?

a. x = 2 or x = 3
b. x = −2 or x = −3
c. x = 1 or x = 6
d. x = 5 or x = 1

45. The absolute minimum of f(x) = (x − 3)² is:

a. 3
b. −3
c. 0
d. 9

46. What is the value of f(−2) if f(x) = |x + 1|?

a. 1
b. 2

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 c. 3
d. −3

47. Which of the following is the inverse of f(x) = x² (for x ≥ 0)?

a. √x
b. −√x
c. x²
d. 1/x²

48. What does the graph of y = −|x − 2| + 3 look like?

a. A V shape opening up, shifted right and up

b. A V shape opening down, shifted right and up
c. A parabola opening up
d. A straight line

49. The x-intercepts of f(x) = x² − 9 are:

a. x = ±3
b. x = ±9
c. x = 3
d. x = −9

50. If f(x) = 2x² and g(x) = x − 1, then (f ∘ g)(2) = ?

a. 2
b. 4
c. 6
d. 2

Chapter 5: Probability and Statistics

🔍 Theory & Explanations:

Probability and statistics are essential tools used to describe uncertainty and to analyze data, which
frequently appear in the IMAT. This chapter covers basic rules of probability, measures of central
tendency, dispersion, and basic interpretations of statistical results.

📌 Key Concepts:
Page 43 of 73
1. Probability Basics

Probability measures how likely an event is to occur: 0 (impossible) to 1 (certain).

P(Event) = (Favorable outcomes) / (Total outcomes)
Complement rule: P(A') = 1 − P(A)
Addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Multiplication rule (independent): P(A ∩ B) = P(A) × P(B)

👉 Example: The probability of rolling an even number on a fair die is 3/6 = 0.5

2. Conditional Probability

P(A | B) = P(A ∩ B) / P(B)

Used when an event depends on another

3. Expected Value (Mean)

E(X) = Σ[x × P(x)] for all x

Used in games of chance or distributions

4. Descriptive Statistics

Mean: Arithmetic average

Median: Middle value
Mode: Most frequent value
Range: Max − Min
Variance (σ²): Measure of spread
Standard Deviation (σ): Square root of variance

5. Distributions

Uniform distribution: All outcomes equally likely

Normal distribution: Bell-shaped curve, mean = median = mode
68-95-99.7 Rule: ~68% within 1σ, 95% within 2σ, 99.7% within 3σ

6. Data Interpretation

Understanding bar charts, histograms, pie charts, box plots

Identifying skewness: right-skewed (mean > median), left-skewed (mean < median)

7. Common IMAT Tips

Use Venn diagrams to visualize set-based probability

For large data sets, mean ≈ median in normal distribution

Page 44 of 73
 Watch out for "at least" and "at most" type phrasing

🔢 IMAT-Style MCQs:

1. What is the probability of drawing a red card from a standard deck?

a. 1/2
b. 1/3
c. 1/4
d. 1/13

2. In a family with two children, what is the probability both are girls?

a. 1/4
b. 1/3
c. 1/2
d. 2/3

3. A box contains 3 red, 2 blue, and 5 green balls. What is the probability
of picking a blue ball?

a. 1/10
b. 2/10
c. 1/5
d. 3/10

4. If the mean of five numbers is 10, what is their total?

a. 10
b. 50
c. 100
d. 5

5. What is the mode of the data set: {1, 2, 2, 3, 4, 5}?

a. 2
b. 3
c. 4
d. 5

Page 45 of 73
6. A die is rolled. What is the probability of getting a number greater
than 4?

a. 1/6
b. 1/2
c. 1/3
d. 2/3

7. The median of the data set {3, 7, 8, 5, 12} is:

a. 7
b. 8
c. 5
d. 6

8. What is the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}?

a. 4
b. 5
c. 3
d. 6

9. Which graph is best for showing the distribution of a continuous

variable?

a. Bar chart
b. Line graph
c. Histogram
d. Pie chart

10. A fair coin is flipped twice. What is the probability of getting at least
one head?

a. 1/4
b. 3/4
c. 1/2
d. 2/3

11. The standard deviation is:

Page 46 of 73
 a. The square of variance
b. The mean of the data
c. The square root of variance
d. The mode

