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Algebra Problem Set: Equations, Factorization, and Integer Solutions

This algebra problem set includes eight questions focusing on solving equations, expanding and simplifying expressions, and factorizing quadratic equations. The tasks involve manipulating variables, calculating values based on given formulas, and understanding the relationships between integers. Students are required to follow mathematical procedures to derive solutions for various scenarios, including geometric designs and monetary calculations for tile purchases. Practice these problems to enhance your algebra skills!

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Algebra Problem Set: Equations, Factorization, and Integer Solutions

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  1. 90147 Algebra

  2. QUESTION ONE • Solve these equations:

  3. QUESTION ONE • Solve these equations:

  4. 13x - 5 = 8x + 3

  5. 13x - 5 = 8x + 3

  6. QUESTION TWO • Expand and simplify:

  7. QUESTION THREE • Factorise completely: • x2 - 2x - 8

  8. QUESTION THREE • Factorise completely: • x2 - 2x - 8

  9. QUESTION FOUR • The diagram shows a design made with 5 rows of small squares . The number of small squares, S, in the design is given by the formula: • where R is the number of rows of small squares in the design.Calculate the number of small squares, S, for a similar design that has 11 rows of small squares.

  10. QUESTION FOUR • The diagram shows a design made with 5 rows of small squares . The number of small squares, S, in the design is given by the formula: • where R is the number of rows of small squares in the design.Calculate the number of small squares, S, for a similar design that has 11 rows of small squares.

  11. QUESTION FOUR • The diagram shows a design made with 5 rows of small squares . The number of small squares, S, in the design is given by the formula: • where R is the number of rows of small squares in the design.Calculate the number of small squares, S, for a similar design that has 11 rows of small squares.

  12. QUESTION FIVE • Simplify:

  13. QUESTION FIVE • Simplify:

  14. QUESTION SIX

  15. QUESTION SIX Solve the equation 225 = (x + 8)2, to find x, the length of the side of the pool.

  16. QUESTION SIX It can’t be negative

  17. QUESTION SEVEN • Mr Smith spends $1210 on 1390 square tiles to use on the bathroom floor. He buys S small tiles for 80 cents each and B big tiles for $1.50 each. • Solve the pair of simultaneous equations to find the number of tiles of each size that Mr Smith bought.

  18. Use calculator • 0.8S + 1.5B = 1210 • S + B = 1390 • S = 1250 • B = 140

  19. QUESTION EIGHT • One integer is 5 more than twice another integer.The squares of these two integers have a difference of 312. • Write at least ONE equation to describe this situation, and use it to find the TWO integers. Show all your working.

  20. Let 1 integer be x • One integer is 5 more than twice another integer.2x + 5 • The squares of these two integers have a difference of 312.

  21. Let 1 integer be x

  22. X is an integer so 7 and 19

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