Class 10 Maths

1. 1.Find the LCM of 12 and 18.

2. 2.Find the HCF of 616 and 32 using Euclid's algorithm.

3. 3.√2 is neither a whole number nor a fraction, so it sits between two ticks on this line. Tap the tick just below it.

   Mark the line with an X.

4. 4.Find the HCF of 96 and 404 using Euclid's algorithm.

5. 5.Sort each number by whether it is rational or irrational.

   Groups: Rational · Irrational

   • 22/7
   • √5
   • √7
   • √9
   • √3
   • 0.75

6. 6.Which of these numbers is irrational?

   • a) √4
   • b) √2
   • c) 0.25
   • d) 7/2

7. 7.For any two numbers, HCF × LCM equals the product of the numbers. The HCF of two numbers is 9 and their LCM is 360. One of the numbers is 45. What is the other?

8. 8.13/125 has a decimal expansion that stops. After how many decimal places does it stop?

   • a) 3
   • b) 2
   • c) 1
   • d) 4

Real numbers · Class 10 Maths · www.arenapublications.com/learn

1. 1.Two adult tickets and one child ticket cost 900 ₹. One adult ticket and one child ticket cost 500 ₹. What does one child ticket cost? Give just the number.

2. 2.Two adult tickets and one child ticket cost 900 ₹. One adult ticket and one child ticket cost 500 ₹. What does one adult ticket cost? Give just the number.

3. 3.The sum of two numbers is 25 and their difference is 7. What is the larger number?

4. 4.Solve the pair x + y = 10 and x - y = 4. What is x?

5. 5.Solve the pair x + y = 10 and x - y = 4. What is y?

6. 6.Solve the pair 3x + 2y = 12 and x = 2. What is y?

7. 7.Solve the pair 5x - 2y = 16 and x + 2y = 8. What is x?

8. 8.Solve the pair 2x + y = 11 and x - y = 1. What is x?

Pair of linear equations · Class 10 Maths · www.arenapublications.com/learn

1. 1.Solve x² - 9 = 0. Give the positive root.

2. 2.Match each quadratic to its factorised form.

   • x² + 5x + 6
   • x² - 5x + 6
   • x² - 4
   • x² + 4x + 4

   • (x + 2)(x + 2)
   • (x + 2)(x - 2)
   • (x + 2)(x + 3)
   • (x - 2)(x - 3)

3. 3.Solve x² - 5x + 6 = 0. Give the smaller root.

4. 4.What is the discriminant, b² - 4ac, of x² - 3x + 5 = 0?

5. 5.Solve x² + 7x + 12 = 0. Give the smaller root.

6. 6.For x² - 7x + 10 = 0, what is the product of the two roots?

7. 7.The product of two consecutive whole numbers is 42. What is the smaller number?

8. 8.What is the discriminant, b² - 4ac, of x² + 4x + 4 = 0?

Quadratic equations · Class 10 Maths · www.arenapublications.com/learn

1. 1.In the AP 3, 7, 11, 15, ... what is the 10th term?

2. 2.In the AP 3, 7, 11, 15, ... what is the common difference?

3. 3.In the AP 20, 17, 14, ... what is the 8th term?

4. 4.In the AP 20, 17, 14, ... what is the common difference?

5. 5.Find the sum of the first 15 terms of 1, 3, 5, 7, ...

6. 6.In the AP 5, 8, 11, ... what is the 20th term?

7. 7.Find the sum of the first 10 terms of 2, 4, 6, 8, ...

8. 8.The first term of an AP is 7 and the common difference is 5. What is the 4th term?

Arithmetic progressions · Class 10 Maths · www.arenapublications.com/learn

1. 1.How far is the point (7, 24) from the origin? Give the answer in units.

2. 2.Find the midpoint of the segment joining (2, 3) and (8, 11). What is its y-coordinate?

3. 3.The point P divides the segment joining (1, 2) and (7, 11) in the ratio 2 : 1, measured from (1, 2). What is the x-coordinate of P?

4. 4.What is the area of the triangle whose vertices are (1, 2), (2, 4) and (3, 6)? Give the answer in square units.

   • a) 2
   • b) 0
   • c) 1
   • d) 3

5. 5.Which of these points is the same distance from the origin as (3, 4)?

   • a) (1, 6)
   • b) (5, 0)
   • c) (2, 3)
   • d) (4, 4)

6. 6.This line runs from 0 to 10. Tap the point that divides it in the ratio 2 : 3, measured from 0.

   Mark the line with an X.

7. 7.Find the distance between the points (1, 2) and (4, 6). Give the answer in units.

8. 8.Find the area of the triangle whose vertices are (2, 1), (8, 1) and (2, 9). Give the answer in square units.

Distance and section formulas · Class 10 Maths · www.arenapublications.com/learn

1. 1.In triangle ABC, DE is parallel to BC. AD is 2 cm, DB is 4 cm and AE is 3 cm. How long is EC, in centimetres?

2. 2.Are any two squares similar to each other?