12. If two events A and B are independent, then P(A ∩ B) equals:

a. P(A) + P(B)
b. P(A) − P(B)
c. P(A) × P(B)
d. P(A ∪ B)

13. In a standard normal distribution, the mean is:

a. 1
b. 0
c. −1
d. 100

14. What is the probability of drawing a king or a queen from a standard

deck?

a. 1/13
b. 2/13
c. 4/13
d. 2/52

15. Which measure is most affected by extreme values?

a. Median
b. Mode
c. Mean
d. Range

16. In a dataset, the most frequent value is called:

a. Mean
b. Median
c. Mode
d. Range

Page 47 of 73
17. If the probability of an event is 0.2, what is the probability it does not
occur?

a. 0.8
b. 0.2
c. 0.5
d. 0.1

18. The sum of all probabilities in a sample space is:

a. 0
b. 1
c. Less than 1
d. Greater than 1

19. Which of the following is a discrete random variable?

a. Height
b. Weight
c. Number of students
d. Time

20. A pie chart is best used for:

a. Showing changes over time

b. Comparing categories
c. Showing proportions
d. Correlation

21. A jar contains 6 red, 3 blue, and 1 yellow marble. What is the
probability of drawing a red marble?

a. 1/10
b. 3/5
c. 2/5
d. 6/10

22. What is the interquartile range (IQR) of the data set {4, 5, 7, 9, 10, 12,
14, 18, 20}?

Page 48 of 73
 a. 6
b. 7
c. 10
d. 12

23. If the probability of event A is 0.4 and event B is 0.5, assuming

independence, what is the probability of both A and B?

a. 0.2
b. 0.9
c. 0.25
d. 0.6

24. A data set has a mean of 10 and a standard deviation of 2. What is

the z-score of 14?

a. 2
b. 1.5
c. 4
d. 0.5

25. What is the probability of getting exactly two heads when flipping
three fair coins?

a. 1/4
b. 3/8
c. 1/2
d. 1/3

26. Which of the following best describes a symmetric distribution?

a. Mean = median = mode

b. Mean > median > mode
c. Mode > mean > median
d. Median > mean > mode

27. A spinner has 4 equal sections numbered 1 through 4. What is the

probability of spinning an even number?

Page 49 of 73
 a. 1/4
b. 1/2
c. 3/4
d. 2/3

28. The variance of a data set is 16. What is its standard deviation?

a. 4
b. 8
c. 2
d. 5

29. If 60% of students passed a test, what is the probability a randomly

selected student did not pass?

a. 0.4
b. 0.6
c. 1.6
d. 0.2

30. The probability of rain tomorrow is 0.25. What are the odds against it
raining?

a. 1:3
b. 3:1
c. 2:3
d. 3:4

31. What is the cumulative frequency of the class 10–20 if frequencies

are: 0–10: 5, 10–20: 7, 20–30: 8?

a. 7
b. 8
c. 12
d. 20

32. In how many ways can you choose 2 students from a group of 5?

a. 10

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 b. 5
c. 15
d. 20

33. A standard deck has 52 cards. What is the probability of drawing a

black face card?

a. 2/13
b. 3/13
c. 1/26
d. 1/13

34. The range of a data set is calculated as:

a. Q3 − Q1
b. Max − Min
c. Median − Mean
d. Mean − Mode

35. What is the expected value of rolling a fair six-sided die?

a. 3.5
b. 3
c. 4
d. 5

36. A test has a mean score of 70 and a standard deviation of 10. A

student scores 80. What is their z-score?

a. 0.5
b. 1
c. 1.5
d. 2

37. If P(A) = 0.7 and P(B) = 0.6, then P(A ∪ B) ≤ ?

a. 0.7
b. 1.3
c. 0.6
d. 1.0

Page 51 of 73
38. A data set has a symmetric distribution. Which is most likely true?

a. Mean < Median

b. Mean > Mode
c. Mean = Median
d. Mode > Median

39. A histogram is useful for:

a. Categorical data
b. Continuous data
c. Qualitative data
d. Discrete variables only

