Algebra questions grade 9

Algebra questions grade 9 DEFAULT

Grade 9 Algebra Quiz

Maths Quiz For Class 9


This is a beautiful Maths quiz for class 9. Mathematics can come across as merely a series of numbers, letters, and problems all put together to ruin your day for those uninterested in the subject. Still, the study is highly...


Questions: 24  |  Attempts: 58813   |  Last updated: Jul 23, 2021

  • Sample Question

    A is 40% of B. What percentage is B of A?

Grade 9 Science Quiz


Grade 9 Science Quiz; Are you a ninth-grader and have a hard time with your science classes? Worry no more, as the quiz below is perfect for helping you revise all that we have covered. Give it a shot and keep an eye out for more...


Questions: 30  |  Attempts: 23277   |  Last updated: Jul 15, 2021

  • Sample Question

    When is an atom stable?

Grade 9 Chemistry Quiz


Can you beat this Grade 9 Chemistry Quiz? Atoms are the smallest and main building blocks of ordinary matter, and they join together to form molecules that make the objects around us. In 9th grade chemistry, we got to dive deeper...


Questions: 10  |  Attempts: 22016   |  Last updated: Aug 24, 2021

  • Sample Question

    Elements consist of single type of atom.

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Grade 9 Algebra Word Problems

Related Pages
Grade 8 Algebra Word Problems
Algebra Word Problems
Solving Equations
More Algebra Lessons

Age Problems with two unknowns or variables

Example:
Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?

Solution:
Let x represent Spenser’s age
Therefore, Taylor’s age is 5x
x + 5x = 18
6x = 18
x = 3
Therefore, Spenser is 3 years old and Taylor is 15 years old.

Grade 9 Algebra Word Problems - Age

Example 1:
A mother is three times as old as her daughter. Six years ago, the mother’s age was six tines that of her daughter. How old are they now?

Solution:
Let x represent the daughter’s age.
Therefore, 3x is the mother’s age.
6(x - 6) = 3x - 6
6x - 6 = 3x - 6
3x = 30
x = 10
Therefore, the daughter’s is 10 years old and the mother is 30 years old.

Example 2:
A father is now three times as old as his son. Eight years ago, the father was five times as old as his son. How old are they now?

Grade 9 Algebra Word Problems - Rate, Distance, Time

Example:
A bus leaves the terminal and averages 40 km/hr. One hour late, a second bus leaves the same terminal and averages 50 km/hr. In how many hours will the second bus overtake the first?

Grade 9 Rate, Distance, Time Word Problems

Example 1:
One motorist travels 5 km.hr faster than another. They leave from the same place and travel in opposite directions. What is the rate of each if they are 195 km apart after 3 hours?

Example 2:
A pilot flew from airport A to airport B at a rate of 100 km/hr and flew back from airport B to airport A at 120 km/hr. The total time it took was 11 hours. How far is it from airport A to airport B?

Grade 9 Algebra Word Problems - Coins

Example:
A coin collection amounting to $25 consists of nickels and dimes. There are 3 times as many nickels and dimes. There are 3 times as many nickels as dimes. How many coins of each kind are there?

Solution:
Let x = number of dimes
3x = number of nickels
10x + 5(3x) = 2500
25x = 2500
x = 100
Therefore, there are 100 dimes and 300 nickels.

Grade 9 Coin Algebra Word Problems

Example:
Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of each kind does he have?

Coin Algebra Word Problems - Grade 9

Example:
Bob has in his pocket a number of pennies, 5 times as many nickels as pennies and 5 more quarters than pennies. The coins amount to $2.27. Find the number of each kind of coin.



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Algebra Questions with Answers for Grade 9

Questions

  1. Simplify the following algebraic expressions.

    1. - 6x + 5 + 12x -6
    2. 2(x - 9) + 6(-x + 2) + 4x
    3. 3x2 + 12 + 9x - 20 + 6x2 - x
    4. (x + 2)(x + 4) + (x + 5)(-x - 1)
    5. 1.2(x - 9) - 2.3(x + 4)
    6. (x2y)(xy2)
    7. (-x2y2)(xy2)

  2. Simplify the expressions.

    1. (a b2)(a3 b) / (a2 b3)
    2. (21 x5) / (3 x4)
    3. (6 x4)(4 y2) / [ (3 x2)(16 y) ]
    4. (4x - 12) / 4
    5. (-5x - 10) / (x + 2)
    6. (x2 - 4x - 12) / (x2 – 2x – 24)

