Algebra Questions and Problems for Grade 7

Grade 7 algebra questions and problems with detailed solutions are presented. Questions on simplifying expressions, solving equations, factoring expressions,....are included.

1. Evaluate each of the expressions for the given value(s) of the variable(s).
   1. 12 x ³ + 5 x ² + 4 x - 6 for x = -1
   2. 2 a ² + 3b ³ - 10 for a = 2 and b = -2
   3. (- 2 x - 1) / (x + 3) for x = 2
   4. 2 + 2 |x - 4| for x = - 4
2. Expand and simplify each of the expressions below.
   1. - 2( x - 8) + 3 (x - 7)
   2. 2 (a + 1) + 5b + 3(a + b) + 3
   3. a (b + 3) + b (a - 2) + 2 a - 5 b + 8
   4. (1 / 2) (4x + 4) + (1 / 3)(6x + 12)
   5. 4 ( - x + 2 - 3(x - 2) )
3. Simplify each of the expressions below.
   1. x / y + 4 / y
   2. (2 x / 4 ) × (1 / 2)
   3. (3 x / 5 ) ÷ (x / 5)
4. Simplify each of the expressions below.
   1. 3 x ² × 5 x ³
   2. [ (2 y) ⁴ 9 x ³] ÷ [ 4 y ⁴ (3 x) ² ]
5. Factor fully each of the expressions below.
   1. 9 x - 3
   2. 24 x + 18 y
   3. b x + d x
6. Solve each of the equations below and check your answer.
   1. 2 x + 5 = 11
   2. 3 x = 6 / 5
   3. 3 (2 x + 2) + 2 = 20
7. Rewrite the expressions 3 × a × a × a - 5 × b × b using exponential.
8. A rectangle has a length given by 2 x + 3 units, where x is a variable. The width of the rectangle is given by x + 1 units. Find the value of x if the perimeter of the rectangle is equal to 32.
9. A rectangle has a length given by 2x - 1 units, where x is a variable. The width of the rectangle is equal to 3 units. Find the value of x if the area of the rectangle is equal to 27.
10. 45% of the students in a school are male? Find the ratio of the number of female to the total number of male students in this school.
11. A car travels at the speed x + 30 kilometers in one hour, where x is an unknown. Find x if this car covers 300 kilometers in 3 hours?
12. Solve the proportion : 4 / 5 = a / 16
13. Find a if the ordered pair (2 , a + 2) is a solution to the equation 2 x + 2 y = 10?
14. Find the greatest common factor of the numbers 25 and 45.
15. Write the number " one billion, two hundred thirty four million, seven hundred fifty thousand two " using digits.
16. Write the number 393,234,000,034 in words.
17. Find the lowest common multiple to the numbers 15 and 35.
18. Find x if 2 / 3 of x is 30?
19. What is 20% of 1 / 3?
20. Order 12 / 5 , 250% , 21 / 10 and 2.3 from the smallest to the largest.
21. The sum of 3 positive consecutive integers is equal to 96. Find the largest of these numbers.
22. Dany scored 93 in physics, 88 in mathematics, and a score in chemistry that is double his score in geography. The average score of all 4 courses is 79. What were his scores in chemistry and geography?
23. Linda scored a total of 265 points in mathematics, physics and English. She scored 7 more marks in mathematics than in English and she scored 5 more marks in physics than in mathematics. Find her scores in all three subjects.
24. There are bicycles and cars in a parking lot. There is a total of 300 wheels including 100 small wheels for bicycles. How many cars and how many bicycles are there?
25. The difference between two numbers is 17 and their sum is 69. Find the largest of these two numbers.

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