# Mathematics Solved Past Paper 9th Class 2015 Karachi Board

SECTION “A” (COMPULSORY)(M.C.Q.S)

1. Choose the correct answer for each from the given options:

(i) 12+ 12+ 12= ———-
* 3
* 10
* 11
* 100

(ii) The Cartesian product of A and B is written as:
* A.B
* AxB
* B.A
* BxA

(iii) The characteristic of log 8.368 is:
* 0
* 1
* -1
* -2

(iv) The arithmetic mean of 2,3 and 4 is:
* 4.5
* 3
* 3.5
* None of them

(v) It is called the multiplicative identity.
* 0
* -1
* 10
* 1 (vii) The number repeated frequently in a given data is:
* Median
* Mean
* Mode
* None of these

(viii) If (x + 1, Y + 2) = (5 ,6) then the value of x is:
* 6
* 3
* 5
* 4

(ix) (6x)°x 4x²= ———-
* 4x²
* 24x²
* x³
* None of these

(x) An angle of less than 900 is called:
* Right angle
* Acute angle
* Obtuse angle
* Vertical angle

(xi) 25+ 45= ———-
* 65
* 85
* 25
* 115

(xii) If log3 N = 4 then value of N is:
* 81
* 27
* 64
* none of these

(xiii) Is a set of points each of which is at the same distance from a fixed point.

* Chord
* Diameter
* Circle

(xiv) Rate of zakat is = ——
* 5%
* 2-1/2%
* 3-1/2%
* 10%

(xv) 2√9 x √9 = – – – – –
* 81
* 18
* 36
* None of these

(xvi) Area of circle = ———
* πr
* πr/2
* 2πr
* πr²

(xvii) {1, 2, 3, ——- } is the set of:
* Integer
* Whole numbers
* Natural number
* even no.

(xviii) The multiplicative inverse of 1/x is:
* x
* x-1
* 1/x2″
* None of these

xix) 60 a²b²÷4ab = —–
* 12ab
* 12a²b
15ab
* None of these

(xx) (x – 6) (x + 6) = ——–

* X²-36
* X² + 36
* x – 6
* x + 6

Answer 10 questions from this section

2. The sum of two numbers in Base five is 4315, One of the numbers is 2145, Find the other

Sum of two numbers in Base 5 is 4315
One number is 2145
Other number = ?
Other Number 4315 – 2145
4315
2145
2125

3. 90 worker men work in a factory. The scheme of their daily wages is given below. Find the A.M. of their wages.  4. Divide: (x2- 5x + 6) -;-(x – 2) 5. If A = 2p – 3q – 4r and B = -4q + 5p – 2r. Find the value of 3A – 4B.

3A  = 3 x (2p – 3q – 4r)
= 6p – 9q -12r
4B  = 4x (-4q + 5p – 2r
= -16q + 20p – 8r
3A – 4B = 6p – 9q – 12r – (-16q + 20p – 8r)
= 6p – 9q – 12r +16q – 20p + 8r)
= -14p + 7q – 4r Ans.

6. 15 spoons of sugar are required for 6 eggs cake. How many spoons of sugar will be required for 8 eggs cake?  8. Use an appropriate formula to Simplify 1025 x 975.

Using formula:
(a + b) (a – b) = a² – b²
1025 = 1000 + 25
975 = 1000 – 25
(1000 + 25) (1000 – 25)
= (1000)² – (25)²
= 1000000 – 625
= 999375 Ans.

9. Annual savings of a person is 2,400 rupees. His wife has ornaments worth Rs.2050. What amount of Zakat is due to him?

Saving of the person = Rs.2,400
Worth of ornaments = 2050
Total = 2400 + 2050 = 4450
Rate of Zakat = 5/2%
Amount of Zakat to be paid: Rs. 111.25 Ans.

10. If log10² = 0.3010, log10³ = 0.4771, and log105= 0.6990 find the value of log1030.

L0910 30              = 10910(2 x 3 x5)
L0910 30              = log102+ Iog103+ log105
Log10 30              = 0.3010 + 0.4771 + 0.6990
L0910 30              = 1.4771 Ans.  12. Define the following
(i) Vertical angles(ii) Supplementary angle

(i) Vertical angles:
The angles whose arms form two pairs of opposite rays are called vertical angles.

(ii) Supplementary angle
If the sum of two angles is 180° they are called supplementary angles and each of the two angles is called supplement of the other. E.g. 60°, 120°

13. A rectangular lawn whose length is 7.5m and breadth is 4m. Find the length of diagonal. 14. 8 masons can build a 10 meters long wall in 22 days. How many masons would be required to build a 165 meters long wall in 6 days. 15. Convert 101110012 numbers into those of decimal system 16. If a diameter of a circle is perpendicular to a chord, it bisects the chord. Prove. Attempt 3 questions from this Section. Formula 18. A woman died. Her heirs were her husband, two daughters and a brother. A “Tarka” worth rupees 2,700 was distributed among her heirs in the ratio 1/4 , 2/3 and 1/12 Find the Share of each.

Ratio between
Husband         :     Two Daughter        :       Brother
1/4                  :         2/3                      :       1/12
Husband Share = 2700 x ¼                = 675
Two Daughters share = 2700 x 2/3    = 1800
Share of one daughter = 1800 x ½     = 900
Share of brother = 2700 x 1/12           = 225

19.(a)Find the product: (2x – 3y) (4×2 + 9y2 + 6xy) (b) The A.M. of ten numbers is 32. Find the sum of numbers. = 320 Sum of Numbers = 320 Ans.

20.(a)Factorize: (i) 3a4 – 48 (ii) ab + cd + be + ad

= 3 [(a4_ 16]
= 3 (a2 + 4) (a2- 4)
= 3 (a2 + 4) (a)2 _ (2)2
= 3 (a2 + 4) (a + 2) (a – 2) Ans.
(ii) ab + cd + be + ad
Rearranging the terms
= ab + be + ad + cd
= a (a + c) +d (a + c) = (a + e) (a + d) Ans.

(b) If x – y = 3 and xy = 10 then find the value of x3 – y3.

X-y = 3
XV = 10 x5 _ y3 = 7
(x _ y)³ = (3)3
x3 -y³ 3xy (x – y) = 27
x3 – y3 _ 3 x 10 x (3) = 27
x³ – y³ 90 = 27
x³ – y³ = 27 + 90
x³ -y³ = 117 Ans .

21. Construct the triangle, the length of whose sides are 4cm, 3cm and 5cm. Draw a circle passing through its vertices. Posted on December 14, 2015 in 9th Class 2015 Karachi Board Past Papers