40. What is the sample space of flipping a coin twice?

a. 2
b. 3
c. 4
d. 6

41. What is the median of the data set {6, 2, 9, 4, 7}?

a. 6
b. 7
c. 5
d. 4

42. The complement of event A is:

a. A only
b. A ∩ B
c. Not A
d. A ∪ B

43. What is the probability of getting a number divisible by 3 on a die?

a. 1/2
b. 1/3
c. 2/3

Page 52 of 73
 d. 5/6

44. What is the standard deviation of {2, 4, 4, 4, 5, 5, 7, 9}?

a. 2
b. 1.87
c. 3
d. 2.5

45. What is the mean of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

a. 5
b. 5.5
c. 6
d. 4.5

46. If the probability of an event is 0.75, what are the odds in favor?

a. 3:1
b. 1:3
c. 3:4
d. 1:4

47. What does a z-score of 0 indicate?

a. The score is above average

b. The score equals the mean
c. The score is below average
d. The score is an outlier

48. If a data set is positively skewed:

a. Mean < Median

b. Mean > Median
c. Mode > Mean
d. Median = Mode

49. Which of the following cannot be a probability?

a. 0.5

Page 53 of 73
 b. 1
c. −0.2
d. 0

50. If 3 coins are flipped, what is the probability of getting all tails?

a. 1/8
b. 1/6
c. 1/4
d. 3/8

Chapter 6: Data Analysis

📘 Theory & Explanation:

Data analysis is the process of systematically applying statistical and logical techniques to describe and
illustrate, condense and recap, and evaluate data. IMAT questions on data analysis often require
interpreting graphs, calculating basic statistical measures, or applying understanding to real-world
problems.

Key Concepts:

Types of Data: Categorical (nominal, ordinal) and Numerical (discrete, continuous)

Tables & Graphs: Interpreting bar graphs, histograms, pie charts, line graphs, box plots,
scatterplots

Measures of Central Tendency: Mean, median, and mode

Measures of Dispersion: Range, interquartile range (IQR), variance, standard deviation

Data Representation:

Box plots show median, quartiles, and outliers.

Histograms display frequency distributions for numerical data.
Scatterplots are used for correlation analysis between two quantitative variables.

Trends and Outliers: Recognizing patterns and detecting data points that deviate significantly
from the rest

Correlation vs Causation: Correlation indicates association, not cause.

👉 Example: A box plot shows the median score of a test is 70, with an IQR of 20. This means the middle
50% of scores lie between 60 and 80.

Page 54 of 73
🔢 IMAT-Style MCQs:

1. Which of the following is a measure of central tendency?

a. Range
b. Median
c. Interquartile range
d. Standard deviation

2. In a box plot, the box represents:

a. Maximum and minimum values

b. 50% of the data
c. Mean and standard deviation
d. All data points

3. Which graph is most appropriate for comparing parts of a whole?

a. Histogram
b. Line graph
c. Pie chart
d. Scatterplot

4. A histogram with a peak on the left and tail on the right is:

a. Symmetric
b. Uniform
c. Right-skewed
d. Left-skewed

5. Which of the following indicates the spread of a dataset?

a. Mean
b. Median
c. Mode
d. Standard deviation

6. What does a high standard deviation indicate?

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 a. The data is tightly clustered
b. The data is widely spread
c. The data has no variation
d. All data points are equal

7. Which of these graphs is best for identifying correlation between two

variables?

a. Histogram
b. Pie chart
c. Box plot
d. Scatterplot

8. If the mean is 70 and the standard deviation is 10, a score of 90 is how

many standard deviations above the mean?

a. 1
b. 2
c. 3
d. 4

9. What does an outlier in a box plot usually appear as?

a. A dot outside the whiskers

b. A larger box
c. A gap in the whiskers
d. The midpoint line

10. A line graph is used to display:

a. Part-to-whole relationships
b. Trends over time
c. Frequency distributions
d. Probability models

11. The IQR of a data set is 15. What does this represent?

a. Mean value
b. Middle 50% of data
c. Total spread of data

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 d. Difference between max and min

