PM Review — Integers

Question 1 Difficulty 1

What is 7 + 5?

A 11
B 12
C 13
D 14

💡 Explanation 7 + 5 equals 12.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 2 Difficulty 1

What is the value of 9 - 3?

A 5
B 6
C 7
D 8

💡 Explanation 9 - 3 equals 6.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 3 Difficulty 1

What is 6 x 4?

A 20
B 24
C 18
D 30

💡 Explanation 6 multiplied by 4 equals 24.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 4 Difficulty 1

What is 15 ÷ 3?

A 5
B 6
C 7
D 8

💡 Explanation 15 divided by 3 equals 5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 5 Difficulty 1

What is the perimeter of a square with side length 4 cm?

A 12 cm
B 16 cm
C 20 cm
D 8 cm

💡 Explanation Perimeter of a square = 4 x side length. Here, 4 x 4 = 16 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 6 Difficulty 1

What is the area of a rectangle with length 5 cm and width 3 cm?

A 15 cm²
B 10 cm²
C 8 cm²
D 20 cm²

💡 Explanation Area of a rectangle = length x width. Here, 5 x 3 = 15 cm².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 7 Difficulty 1

What is the next number in the series: 2, 4, 6, ...?

A 7
B 8
C 9
D 10

💡 Explanation The series increases by 2. So, 6 + 2 = 8.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 8 Difficulty 1

What is the smallest prime number?

A 1
B 2
C 3
D 4

💡 Explanation The smallest prime number is 2.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 9 Difficulty 1

What is the value of 3²?

A 6
B 9
C 12
D 15

💡 Explanation 3 squared (3²) equals 9.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 10 Difficulty 1

What is the sum of angles in a triangle?

A 90°
B 180°
C 270°
D 360°

💡 Explanation The sum of angles in a triangle is always 180°.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 11 Difficulty 2

What is the least common multiple (LCM) of 4 and 6?

A 12
B 24
C 6
D 4

💡 Explanation The LCM of 4 and 6 is 12.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 12 Difficulty 2

What is the greatest common divisor (GCD) of 12 and 16?

A 2
B 4
C 6
D 8

💡 Explanation The GCD of 12 and 16 is 4.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 13 Difficulty 2

What is 25% of 200?

A 50
B 60
C 70
D 80

💡 Explanation 25% of 200 is (25/100) * 200 = 50.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 14 Difficulty 2

If a shirt costs ₹400 after a 20% discount, what was the original price?

A ₹500
B ₹450
C ₹400
D ₹350

💡 Explanation Let the original price be x. 80% of x = 400. So, x = ₹500.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 15 Difficulty 2

What is the value of the expression: 5 + 3 x 2?

A 11
B 16
C 14
D 8

💡 Explanation According to the order of operations, 3 x 2 = 6, then 5 + 6 = 11.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 16 Difficulty 2

What is the next number in this sequence: 3, 6, 9, 12, ...?

A 13
B 14
C 15
D 16

💡 Explanation The series increases by 3 each time. So, 12 + 3 = 15.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 17 Difficulty 2

What is the area of a triangle with base 10 cm and height 5 cm?

A 25 cm²
B 30 cm²
C 50 cm²
D 15 cm²

💡 Explanation Area of a triangle = (1/2) x base x height = (1/2) x 10 x 5 = 25 cm².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 18 Difficulty 2

What is the volume of a cube with side length 3 cm?

A 9 cm³
B 27 cm³
C 18 cm³
D 12 cm³

💡 Explanation Volume of a cube = side³ = 3³ = 27 cm³.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 19 Difficulty 2

What is the mode of the following set of numbers: 2, 3, 4, 4, 5?

A 2
B 3
C 4
D 5

💡 Explanation The mode is the number that appears most frequently. Here, 4 appears twice.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 20 Difficulty 2

If a car travels 60 km in 1 hour, how far will it travel in 3 hours?

A 120 km
B 180 km
C 200 km
D 150 km

💡 Explanation Distance = speed x time = 60 km/h x 3 h = 180 km.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 21 Difficulty 3

What is the value of x in the equation 2x + 3 = 11?

A 4
B 5
C 6
D 3

💡 Explanation Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 22 Difficulty 3

If the angles of a triangle are in the ratio 2:3:4, what is the largest angle?

A 60°
B 80°
C 90°
D 100°

💡 Explanation Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180. So, x = 20. Largest angle = 4x = 80°.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 23 Difficulty 3

What is the probability of rolling a 3 on a standard six-sided die?

A 1/6
B 1/3
C 1/4
D 1/5

💡 Explanation There is 1 favorable outcome (rolling a 3) out of 6 total outcomes, so the probability is 1/6.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 24 Difficulty 3

If a bag contains 3 red, 5 blue, and 2 green balls, what is the probability of drawing a red ball?

