Mathematics Practice Questions: This collection of advanced maths practice questions is designed to test and enhance the problem-solving skills of students.

These questions cover a wide range of mathematical topics, including algebra, geometry, and arithmetic operations, tailored for students seeking to deepen their understanding of mathematical concepts.

Mathematics Practice Questions

Q.1: A store is offering a 20% discount on all items. If an additional 5% off is applied at the register, what is the final cost of an item originally priced at ₹250?

A. ₹200
B. ₹190
C. ₹180
D. ₹175

Q.2: If 3x-9=0, then x equals:

A. 0
B. 2
C. 3
D. 6

Q.3: Which of the following is NOT equivalent to 45(13 + 11)?

A. 45 * 24
B. 13(45 + 11)
C. 45 * 13 + 45 * 11
D. 585 + 495

Q.4: One angle of a triangle is 90° and another is 45°. The measure of the third angle is:

A. 45°
B. 50°
C. 55°
D. 60°

Q.5: Converting 3 kilograms into grams results in:

A. 3000 grams
B. 30000 grams
C. 300 grams
D. 30 grams

Q.6: The graph showing the increase in sales over the last 5 years depicts a 100% increase in 2020. Which year had the lowest sales?

A. 2016
B. 2017
C. 2018
D. 2019

Q.7: The largest drop in temperature over a week occurred between:

A. Monday and Tuesday
B. Tuesday and Wednesday
C. Wednesday and Thursday
D. Thursday and Friday

Q.8: Calculate the mean number of goals scored in a season with scores of 30, 40, 50, 60, and 70.

A. 45
B. 50
C. 55
D. 60

Q.9: Which of the following equals 6.5×10^-3?

A. 0.0065
B. 0.065
C. 65
D. 650

Q.10: A map scale shows 1 inch equals 5 miles. The distance between City A and City B on the map is 8 inches. How many real miles are between the two cities?

A. 35 miles
B. 40 miles
C. 45 miles
D. 55 miles

Q.11: The correct graph for the inequalities x>2 and x<5 would be:

A. A line segment from 2 to 5
B. Rays extending from 2 to the right and from 5 to the left
C. A ray from 2 to the right
D. A ray from 5 to the left

Q.12: How many 4 inch cubes can fit into a box that is 8 inches by 12 inches by 4 inches?

A. 6
B. 12
C. 24
D. 48

Q.13: Mark is three times as old as his sister. If the difference in their ages is 10 years, how old is his sister?

A. 5 years
B. 10 years
C. 15 years
D. 20 years

Q.14: Which of the following fractions is NOT equivalent to 3/4?

A. 6/8
B. 9/12
C. 15/20
D. 12/18

Q.15: The cost to carpet a room that is 10 feet wide by 12 feet long at ₹10 per square foot is:

A. ₹1200
B. ₹1000
C. ₹900
D. ₹800

Q.16: In a math competition, the first place winner gets 2/3 of the prize money. The second place winner gets 1/2 of what the first place winner received. What was the total amount of prize money if the second place winner received ₹4000?

A. ₹12,000
B. ₹16,000
C. ₹24,000
D. ₹32,000

Q.17: You are standing 100 ft away from a tower that is 100 feet tall. The approximate distance from you to the top of the tower in a straight line is:

A. 100 feet
B. 141 feet
C. 150 feet
D. 200 feet

Q.18: A cyclist rides a certain distance at 15 miles per hour and returns over the same path at 10 miles per hour. What is the cyclist’s average speed for the round trip?

A. 12 miles per hour
B. 11.5 miles per hour
C. 12.5 miles per hour
D. 13 miles per hour

Q.19: If fencing costs ₹15 per foot and you want to enclose a rectangular yard that is 30 feet by 40 feet, how much will it cost?

A. ₹2100
B. ₹1050
C. ₹1500
D. ₹3150

Q.20: If 4x=5x-25, then x+10 equals:

A. 15
B. 20
C. 25
D. 35

Q.21: Paul is twice as old as Kevin. If the difference in their ages is 14 years, how old is Kevin?