12. In a scatterplot, data points that follow a downward trend suggest:

a. Positive correlation
b. No correlation
c. Negative correlation
d. Inverse variance

13. A symmetrical distribution has:

a. Equal mean and mode

b. Equal mean, median, and mode
c. Higher mode than mean
d. Lower median than mode

14. If Q1 = 25 and Q3 = 75, what is the IQR?

a. 25
b. 50
c. 100
d. 75

15. Which of the following would be most affected by a single extreme

value?

a. Median
b. Mode
c. Mean
d. Interquartile range

16. Which graph type is ideal for displaying frequency of discrete data?

a. Pie chart
b. Histogram
c. Bar chart
d. Line graph

17. The purpose of a trend line in a scatterplot is to:

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 a. Connect all points
b. Smooth the data
c. Show direction of relationship
d. Calculate median

18. What does a correlation coefficient of −1 indicate?

a. No correlation
b. Perfect negative correlation
c. Strong positive correlation
d. Weak negative correlation

19. Which is true about categorical data?

a. It can be counted or measured

b. It is non-numerical
c. It is always ordinal
d. It follows a normal distribution

20. The central line inside a box plot box shows:

a. Mean
b. Median
c. Mode
d. Range

21. Which of the following best represents the variability in a data set?

a. Median
b. Range
c. Mode
d. Frequency

22. If a bar chart displays categories of fruits, what kind of data is it

showing?

a. Ordinal
b. Nominal
c. Discrete
d. Continuous

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23. A bell-shaped curve on a histogram usually suggests:

a. Uniform distribution
b. Normal distribution
c. Skewed distribution
d. Categorical data

24. What is the median of the data set: {3, 7, 9, 10, 15, 18, 21}?

a. 9
b. 10
c. 11
d. 15

25. A negatively skewed histogram would most likely have:

a. Mean > Median

b. Median > Mean
c. Mode > Median
d. Median = Mode

26. What does a steep slope in a line graph usually indicate?

a. Slow change
b. Constant values
c. Rapid change
d. No variation

27. Which of the following is used to display percentages in sectors?

a. Pie chart
b. Bar graph
c. Histogram
d. Box plot

28. Which measure is best when the data is heavily skewed?

a. Mean
b. Median
c. Mode

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 d. Range

29. If the minimum is 15 and the maximum is 45, what is the range?

a. 30
b. 25
c. 60
d. 15

30. Which measure provides the average squared distance from the
mean?

a. Range
b. Variance
c. Standard deviation
d. Mean absolute deviation

31. A scatterplot with no clear pattern shows:

a. Positive correlation
b. Negative correlation
c. No correlation
d. Inverse trend

32. In a class of 30 students, test scores were recorded and the highest
score was 98. This value is:

a. Median
b. Mean
c. Mode
d. Maximum

33. The midpoint of a class interval in a frequency table is called:

a. Mean
b. Median
c. Class mark
d. Range

34. Which tool is best to detect an outlier quickly?

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 a. Bar graph
b. Box plot
c. Pie chart
d. Frequency table

35. A histogram differs from a bar graph because:

a. Bars touch in a histogram

b. Bar graphs show frequency
c. Histograms are for categorical data
d. Histograms use colors

36. Which of the following data types is best visualized using a pie
chart?

a. Categorical
b. Continuous
c. Discrete
d. Ordinal

37. What does the spread of a box plot tell us?

a. Correlation
b. Central tendency
c. Dispersion
d. Skewness

38. If the mode of a data set is much higher than the mean, it may be:

a. Positively skewed
b. Negatively skewed
c. Normally distributed
d. Uniformly distributed

39. In statistics, frequency means:

a. Average
b. The number of times a value occurs
c. Median value
d. Maximum value