A 1/5
B 1/2
C 3/10
D 3/5

💡 Explanation Total balls = 3 + 5 + 2 = 10. Probability of red = 3/10.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 25 Difficulty 3

What is the area of a circle with radius 7 cm?

A 154 cm²
B 140 cm²
C 144 cm²
D 150 cm²

💡 Explanation Area = πr². Using π ≈ 3.14, Area = 3.14 x 7² = 3.14 x 49 = 153.86 cm², approx. 154 cm².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 26 Difficulty 3

What is the surface area of a cube with side length 4 cm?

A 64 cm²
B 48 cm²
C 32 cm²
D 36 cm²

💡 Explanation Surface area of a cube = 6 x side² = 6 x 4² = 6 x 16 = 96 cm².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 27 Difficulty 3

What is the value of 2x - 3 = 7?

A 4
B 5
C 6
D 10

💡 Explanation Add 3 to both sides: 2x = 10. Then divide by 2: x = 5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 28 Difficulty 3

What is the mean of the set of numbers: 2, 3, 6, 8?

A 4
B 5
C 6
D 7

💡 Explanation Mean = (2 + 3 + 6 + 8) / 4 = 19 / 4 = 4.75, approx. 5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 29 Difficulty 3

If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, what type of triangle is it?

A Acute
B Right
C Obtuse
D Equilateral

💡 Explanation This is a right triangle because 5² + 12² = 13².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 30 Difficulty 3

What is the circumference of a circle with diameter 10 cm?

A 31.4 cm
B 25.12 cm
C 20 cm
D 15.7 cm

💡 Explanation Circumference = πd = 3.14 x 10 = 31.4 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 31 Difficulty 4

What is the solution for x in the equation 3(x - 4) = 9?

A 1
B 5
C 7
D 4

💡 Explanation First divide by 3: x - 4 = 3. Then add 4: x = 7.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 32 Difficulty 4

In a right triangle, if one leg is 6 cm and the hypotenuse is 10 cm, what is the length of the other leg?

A 4 cm
B 5 cm
C 8 cm
D 7 cm

💡 Explanation Using Pythagoras' theorem: c² = a² + b². 10² = 6² + b², thus 100 = 36 + b², so b² = 64, b = 8 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 33 Difficulty 4

If 5x + 3 = 2x + 21, what is the value of x?

A 3
B 5
C 6
D 4

💡 Explanation Rearranging gives 5x - 2x = 21 - 3, so 3x = 18, thus x = 6.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 34 Difficulty 4

What is the area of a trapezium with bases 10 cm and 6 cm, and height 4 cm?

A 32 cm²
B 40 cm²
C 42 cm²
D 36 cm²

💡 Explanation Area = 1/2 * (base1 + base2) * height = 1/2 * (10 + 6) * 4 = 32 cm².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 35 Difficulty 4

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

A 720°
B 540°
C 360°
D 180°

💡 Explanation The sum of interior angles = (n - 2) × 180°, where n is the number of sides. For a hexagon, 4 × 180° = 720°.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 36 Difficulty 4

What is the value of x in the proportion 3/4 = x/20?

A 15
B 12
C 18
D 16

💡 Explanation Cross-multiply: 3 * 20 = 4 * x, so 60 = 4x. Thus, x = 60/4 = 15.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 37 Difficulty 4

If a cylinder has a radius of 3 cm and a height of 5 cm, what is its volume?

A 45 cm³
B 60 cm³
C 75 cm³
D 90 cm³

💡 Explanation Volume of a cylinder = πr²h = 3.14 * 3² * 5 = 45 cm³.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 38 Difficulty 4

What is the distance between the points (2, 3) and (5, 7)?

A 4
B 5
C 6
D 7

💡 Explanation Using the distance formula: √[(x2 - x1)² + (y2 - y1)²] = √[(5 - 2)² + (7 - 3)²] = √(9 + 16) = √25 = 5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 39 Difficulty 4

What is the equivalent fraction of 1/2 with a denominator of 8?

A 3/8
B 4/8
C 5/8
D 6/8

💡 Explanation To find an equivalent fraction with a denominator of 8, multiply both the numerator and denominator of 1/2 by 4: (1*4)/(2*4) = 4/8.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 40 Difficulty 4

What is the area of a circle with diameter 10 cm?

A 78.5 cm²
B 50 cm²
C 100 cm²
D 31.4 cm²

💡 Explanation Area = πr². Diameter = 10 cm, so radius = 5 cm. Area = π * 5² = π * 25 = 78.5 cm².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?