A. 7 years
B. 14 years
C. 21 years
D. 28 years

Q.22: A line segment is plotted between the coordinates (1,1) and (4,4). What is the slope of this line?

A. 0
B. 1
C. 2
D. 3

Q.23: Standing 80 feet away from a building that is 50 feet tall, what is the distance to the top of the building from your position?

A. 50 feet
B. 94 feet
C. 100 feet
D. 130 feet

Q.24: If a recipe adjustment saves 10% on sugar, and the original recipe called for 500 grams, how much sugar is used now?

A. 450 grams
B. 475 grams
C. 490 grams
D. 500 grams

Q.25: A room measures 10 feet by 15 feet. How many square feet of carpet is needed to cover the floor?

A. 100
B. 125
C. 150
D. 175

Q.26: The sequence 5, 10, 20, _, 80 follows what pattern?

A. 35
B. 40
C. 45
D. 50

Q.27: How many 2x2x2 inch cubes can fit in a box that is 4x8x2 inches?

A. 4
B. 8
C. 16
D. 32

Q.28: Which of the following fractions is NOT equivalent to 50%?

A. 1/2
B. 2/4
C. 5/10
D. 3/5

Q.29: Fencing a garden that is 50 feet by 30 feet costs $10 per foot. How much will it cost in total?

A. $800
B. $1600
C. $2400
D. $3200

Q.30: Jack has 5 blue, 3 red, and 2 green marbles. How many marbles must he draw to ensure he has at least one of each color?

A. 6
B. 7
C. 8
D. 9

Answers & Explanations

Q.1: Final Cost Calculation

• Answer: B
• Explanation: The original price of the item is ₹250. A 20% discount reduces the price by ₹50 (₹250 * 20% = ₹50), resulting in a new price of ₹200. An additional 5% discount on ₹200 reduces it by ₹10 (₹200 * 5% = ₹10), making the final cost ₹190.

Q.2: Solving for x in an Equation

• Answer: C
• Explanation: Solve 3x−9=0 by adding 9 to both sides, giving 3x=9. Dividing both sides by 3 gives x=3.

Q.3: Identifying Non-equivalent Expression

• Answer: B
• Explanation: 45×(13+11)=45×24=1080. The option 13(45+11)=13×56=728 does not equal 1080, making it the incorrect choice.

Q.4: Calculating Triangle Angles

• Answer: A
• Explanation: The sum of the angles in a triangle is 180°. Given one angle is 90° and another is 45°, the third angle is 180°−(90°+45°)=45°.

Q.5: Unit Conversion

• Answer: A
• Explanation: 1 kilogram equals 1000 grams, so 3 kilograms equals 3×1000=3000.

Q.6: Analyzing Sales Data

• Answer: A
• Explanation: Without the data graph, this question assumes a hypothetical where 2016, being the earliest year, might typically represent the lowest initial sales, which doubled by 2020.

Q.7: Temperature Drop

• Answer: C
• Explanation: The question suggests a notable temperature drop, hypothetically the largest between Wednesday and Thursday.

Q.8: Average Calculation

• Answer: B
• Explanation: To find the mean of 30, 40, 50, 60, and 70, add them together (250) and divide by the number of values (5), which results in 50.

Q.9: Scientific Notation

• Answer: A
• Explanation: 6.5×10^-3 moves the decimal point three places to the left, resulting in 0.0065.

Q.10: Map Scale Conversion

• Answer: B
• Explanation: With 1 inch representing 5 miles, 8 inches represents 8×5=40 miles.

Q.11: Graphing Inequalities

• Answer: C
• Explanation: A ray starting at 2 and going to the right (not including 2 and including values less than 5) correctly represents x>2 and x<5.

Q.12: Volume and Fitting

• Answer: A
• Explanation: The volume of the box is 8×12×4=384 cubic inches. Each 4-inch cube has a volume of 64 cubic inches. Thus, 384/64=6 cubes can fit.

