Algebra Model Question Paper

9th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 50
5 x 1 = 5
1. Which of the following statement is true for the equation 2x + 3y = 15

(a)

the equation has unique solution

(b)

the equation has two solution

(c)

the equation has no solution

(d)

the equation has infinite solutions

2. Which of the following is a solution of the equation 2x − y = 6

(a)

(2,4)

(b)

(4,2)

(c)

(3, −1)

(d)

(0,6)

3. Which condition does not satisfy the linear equation ax + by + c = 0

(a)

a $\neq$ 0 , b = 0

(b)

a = 0 , b $\neq$ 0

(c)

a = 0 , b = 0 , c $\neq$ 0

(d)

a $\neq$0, b $\neq$ 0

4. The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is

(a)

k = 3

(b)

k = 2

(c)

k = 4

(d)

k = -3

5. If $\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { { c }_{ 1 } }{ { c }_{ 2 } }$ where a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 then the given pair of linear equation has __________ solution(s)

(a)

no solution

(b)

two solutions

(c)

infinite

(d)

unique

6. 8 x 2 = 16
7. Check whether $\frac { 1 }{ 4 }$ is a solution of the equation 3(x + 1) = 3( 5–x) – 2( 5 + x).

8. Solve the following linear equations
(i) $\frac { 2(x+1) }{ 3 } =\frac { 3(x-2) }{ 5 }$
(ii) $\frac { 2 }{ x+1 } =4-\frac { x }{ x+1 } ,(x\neq -)$

9. Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.

10. Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age.

11. The sum of a two digit number and the number formed by interchanging the digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sums of the digits of the first number. Find the first number.

12. Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

13. The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey of 10 km the charge paid is Rs 75 and for a journey of 15 km the charge paid is Rs 110. What will a person have to pay for travelling a distance of 25 km? (You may also try to illustrate through a graph).

14. 4 men and 4 boys can do a piece of work in 3 days. While 2 men and 5 boys can finish it in 4 days. How long would it take for 1 boy to do it? How long would it take for 1 men to do it?

15. 3 x 3 = 9
16. (Computing slope made easier!) Find the slope and y-intercept of the line given by the equation 2y – 3x = 12.

17. Given 4a + 3b = 65 and a + 2b = 35 solve by elimination method.

18. Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) $\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0$

19. 4 x 5 = 20
20. Use graphical method to solve the following system of equations x + y = 5; 2x – y = 4.

21. The sum of the digits of a given two digit number is 5. If the digits are reversed, the new number is reduced by 27. Find the given number.

22. Solve for x and y: 8x − 3y = 5xy, 6x − 5y = −2xy by the method of elimination.

23. Solve 2x = −7y + 5; −3x = −8y −11 by cross multiplication method.