  3. Solve for x the following linear equations.

    1. 2x = 6
    2. 6x - 8 = 4x + 4
    3. 4(x - 2) = 2(x + 3) + 7
    4. 0.1 x - 1.6 = 0.2 x + 2.3
    5. - x / 5 = 2
    6. (x - 4) / (- 6) = 3
    7. (-3x + 1) / (x - 2) = -3
    8. x / 5 + (x - 1) / 3 = 1/5

  4. Find any real solutions for the following quadratic equations.

    1. 2 x2 - 8 = 0
    2. x2 = -5
    3. 2x2 + 5x - 7 = 0
    4. (x - 2)(x + 3) = 0
    5. (x + 7)(x - 1) = 9
    6. x(x - 6) = -9

  5. Find any real solutions for the following equations.

    1. x3 - 1728 = 0
    2. x3 = - 64
    3. sqrt(x) = -1
    4. sqrt(x) = 5
    5. sqrt(x/100) = 4
    6. sqrt(200/x) = 2

  6. Evaluate for the given values of a and b.

    1. a2 + b2 , for a = 2 and b = 2
    2. |2a - 3b| , for a = -3 and b = 5
    3. 3a3 - 4b4 , for a = -1 and b = -2

  7. Solve the following inequalities.

    1. x + 3 < 0
    2. x + 1 > -x + 5
    3. 2(x - 2) < -(x + 7)

  8. For what value of the constant k does the quadratic equation x2 +2x = - 2k have two distinct real solutions?
  9. For what value of the constant b does the linear equation 2x + by = 2 have a slope equal to 2?
  10. What is the y intercept of the line -4x + 6y = -12?
  11. What is the x intercept of the line -3x + y = 3?
  12. What is point of intersection of the lines x - y = 3 and -5x - 2y = -22?
  13. For what value of the constant k does the line -4x + ky = 2 pass through the point (2,-3)?
  14. What is the slope of the line with equation y - 4 = 10?
  15. What is the slope of the line with equation 2x = -8?
  16. Find the x and y intercepts of the line with equation x = - 3?
  17. Find the x and y intercepts of the line with equation 3y - 6 = 3?
  18. What is the slope of a line parallel to the x axis?
  19. What is the slope of a line perpendicular to the x axis?
Solutions and detailed explanations to the above questions.

Answers to the Above Questions

    1. 6x - 1
    2. - 6
    3. 9x 2 + 8 x - 8
    4. 3
    5. -1.1x - 20
    6. x3y3
    7. - x3y4

    1. a2
    2. 7x
    3. (1/2)x2y
    4. x - 3
    5. -5
    6. (x + 2)/(x + 4)

    1. x = 3
    2. x = 6
    3. x = 21/2
    4. x = -39
    5. x = -10
    6. x = -14
    7. no solution
    8. x = 1


    1. solution set {-2,2}
    2. no real solutions
    3. solution set {1,-7/2}
    4. solution set {2,-3}
    5. solution set {2,-8}
    6. solution set {3}

    1. x = 12
    2. x = -4
    3. no solutions
    4. x = 25
    5. x = 1600
    6. x = 50

  1. Evaluate for the given values of a and b.

    1. 8
    2. 21
    3. -67


    1. x < -3
    2. x > 2
    3. x < -1

  2. k < 1/2
  3. b = -1
  4. (0 , -2)
  5. (-1 , 0)
  6. (4 , 1)
  7. k = -10/3
  8. slope = 0
  9. The slope is undefined
  10. x - intercept: (-3,0) , no y - intercept.
  11. no x - intercept , y - intercept: (0 , 3)
  12. slope = 0
  13. The slope is undefined.
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9th Grade Math Worksheets

Looking for free printable 9th grade Math Worksheets and activities to help your student prepare for the 9th Grade math course?

Want to measure your 9th-grade student’s knowledge of Math concepts and assess their exam readiness? If so, then look no further. Here is a comprehensive collection of FREE printable 9th grade Math worksheets that would help students in 9th Grade Math preparation and practice.

Download our free Mathematics worksheets for 9th Grade Math.

Hope you enjoy it!

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The Absolute Best Book to Ace the 9th Grade Math Test

9th Grade Math Concepts

The Basics

Expressions and Equations

Linear Functions

Factoring

Inequalities and System of Equations

Monomials Operations

Quadratic

Polynomial Operations

Radical Expressions

Rational Expressions

 Statistics and Probabilities

Statistics and Probabilities

9th Grade Math Practice Questions

Fractions and Decimals

Real Numbers and Integers

Proportions and Ratios

Percent

Algebraic Expressions

Equations and Inequalities

Linear Functions

Polynomials

Exponents and Radicals

Statistics

Geometry

Solid Figures

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"9th Grade Math Worksheets" Tags

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9 algebra questions grade

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Year 9 and 10 - Solving Linear Equations

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