Q.13: Solving Age Problems

• Answer: A
• Explanation: If Mark is three times older than his sister and the difference is 10 years, his sister is 10/2=510 / 2 = 510/2=5 years old.

Q.14: Fraction Equivalence

• Answer: D
• Explanation: 3/4 is equivalent to 9/12 and 15/20, but not to 12/18 which simplifies to 2/3.

Q.15: Cost Calculation

• Answer: A
• Explanation: The area is 10×12=120 sq ft, and at ₹10 per sq ft, the cost is 120 \times 10 = ₹1200.

Q.16: Prize Money Distribution

• Answer: C
• Explanation: If the second place winner received ₹4000, which is 1/2 of what the first place received, the first place received ₹8000. The total prize money is 2/3 of the total, so 8000 / (2/3) = ₹12,000, and with the second place, it’s 8000 + 4000 = ₹12,000.

Q.17: Distance Calculation

• Answer: B
• Explanation: Using the Pythagorean theorem, 100²+100² =20000. The square root of 20000 is approximately 141 feet.

Q.18: Average Speed

• Answer: A
• Explanation: Using the harmonic mean for average speed, (2×15×10)/(15+10)=12 mph.

Q.19: Fencing Cost

• Answer: A
• Explanation: The perimeter is (30+40)×2=140 feet, and at ₹15 per foot, the cost is 140 times 15 = ₹2100.

Q.20: Solving for x

• Answer: C
• Explanation: Solve 4x=5x−25. Then, x+10=25+10=35.

Q.21: Calculating Relative Ages

• Answer: A
• Explanation: If Paul is twice as old as Kevin and their age difference is 14, then Kevin is 14 years old and Paul is 14×2=28 years old.

Q.22: Calculating the Slope of a Line

• Answer: B
• Explanation: The slope mmm of the line through points (1,1) and (4,4) is (4−1)/(4−1)=3/3=1.

Q.23: Calculating the Distance Using Pythagoras

• Answer: B
• Explanation: Using the Pythagorean theorem, sqrt{80^2 + 50^2} = sqrt{8900} ​≈94 feet.

Q.24: Reduction in Sugar Usage

• Answer: A
• Explanation: 10% of 500 grams is 50 grams, so the new amount used is 500−50=450 grams.

Q.25: Area of a Room

• Answer: C
• Explanation: The area of the room is 10×15=150 square feet.

Q.26: Identifying the Pattern in a Sequence

• Answer: B
• Explanation: The sequence doubles each time. Therefore, the missing term after 20, doubling it, is 40.

Q.27: Fitting Small Cubes in a Larger Box

• Answer: B
• Explanation: The box volume is 4×8×2=64 cubic inches. Each cube has a volume of 8 cubic inches (2×2×2). So, 64/8=8 cubes can fit.

Q.28: Non-equivalent Fraction

• Answer: D
• Explanation: 1/2 equals 50%, but 3/5 equals 60%.

Q.29: Cost of Fencing

• Answer: B
• Explanation: The perimeter of the garden is (50+30)×2=160 feet. At $10 per foot, the cost is 160 times $10 = $1600.

Q.30: Probability of Drawing Marbles

• Answer: D
• Explanation: To ensure he draws at least one of each color, Jack must draw all the marbles except for the one color with the highest count, which is blue (5). So, he needs to draw 5+3+1=9 marbles.

Also Read:

• CBSE Class 12 Maths Notes
• CBSE Class 11 Maths Notes
• CBSE Class 10 Maths Notes
• CBSE Class 9 Maths Notes
• CBSE Class 8 Maths Notes

Conclusion

In conclusion, practicing mathematics through a variety of questions is essential for developing a deeper understanding of concepts and honing problem-solving skills. Whether it’s algebra, geometry, calculus, or statistics, consistent practice helps solidify foundational knowledge and enhances analytical thinking.

By tackling a diverse range of problems, students can identify their strengths and weaknesses, allowing them to focus on areas needing improvement. Remember, mathematics is not just about finding the right answer but understanding the process and logic behind it. Keep challenging yourself with new questions, and over time, you’ll see significant progress in your mathematical abilities.