Algebra Questions with Answers for Grade 9
Grade 9 ratio algebra questions with answers are presented. Questions on solving linear and quadratic equations, simplifying expressions including expressions with fractions, finding slopes of lines are included. Solutions and detailed explanations are also included.
Questions

Simplify the following algebraic expressions.
  6x + 5 + 12x 6
 2(x  9) + 6(x + 2) + 4x
 3x^{2} + 12 + 9x  20 + 6x^{2}  x
 (x + 2)(x + 4) + (x + 5)(x  1)
 1.2(x  9)  2.3(x + 4)
 (x^{2}y)(xy^{2})
 (x^{2}y^{2})(xy^{2})

Simplify the expressions.
 (a b^{2})(a^{3} b) / (a^{2} b^{3})
 (21 x^{5}) / (3 x^{4})
 (6 x^{4})(4 y^{2}) / [ (3 x^{2})(16 y) ]
 (4x  12) / 4
 (5x  10) / (x + 2)
 (x^{2}  4x  12) / (x^{2} – 2x – 24)

Solve for x the following linear equations.
 2x = 6
 6x  8 = 4x + 4
 4(x  2) = 2(x + 3) + 7
 0.1 x  1.6 = 0.2 x + 2.3
  x / 5 = 2
 (x  4) / ( 6) = 3
 (3x + 1) / (x  2) = 3
 x / 5 + (x  1) / 3 = 1/5

Find any real solutions for the following quadratic equations.
 2 x^{2}  8 = 0
 x^{2} = 5
 2x^{2} + 5x  7 = 0
 (x  2)(x + 3) = 0
 (x + 7)(x  1) = 9
 x(x  6) = 9

Find any real solutions for the following equations.
 x^{3}  1728 = 0
 x^{3} =  64
 sqrt(x) = 1
 sqrt(x) = 5
 sqrt(x/100) = 4
 sqrt(200/x) = 2

Evaluate for the given values of a and b.
 a^{2} + b^{2} , for a = 2 and b = 2
 2a  3b , for a = 3 and b = 5
 3a^{3}  4b^{4} , for a = 1 and b = 2

Solve the following inequalities.
 x + 3 < 0
 x + 1 > x + 5
 2(x  2) < (x + 7)

For what value of the constant k does the quadratic equation x^{2} +2x =  2k have two distinct real solutions?

For what value of the constant b does the linear equation 2x + by = 2 have a slope equal to 2?

What is the y intercept of the line 4x + 6y = 12?

What is the x intercept of the line 3x + y = 3?

What is point of intersection of the lines x  y = 3 and 5x  2y = 22?

For what value of the constant k does the line 4x + ky = 2 pass through the point (2,3)?

What is the slope of the line with equation y  4 = 10?

What is the slope of the line with equation 2x = 8?

Find the x and y intercepts of the line with equation x =  3?

Find the x and y intercepts of the line with equation 3y  6 = 3?

What is the slope of a line parallel to the x axis?

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

 6x  1
  6
 9x^{ 2} + 8 x  8
 3
 1.1x  20
 x^{3}y^{3}
  x^{3}y^{4}

 a^{2}
 7x
 (1/2)x^{2}y
 x  3
 5
 (x + 2)/(x + 4)

 x = 3
 x = 6
 x = 21/2
 x = 39
 x = 10
 x = 14
 no solution
 x = 1

 solution set {2,2}
 no real solutions
 solution set {1,7/2}
 solution set {2,3}
 solution set {2,8}
 solution set {3}

 x = 12
 x = 4
 no solutions
 x = 25
 x = 1600
 x = 50

Evaluate for the given values of a and b.
 8
 21
 67

 x < 3
 x > 2
 x < 1

k < 1/2

b = 1

(0 , 2)

(1 , 0)

(4 , 1)

k = 10/3

slope = 0

The slope is undefined

x  intercept: (3,0) , no y  intercept.

no x  intercept , y  intercept: (0 , 3)

slope = 0

The slope is undefined.
More References and Links
Middle School Math (Grades 6, 7, 8, 9)  Free Questions and Problems With Answers
High School Math (Grades 10, 11 and 12)  Free Questions and Problems With Answers
Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
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