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40. The data point that occurs most frequently is:

a. Median
b. Mode
c. Mean
d. Range

41. What is the mean of the dataset {6, 8, 10, 12, 14}?

a. 10
b. 12
c. 11
d. 9

42. Which graph would you use to identify a trend in temperature over
several months?

a. Bar chart
b. Line graph
c. Pie chart
d. Histogram

43. A scatterplot shows a tight cluster of points sloping upward. This

indicates:

a. Weak negative correlation

b. Strong positive correlation
c. No correlation
d. Skewed distribution

44. The highest bar in a histogram represents:

a. The class with the most data points

b. The median
c. The mode
d. The average

45. What does a pie chart with nearly equal slices indicate?

a. Uneven frequency distribution

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 b. Even distribution of categories
c. Skewed data
d. Negative trend

46. A symmetrical bell-shaped curve is a feature of:

a. Normal distribution
b. Skewed distribution
c. Uniform distribution
d. Bimodal distribution

47. Which value changes the most in a dataset with an outlier?

a. Median
b. Mean
c. Mode
d. Range

48. In a frequency table, the total number of observations is calculated

by:

a. Finding the mean

b. Summing all frequencies
c. Dividing by the number of classes
d. Finding the range

49. A box plot with a long whisker on the left suggests:

a. Positive skew
b. Negative skew
c. Symmetry
d. No outliers

50. Which measure is least useful when comparing the variability of two
data sets with the same mean?

a. Standard deviation
b. Interquartile range
c. Median
d. Variance

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Chapter 7: Measures and Units

📘 Theory & Explanation:

This chapter deals with measurement systems, unit conversions, and interpreting physical quantities. In
IMAT, this section often features practical math—converting units, estimating measurements, and
applying formulas involving dimensional analysis.

Key Concepts:

Basic Units of Measurement:

Length: meter (m)

Mass: kilogram (kg)
Time: second (s)
Temperature: kelvin (K)
Volume: liter (L) or cubic meters (m³)

SI Unit Prefixes:

milli (10⁻³), centi (10⁻²), deci (10⁻¹), kilo (10³), mega (10⁶)

Derived Units:

Speed = m/s
Acceleration = m/s²
Force = Newton (kg·m/s²)
Pressure = Pascal (N/m²)

Dimensional Analysis:

Used to check the consistency of equations

Helps convert between units using conversion factors

Converting Units:

Multiply or divide by powers of ten

Use ratios (e.g., 1 inch = 2.54 cm)

👉 Example: To convert 72 km/h to m/s:

$72 km/h = 72 × rac{1000}{3600} = 20 m/s$

🔢 IMAT-Style MCQs:

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1. What is the SI unit of force?

a. Joule
b. Watt
c. Newton
d. Pascal

2. Convert 5 kilometers into meters.

a. 50
b. 500
c. 5000
d. 50000

3. If speed = distance/time, the SI unit for speed is:

a. m²/s
b. m/s
c. m/s²
d. kg·m/s

4. 1 liter is equivalent to how many cubic centimeters?

a. 10
b. 100
c. 1000
d. 10000

5. A man walks 1.8 kilometers. How many meters does he walk?

a. 180
b. 1800
c. 18
d. 18000

6. What is the SI unit of pressure?

a. Joule
b. Pascal
c. Watt

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 d. Newton

7. 1 megabyte is equivalent to how many bytes?

a. 1,000
b. 10,000
c. 1,000,000
d. 10,000,000

8. Which of the following is a derived SI unit?

a. Meter
b. Kilogram
c. Second
d. Newton

9. If density = mass/volume, what is its SI unit?

a. kg/m³
b. kg·m/s
c. N/m²
d. g/cm³

10. Convert 1200 milliliters to liters.

a. 0.12
b. 1.2
c. 12
d. 120

11. If 1 inch = 2.54 cm, how many centimeters are in 12 inches?

a. 30.48
b. 28.48
c. 25.40
d. 20.48

12. Which of the following quantities is dimensionless?

a. Speed

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 b. Acceleration
c. Angle (in radians)
d. Force

13. The SI unit of work is:

a. Newton
b. Pascal
c. Joule
d. Watt

14. Convert 0.75 kilograms to grams.

a. 7.5
b. 75
c. 750
d. 7500

15. 1 hour is equivalent to how many seconds?