   • a) Only if they are the same size
   • b) Only if they are drawn on grid paper
   • c) Yes, always
   • d) No, never

3. 3.Which of these is true of two similar triangles?

   • a) They must be right-angled
   • b) They must be the same size
   • c) Matching sides are equal
   • d) Matching sides are in the same ratio

4. 4.Two similar triangles have sides in the ratio 1:4. The area of the smaller is 5 square centimetres. What is the area of the larger, in square centimetres?

5. 5.Sort each pair of shapes by whether they must always be similar.

   Groups: Always similar · Not always similar

   • Two rectangles
   • Two squares
   • Two rhombuses
   • Two equilateral triangles
   • Two circles
   • Two isosceles triangles

6. 6.The Basic Proportionality Theorem says that a line drawn parallel to one side of a triangle...

   • a) cuts the other two sides exactly in half
   • b) divides the other two sides in the same ratio
   • c) is equal in length to the side it is parallel to
   • d) makes the triangle isosceles

7. 7.Two similar triangles have sides in the ratio 3:5. The perimeter of the smaller is 18 cm. What is the perimeter of the larger, in centimetres?

8. 8.Two similar triangles have sides in the ratio on the left. Match it to the ratio of their areas.

   • 1:2
   • 1:3
   • 2:3
   • 3:4
   • 1:5

   • 1:25
   • 1:4
   • 9:16
   • 4:9
   • 1:9

Similar triangles · Class 10 Maths · www.arenapublications.com/learn

1. 1.How many points does a tangent share with its circle?

   • a) Infinitely many
   • b) 1
   • c) 2
   • d) 0

2. 2.PA and PB are the two tangents drawn from a point P, and PA is 12 cm long. What is the total length of PA and PB, in centimetres?

3. 3.A tangent from a point P touches a circle with centre O at A. The radius OA is 8 cm and the hypotenuse OP is 17 cm. How long is the tangent PA, in centimetres?

4. 4.A tangent PA is 24 cm long and the hypotenuse OP of triangle OAP is 25 cm. How long is the radius OA, in centimetres?

5. 5.OAPB is a quadrilateral with right angles at A and B, and its angle at P is 70°. What is its angle at O, in degrees?

6. 6.Sort each point by how many tangents can be drawn from it to a given circle.

   Groups: No tangents · Exactly one tangent · Exactly two tangents

   • A point outside the circle
   • A point inside the circle
   • A point on the circle itself
   • The centre of the circle

7. 7.Three straight lines are drawn on this circle. Tap the tangent.

   Write the number of the part.

8. 8.Two tangents are drawn from a point P to a circle, touching it at A and B. How does PB compare with PA?

   • a) It depends on the radius
   • b) PB is half of PA
   • c) PB is the same length as PA
   • d) PB is twice PA

Circles and tangents · Class 10 Maths · www.arenapublications.com/learn

1. 1.What is tan 30°?

   • a) √3/2
   • b) 1/2
   • c) √3
   • d) 1/√3

2. 2.For any angle θ, what does sin²θ + cos²θ come to?

3. 3.In a right-angled triangle the side opposite an angle is 3 cm and the side next to it is 4 cm. What is the tangent of that angle? Give your answer as a fraction.

4. 4.What is sin 60°?

   • a) 1/2
   • b) 1/√3
   • c) √3/2
   • d) √3

5. 5.Match each trigonometric ratio to its value.

   • sin 30°
   • cos 30°
   • tan 45°
   • sin 0°
   • tan 60°

   • 1
   • √3
   • 0
   • √3/2
   • 1/2

6. 6.What is cos 0°?

7. 7.What is sin 90°?

8. 8.What is sin 30°? Give your answer as a fraction.

Introduction to trigonometry · Class 10 Maths · www.arenapublications.com/learn

1. 1.A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. Take √3 = 1.73. How far up the wall does it reach, in metres?

2. 2.A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. How far is the bottom of the ladder from the wall, in metres?

3. 3.A tree is 20 m tall. From a point on level ground the angle of elevation of its top is 30°. Take √3 = 1.73. How far is that point from the base of the tree, in metres?

4. 4.From a window you look down at a car, and from the car someone looks up at the window. How do the angle of depression and the angle of elevation compare?

   • a) The angle of elevation is larger
   • b) They are equal
   • c) They add up to 90°
   • d) The angle of depression is larger

5. 5.Match each angle to its tangent.

   • 30°
   • 45°
   • 60°

   • 1
   • 1/√3
   • √3

6. 6.A pole stands upright on level ground. From a point 10 m from its base, the angle of elevation of the top of the pole is 45°. How tall is the pole, in metres?

7. 7.The Sun is 45° above the horizon. How long a shadow does an upright pole 12 m tall cast on level ground, in metres?

8. 8.The angle of elevation of the top of a tower from a point on level ground is 60°, and the point is 45 m from the base of the tower. Take √3 = 1.73. How tall is the tower, in metres?

Heights and distances · Class 10 Maths · www.arenapublications.com/learn

1. 1.Match each sector to its area, in square centimetres. Take π = 22/7.

