Algebraic Expressions and Algebraic Formulas

Maths, SSC-KPK Class 9. This chapter is split into 24 topics and has 607 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Products using a^3 +- b^3 identities 30 questions
2. Unit 4 review exercise and summary 23 questions
3. Cube formulas: (a+b)^3 and (a-b)^3 30 questions
4. Algebraic expressions: terms, coefficients, variables 25 questions
5. Finding a^2 + b^2 and ab from a + b and a - b (Part 2) 20 questions
6. Finding a^2 + b^2 and ab from a + b and a - b (Part 1) 21 questions
7. Order, types and classification of surds 22 questions
8. Surds: definition and identification 24 questions
9. Reducing rational expressions to lowest terms 30 questions
10. Conjugate surds and rationalization 27 questions
11. Finding x^3 +- 1/x^3 and powers of x +- 1/x (Part 2) 20 questions
12. Values of x +- 1/x and x^2 + 1/x^2 for surd values of x 30 questions
13. Finding a^3 + b^3 and a^3 - b^3 from given values 30 questions
14. Division of rational expressions 20 questions
15. Simplifying surds and exercise problems 27 questions
16. Rational expressions: definition and recognising them 25 questions
17. Sum of rational expressions 21 questions
18. Finding x^3 +- 1/x^3 and powers of x +- 1/x (Part 1) 21 questions
19. Algebraic formulas: (a+b)^2 and (a-b)^2 identities 30 questions
20. Product of rational expressions 23 questions
21. Lowest terms of a rational expression: examining 24 questions
22. Value of an algebraic expression at given numbers 30 questions
23. The formula (a + b + c)^2 and its applications 30 questions
24. Difference of rational expressions 24 questions

Sample questions: Algebraic Expressions and Algebraic Formulas

10 sample questions with the correct answer and an explanation. Try to answer each one before reading the explanation.

Q1. Which statement is TRUE?

• A. Every polynomial is a rational expression but every rational expression need not be a polynomial(correct answer)
• B. No polynomial is a rational expression
• C. Rational expressions are always integers
• D. Every rational expression is a polynomial

Answer: A.From the Note. The correct answer is: Every polynomial is a rational expression but every rational expression need not be a polynomial.

Q2. To test whether p(x)/q(x) is in lowest terms we

• A. factorize numerator and denominator and look for a common factor(correct answer)
• B. square both
• C. add the numerator and denominator
• D. divide p by 2

Answer: A.Section 4.1.5. The correct answer is: factorize numerator and denominator and look for a common factor.

Q3. Reduce ((x − 2)(x² + 2x + 4))/((x − 2)(x + 2)) to its lowest terms: the result is

• A. (x² + 2x + 4)/(x + 3)
• B. (x² + 2x + 4)/(x + 2)(correct answer)
• C. ((x − 2)(x² + 2x + 4))/((x − 2)(x + 2))
• D. (x² + 2x + 5)/(x + 2)

Answer: B.Factorize: (x − 2)(x² + 2x + 4) over (x − 2)(x + 2); cancel the common factor to get (x² + 2x + 4)/(x + 2).

Q4. Reduce ((x + 3)(x² − 3x + 9))/((x − 3)(x + 3)) to its lowest terms: the result is

• A. ((x + 3)(x² − 3x + 9))/((x − 3)(x + 3))
• B. (x² − 3x + 10)/(x − 3)
• C. (x² − 3x + 9)/(x − 2)
• D. (x² − 3x + 9)/(x − 3)(correct answer)

Answer: D.Factorize: (x + 3)(x² − 3x + 9) over (x − 3)(x + 3); cancel the common factor to get (x² − 3x + 9)/(x − 3).

Q5. (y + 9)/(y² + 3) + (−7y + 7)/(y² + 3) simplifies to

• A. (−6y + 16)/(2y² + 6)
• B. (−6y + 16)/(y² + 3)(correct answer)
• C. (−7y + 7)(y + 9)/((y² + 3)²)
• D. (8y + 2)/(y² + 3)

Answer: B.Take the LCM of the denominators and add the adjusted numerators: the result is (−6y + 16)/(y² + 3).

Q6. x/(x + 2) + 3/(x − 1) simplifies to

• A. (x + 3)/(2x + 1)
• B. 3x/((x + 2)(x − 1))
• C. (x² − 4x − 6)/(x² + x − 2)
• D. (x² + 2x + 6)/(x² + x − 2)(correct answer)

Answer: D.Take the LCM of the denominators and add the adjusted numerators: the result is (x² + 2x + 6)/(x² + x − 2).

Q7. y/(y + 4) + 2y/(y − 4) simplifies to

• A. 3y/(2y)
• B. (−y² − 12y)/(y² − 16)
• C. 2y²/((y + 4)(y − 4))
• D. (3y² + 4y)/(y² − 16)(correct answer)

Answer: D.Take the LCM of the denominators and add the adjusted numerators: the result is (3y² + 4y)/(y² − 16).

Q8. t/(t² − 25) + 3t/(t + 5) simplifies to

• A. 3t²/((t + 5)(t² − 25))
• B. (3t² − 14t)/(t² − 25)(correct answer)
• C. (−3t² + 16t)/(t² − 25)
• D. 4t/(t² + t − 20)

Answer: B.Take the LCM of the denominators and add the adjusted numerators: the result is (3t² − 14t)/(t² − 25).

Q9. x/(x + 1) + (x + 1)/x simplifies to

• A. (2x² + 2x + 1)/(x² + x)(correct answer)
• B. (−2x − 1)/(x² + x)
• C. x(x + 1)/(x(x + 1))
• D. (2x + 1)/(2x + 1)

Answer: A.Take the LCM of the denominators and add the adjusted numerators: the result is (2x² + 2x + 1)/(x² + x).

Q10. a/(a + b) + b/(a − b) simplifies to

• A. (a² + b²)/(a² − b²)(correct answer)
• B. (a² − 2ab − b²)/(a² − b²)
• C. ab/((a + b)(a − b))
• D. (a + b)/(2a)

Answer: A.Take the LCM of the denominators and add the adjusted numerators: the result is (a² + b²)/(a² − b²).