a. 360
b. 3600
c. 36,000
d. 60

16. Which prefix represents one-millionth?

a. Micro
b. Milli
c. Nano
d. Pico

17. What is the SI unit of electric current?

a. Coulomb
b. Volt
c. Ampere
d. Ohm

18. Convert 4.5 hours into seconds.

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 a. 16200
b. 18000
c. 14400
d. 12600

19. A rectangular tank has a volume of 2.5 m³. How many liters does it
hold?

a. 250
b. 2500
c. 25000
d. 250000

20. If a car travels at 72 km/h, what is its speed in m/s?

a. 10
b. 20
c. 30
d. 40

21. What is the SI unit of power?

a. Watt
b. Volt
c. Joule
d. Ampere

22. Convert 150 centimeters to meters.

a. 0.15
b. 1.5
c. 15
d. 1500

23. A force of 10 N is applied over an area of 2 m². What is the pressure?

a. 5 Pa
b. 20 Pa
c. 0.2 Pa
d. 12 Pa

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24. Which SI prefix means one-billionth?

a. Milli
b. Micro
c. Nano
d. Pico

25. 2.5 km is equal to:

a. 250 m
b. 2500 m
c. 25000 m
d. 25 m

26. What unit is used to measure frequency?

a. Ampere
b. Hertz
c. Watt
d. Newton

27. Convert 2500 grams to kilograms.

a. 0.25
b. 2.5
c. 25
d. 250

28. Which of the following has the same dimension as energy?

a. Force × distance
b. Mass × acceleration
c. Pressure × volume
d. Both a and c

29. 5 minutes is how many seconds?

a. 300
b. 500
c. 600

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 d. 120

30. Which is the correct derived SI unit for electric resistance?

a. Ohm
b. Volt
c. Ampere
d. Coulomb

31. What is the dimensional formula for speed?

a. [M L T⁻¹]
b. [L T⁻¹]
c. [L T]
d. [M L T]

32. Convert 3.6 MJ (megajoules) to joules.

a. 3600
b. 3,600,000
c. 360
d. 36,000

33. A room has dimensions 5 m × 4 m × 3 m. What is its volume in liters?

a. 600
b. 6000
c. 60,000
d. 600,000

34. Which quantity is dimensionless?

a. Density
b. Strain
c. Pressure
d. Velocity

35. Convert 90 km/h into m/s.

a. 25

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 b. 20
c. 15
d. 30

36. The SI unit of temperature is:

a. Celsius
b. Fahrenheit
c. Kelvin
d. Calorie

37. If power = work/time, what is the SI unit of power?

a. Joule·second
b. Watt
c. Newton·meter
d. Joule/hour

38. The density of water is approximately:

a. 1 kg/m³
b. 10 kg/m³
c. 100 kg/m³
d. 1000 kg/m³

39. Convert 2 hours 30 minutes into seconds.

a. 7500
b. 9000
c. 7200
d. 5400

40. Which of the following is NOT a derived unit?

a. Joule
b. Pascal
c. Kelvin
d. Watt

41. What is the unit of luminous intensity in the SI system?

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 a. Candela
b. Lux
c. Lumen
d. Watt

42. Which of the following conversions is correct?

a. 1 kg = 100 g
b. 1 L = 1000 mL
c. 1 m = 10 cm
d. 1 h = 1000 s

43. If you multiply voltage and current, the unit of the result is:

a. Joule
b. Watt
c. Coulomb
d. Volt

44. Convert 5.4 km to meters.

a. 540
b. 5400
c. 54000
d. 5.4

45. The SI unit of capacitance is:

a. Farad
b. Coulomb
c. Ampere
d. Ohm

46. What is the SI unit for pressure?

a. N/m²
b. kg·m/s²
c. J/m³
d. N/m

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47. What is the unit of energy commonly used in food labeling?

a. Calorie
b. Joule
c. Watt
d. Newton

48. Which is greater: 3 hours or 10,000 seconds?

a. 3 hours
b. 10,000 seconds
c. Both equal
d. Cannot determine

49. What quantity is measured in m²?

a. Volume
b. Speed
c. Area
d. Force

50. Which of the following has units of kg·m/s?

a. Force
b. Work
c. Momentum
d. Acceleration

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