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Mathematics Reasoning - Year 7

Math Worksheet

  1. Consider the sequence: $2, 6, 12, 20, 30, \dots$. What is the next term in the sequence?

  2. Sarah is three times as old as her brother Tom. In $5$ years, Sarah will be twice as old as Tom. How old is Tom now?

  3. If $5$ workers can paint $5$ houses in $5$ days, how many days will it take $10$ workers to paint $10$ houses? (Assume all workers work at the same rate).

  4. A rectangular garden has a perimeter of $40$ meters. If the length of the garden is $12$ meters, what is its area in square meters?

  5. The sum of three consecutive odd numbers is $57$. What is the largest of these numbers?

  6. You have $9$ marbles. One of them is slightly heavier than the others. Using a balance scale, what is the minimum number of weighings needed to find the heavier marble?

  7. A number is divisible by $4$, $6$, and $9$. Which of the following numbers is it definitely divisible by?

  8. If $A=1, B=3, C=7, D=15, \dots$, what letter corresponds to the number $63$?

  9. A farmer has chickens and pigs. If he counts $30$ heads and $84$ legs, how many chickens does he have?

  10. A book is open. The product of the two page numbers is $420$. What are the two page numbers?

  11. The average of five numbers is $15$. If a new number is added, the average becomes $18$. What is the new number?

  12. A train leaves station A at $10:00 \text{ AM}$ traveling at $60 \text{ km/h}$ towards station B. Another train leaves station B at $10:00 \text{ AM}$ traveling at $40 \text{ km/h}$ towards station A. The stations are $500 \text{ km}$ apart. At what time will the two trains meet?

  13. In a triangle, one angle is $50^\circ$. The other two angles are in the ratio $2:3$. What is the measure of the largest angle in the triangle?

  14. Four friends are sitting in a row. Alex is to the right of Ben. Chloe is immediately to the left of David. Ben is not at either end. David is not at the far right. Which of the following is the correct order of the friends from left to right?

  15. What is the sum of all integers from $1$ to $100$ that are multiples of both $3$ and $5$?

  16. A recipe calls for $2$ cups of flour for every $3$ cups of milk. If you use $5$ cups of milk, how much flour should you use?

  17. A tap fills a tank at a rate of $10$ liters per minute. Another tap drains the tank at a rate of $6$ liters per minute. If both taps are open, and the tank has a capacity of $120$ liters, how long will it take to fill the tank from empty?

  18. How many different $3$-digit numbers can be formed using the digits $1, 2, 3$ if each digit can be used only once?

  19. Five years ago, John was twice as old as Mary. In five years, John will be $1.5$ times as old as Mary. How old is John now?

  20. What is the missing number in the sequence: $1, 1, 2, 3, 5, 8, \_, 21$?

Answer Sheet

  1. Consider the sequence: 2,6,12,20,30,…. What is the next term in the sequence? → 42
  2. Sarah is three times as old as her brother Tom. In 5 years, Sarah will be twice as old as Tom. How old is Tom now? → 5 years
  3. If 5 workers can paint 5 houses in 5 days, how many days will it take 10 workers to paint 10 houses? (Assume all workers work at the same rate). → 5 days
  4. A rectangular garden has a perimeter of 40 meters. If the length of the garden is 12 meters, what is its area in square meters? → 96 m2
  5. The sum of three consecutive odd numbers is 57. What is the largest of these numbers? → 21
  6. You have 9 marbles. One of them is slightly heavier than the others. Using a balance scale, what is the minimum number of weighings needed to find the heavier marble? → 2
  7. A number is divisible by 4, 6, and 9. Which of the following numbers is it definitely divisible by? → 36
  8. If A=1,B=3,C=7,D=15,…, what letter corresponds to the number 63? → F
  9. A farmer has chickens and pigs. If he counts 30 heads and 84 legs, how many chickens does he have? → 18
  10. A book is open. The product of the two page numbers is 420. What are the two page numbers? → 20, 21
  11. The average of five numbers is 15. If a new number is added, the average becomes 18. What is the new number? → 33
  12. A train leaves station A at 10:00 AM traveling at 60 km/h towards station B. Another train leaves station B at 10:00 AM traveling at 40 km/h towards station A. The stations are 500 km apart. At what time will the two trains meet? → 3:00 PM
  13. In a triangle, one angle is 50∘. The other two angles are in the ratio 2:3. What is the measure of the largest angle in the triangle? → 78∘
  14. Four friends are sitting in a row. Alex is to the right of Ben. Chloe is immediately to the left of David. Ben is not at either end. David is not at the far right. Which of the following is the correct order of the friends from left to right? → Chloe, David, Ben, Alex
  15. What is the sum of all integers from 1 to 100 that are multiples of both 3 and 5? → 315
  16. A recipe calls for 2 cups of flour for every 3 cups of milk. If you use 5 cups of milk, how much flour should you use? → 3 \frac{1}{3} cups
  17. A tap fills a tank at a rate of 10 liters per minute. Another tap drains the tank at a rate of 6 liters per minute. If both taps are open, and the tank has a capacity of 120 liters, how long will it take to fill the tank from empty? → 30 minutes
  18. How many different 3-digit numbers can be formed using the digits 1,2,3 if each digit can be used only once? → 6
  19. Five years ago, John was twice as old as Mary. In five years, John will be 1.5 times as old as Mary. How old is John now? → 25 years
  20. What is the missing number in the sequence: 1,1,2,3,5,8,_,21? → 13