   • radius 7 cm, angle 45°
   • radius 7 cm, angle 135°
   • radius 14 cm, angle 180°
   • radius 21 cm, angle 45°

   • 19.25
   • 308
   • 57.75
   • 173.25

2. 2.A circle has been cut into three sectors. Tap the sector with the largest area.

   Write the number of the part.

3. 3.A sector of a circle of radius 7 cm has an angle of 90° at the centre. Take π = 22/7. What is its area, in square centimetres?

4. 4.The minute hand of a clock is 21 cm long. Take π = 22/7. What area does it sweep in 5 minutes, in square centimetres?

5. 5.A sector of a circle of radius 7 cm has an angle of 90° at the centre. Take π = 22/7. How long is its arc, in centimetres?

6. 6.A sector of a circle of radius 6 cm has an angle of 60° at the centre. Take π = 3.14. What is its area, in square centimetres?

7. 7.Through how many degrees does the minute hand of a clock turn in 20 minutes?

8. 8.A sector of a circle of radius 21 cm has an angle of 60° at the centre. Take π = 22/7. What is the perimeter of the sector, in centimetres?

Areas related to circles · Class 10 Maths · www.arenapublications.com/learn

1. 1.A solid is a cylinder of radius 7 cm and height 10 cm with a cone of radius 7 cm and height 12 cm standing on top of it. Take π = 22/7. What is the volume of the cylinder part, in cubic centimetres?

2. 2.A toy is a cone standing on a hemisphere, both of radius 7 cm. The cone is 24 cm tall. What is the cone's slant height, in centimetres?

3. 3.A solid is a cylinder of radius 7 cm and height 10 cm with a cone of radius 7 cm and height 12 cm standing on top of it. Take π = 22/7. What is the volume of the cone part, in cubic centimetres?

4. 4.A solid is a cylinder of radius 7 cm and height 10 cm with a cone of radius 7 cm and height 12 cm standing on top of it. Take π = 22/7. What is the total volume of the solid, in cubic centimetres?

5. 5.A cone has a radius of 7 cm and a slant height of 25 cm. Take π = 22/7. What is its curved surface area, in square centimetres?

6. 6.A toy is a cone of slant height 25 cm standing on a hemisphere, both of radius 7 cm. Take π = 22/7. What is the total surface area of the toy, in square centimetres?

7. 7.It takes exactly three coneloads to fill a cylinder of the same radius and height. That cylinder holds 1848 cubic centimetres. How much does the cone hold, in cubic centimetres?

8. 8.A cylinder of radius 7 cm and height 10 cm has a cone of radius 7 cm and slant height 25 cm standing on top of it. Its outside is the cone's curved surface, the cylinder's curved surface and the circular base. Take π = 22/7. What is the total surface area, in square centimetres?

Combined solids · Class 10 Maths · www.arenapublications.com/learn

1. 1.What is the class mark of the class 40–70?

2. 2.Which average of grouped data can be read straight off an ogive?

   • a) The mode
   • b) The mean
   • c) The median
   • d) The range

3. 3.A less-than ogive is drawn for 50 observations. At what cumulative frequency do you read across the curve to find the median?

4. 4.A grouped table has the classes 0–10, 10–20 and 20–30 with frequencies 3, 5 and 2. What is the mean, using class marks?

5. 5.A grouped table has the classes 0–10, 10–20, 20–30 and 30–40 with frequencies 2, 4, 3 and 1. What is the cumulative frequency up to 20?

6. 6.A grouped table has the classes 0–10, 10–20, 20–30 and 30–40 with frequencies 2, 4, 3 and 1. Which class has the highest frequency? Give its lower limit.

7. 7.Match each class to its class mark.

   • 0–10
   • 20–40
   • 25–45
   • 50–70

   • 35
   • 30
   • 5
   • 60

8. 8.A grouped table has the classes 0–10, 10–20, 20–30 and 30–40 with frequencies 2, 4, 3 and 1. What is the total frequency?

Statistics of grouped data · Class 10 Maths · www.arenapublications.com/learn

1. 1.A card is drawn from a full pack of 52. What is the probability it is red? Give your answer as a fraction.

2. 2.A fair die is rolled. What is the probability of getting a 4? Give your answer as a fraction.

3. 3.A fair coin is tossed. What is the probability of getting a head? Give your answer as a fraction.

4. 4.What is the probability of an event that is certain to happen?

   • a) 0.5
   • b) It depends on the event
   • c) 1
   • d) 0

5. 5.A fair die is rolled. What is the probability of getting an even number? Give your answer as a fraction.

6. 6.A bag holds 3 red balls and 5 blue balls. One is taken out without looking. What is the probability it is blue? Give your answer as a fraction.

7. 7.Which of these could never be a probability?

   • a) 0
   • b) 0.25
   • c) 1
   • d) 1.5

8. 8.A fair die is rolled. What is the probability of getting a number greater than 4? Give your answer as a fraction.

Probability · Class 10 Maths · www.arenapublications.com/learn