Model Questions: General Mathematics Model/Sample Question for Class-IX/Grade-IX

Class - IX

Subject: General Mathematics

Time : 3 hrs. Marks. 100

Answer any one 5x1=5

1. (i) Determine the set of natural numbers which on dividing 605 and 821 leaves 29 as remainder in each case.

(ii) If U = { 1, 2, 3, 4, 5, 6 }

A = { 1, 3, 5, }

B = { 2, 4, 6 }

C = { 2, 3, 4, 5 }

then prove that ( AUBUC)

= A

(iii) IF ( x+y, a² -b² ) = ( a+b, ax -by ) then find (x, y ).

2. prove that,

is an irrational number. 5x1=5

3. Answer any two : 3x2=6

(i) If x +

= 4 then find the value of

(ii) If (x+y)² =3 and ( x-y)² =2 then prove that 2xy (x²+y²) =

(iii) If x =

then find the value of x² +

(iv) If x +y =a, x² + y² = b and x³ + y³ = 3ab then prove that, a³ + 2c³ =3ab

4. Resolve into factors : any two 2x2=4

(i) x² - x - ( a² +5a +6)

(ii) (a-1) x² + a²xy + ( a+1) y²

(iii) 2a³ + 3a²b + 3ab² - 8b³

(iv) (x + 1) (x + 3) ( x+5) (x +7) +15

5. Answer any one : 5x1=5

(i) (x+2) is a factor of x² + px +q and x² +p x +q then prove that,

(ii) Find the H. C. F of the following a³ -1, a³+1, a⁴ +a² +1, (a+1)²

(iii) If the L. C. M and H. C.F. of the two numbers are x³ - 10x² + 11x +70 and ( x-7) respectively

and one of the number is x² -5x -14 then find the other number.

6. Answer any two : 5x2=10

(i) At 4% profit it the difference of simple and compound profit for 2 years is TK. 1 then

find the capital?

(ii) Purchasing 2 oranges at Tk. 5. How many oranges are to be sold at Tk. 75 to make a profit

of a% ?

(iii) The salary of Mr. Matin is x% higher than that of Mr. Jalil. As a result the salary of Mr. Jalil

is y% less than that of Mr. Matin. Express y as a function of x.

(iv) A boat man can row d km in t₂ hours against the current. To cover the same distance he takes

t₁ hours in favour of the current. What are the speeds of the current and the boat?

7. Answer any one : 5x1=5

(i)

(ii)

8. Answer any two : 5x2=10

(i) If

then prove that x, y, z are in continued proportion.

(ii) If

then prove that,

(iii) Solve :

(iv) If a, b, c are in continued proportion then prove that, a² b²c² (

) = a³ + b³ +c³

9. Answer any two : 5x2=10

(i) If the length fo each side of a square is increased by 5% then what is the percentage of increase in the area enclosed by the square?

(ii) 3 benches in a class room remain vacant, if 4 students sit in each bench. But 4 students are to remain standing if 3 students sit in each bench. What is the number of the students in that class?

(ii) A man covered some distance at the rate of 40km/hour and the rest at the rate of 60km/hour. He covered a total distance of 240 km in 5 hours. How far did he travel in 40km/ hour?

(iv) The hypotenuse of a right angled triangle is 10 cm and its perimeter is 24 cm. What is the area of the triangular region?

(v) A man bought some pens at Tk. 240 if he would have got 1 more pen then the price of each pen have been less by Tk. 1 on the average. How many pens did he buy?

10. Answer any one : 5x1=5

(i)