Time allowed: 20 Minutes (Science Group)9th class mathematics paper 2018 federal board

— NOTE: Section-A is compulsory. All parts of this section are to be answered on the question paper itself.

tt should be completed in the first 20 minutes and handed over to the Centre Superintendent.

—_ Deleting/overwriting ie not allowed. Do not use lead pencil.

om Q.1 Circle the correct option le. A/B/C /D. Each part carries one mark.

— 0] A square matrix is called singular if its determinant is:

A Negative 8. Positive Cc. Zero 0. One

~ ai) The value of i’* is.

~ A 1 B. -1 c. i D. ~i

_ (it) The logarithm of any number to itself as base 1:

A 1 B. 0 c -1 D. 10

_ (iy) a? – ab +d” ig a factor of:

A a-b 8. a+h? c. (a+by 0. (a-sy

{v) When 9×7 = 6x +2 is divided by x, the remainder is:

~ A 9 B 6 c 2 DB (3

~ (i ACFof Sx7y?z) and30.x°)°zis:

_ A Sxty*z? 8. 5×7 yz c 30x*y?2? oO. 30x’ yz

— (vid) x=5 is a possible soluton of the inequality:

_ A x< B x+3<0 c x+5>0 D. x-10>0

(vil) The point (-3,-) lies in the quadrant.

~ AT BO Cc ot DOU

~~ {io The midpoint of the line segment joining the points (-4,9) and {~4,-3) is:

~ ‘ A (-8,6) 6 (-4,3) + Cc. (0,6) D. (0,~6)

~ ow A Ray has end points. . :

A No 8. One Cc. Two D. Infinite

~ (xl) Sum of the adjacent angles of a parallelogram is: . : :

~ A 90° 8. 180° c. 270° 0. 360° °°

_ (ail) in the bisection of right angle, each angle is of: .

A 30°), 8. 45° Cc 60° 0. 90°

~ (xin) Right bisection of a line segment means to draw a perpendicular at the of that line segment.

_ A Any point B. Midpoint Cc. Two points o. Infinite points

(xiv) If hypotenuse of an isosceles right tangle is 22m , then each of the other side is of jength: .

~ A Jom R a Co fame Tr Awe

## section mathematics paper 2018 federal board

Time allowed: *2:40 Hours Total Marks Sections B and C: 60
NOTE: Attempt any twelve parts from Section ‘8’ and any three questions from Section ‘C’ on the separately
* provided answer book. Use supplementary answer sheet i.e, Sheet-B if required. Write your answers

neatly and legibly. Logbook and graph paper will be provided on demand.

~ a

SECTION — B (Marke 36)

— Q@.2 = Attempt any TWELVE parts. All parts carry equal marks. (12×38 36)

_ 13 1 27 21

i Let A= , Be , CF ify that 4(8-C)= AB- AC

_ a 2 OF SS 75! ¢ i i verity AB-C)

3-1

_ (i) if B= E ; [en show that BB” = /

os (ii) Solve the system of linear equations using matrix inverse method, x+ y= 75, x-4y=0

a? Pe (at arr

_ (iv) Simplify (=) [¢) + 5(a’ ay

a a

— (v) Solve the following equation for real x andy (3- 2’) x+ yi) = 2(x-2yi)+ 27-1

f

- (vl) Prove that log, | m\ = log, m—log,n

qa

392

_ (vil) Use jog to find the value of SEL

## 127« 4246 9th class

- (vil) Perform the indicated operation and simplity —2>2——~
**2*

x’+6×49 2x°-18

_ (x) If $x-6y =13 and xy <6, then find the value of 125x° ~ 216°

_ () — Factorize 4x‘ +81

(xi) The polynomial x° + Lx” +mx+ 24 has a factor x+4 and it leaves a remainder of 36 when divided by

~ (x2). Find the values of / and m. - (x1) Factorize the potynomial by factor theorem x° ~6x’ +3x+10

_ (in) Find H.C-F by division method 2x’-4x‘-6x , x°+x4-3x’-3x’

(xiv) Find the value of & for which the following expression will become a perfect square.

~_ 4×4 12x” +37x) -42x+k

~ (xv) ~~ Solve the equation 7-1-4 ,xeal

x-) x+l x41

~ (xvi) Solve the double inequality —2 { at where xe R

\

(xvii) Solve the following pair of equations x=3y , 2x—3y = —6 using table of value of x andy

_ (xviii) Find the length of the diameter of the circle having centre at (-3,6) and passing through P(I, 3)

_ SECTION — C (Marka 24)

## section paper 2018 federal board

pare — 3 te Seeker anewer sheet m7 eer 7 required. Write your answers

neatly and legibly. Logbook and graph paper will be provided on demand.

= eee

SECTION ~ B (Marts 36)

_ Q.2 Attempt any TWELVE parts. All parts carry equal marks. {12×3=36)

: 2b] 0-77

_ () Find the values of a, b. c andd which satisfy the matrix equation [? , ; ‘al = 3 5 |

_ “1s “1 2]

i For the matrices 4 = , B= verify that (AB) =B’A’

- E 0 PT ‘| iy tat (AB)

(ii) Use matrices to solve the folowing system of linear equations by the Cramer’s Rule

— Bx-4ys4 , x+2y=8

— (w} Simplity and write your answer in the form of a+ bi, —

Q+x)I-)

_ ee (81)*.3° = (3) “.(243) (v) Use law of exponents to simplify —-———__—-*– x? -12x+4

_ (0″)3″)

x ” 1

_ (vi) Find the vate of x log $= Fx

3 nSé

_ (vil) Use log to find the vatue of (38y 0.056

_ (388)

(vil) Wex#y+2=12 and x? + y? +2? = 64. then find tne value of xy yz +20.

~ (og =/5 +2 , Find the vaiue of g at

— q

00 Factorize (x? -4x(x? – 4x~1)-20

~ (xi) For what value of m is the polynomial P(x) = 4x° – 7x? + 6x —3m exactly divisible by x+2

~ (xii) Factorize the cubic polynomial by factor theorem 3x

_ (xiii) Find H1.C.F by factorization, x’ -27 , x7+6x-27 , 2x?-18

(xv) Use division method to find the square root of x‘ -10x° +37x? -60x+36

~ (xv) Solve the equation = ~x=l- 3

~ (xvi) Solve the inequality 4x-15357+2x, xER

_ (xvi) Solve the following pair of equations in x and y. 2x+y-1=0 , x =—yusing table for values of x

and y.

(xviii) The end point P of a line segment PQ is (-3,6) and its midpoint is (5,8). Find the coordinates

_ of the end point Q .

~ SECTION – C (Marks 24)

~ Note: Attempt any THREE questions. All questions carry equal marks. (3×8 = 24)

™ @3 Show that the points 4/-6.-5). BSS —4) CYS —®) and PK -® are the vartinse af a raptancie

## section 9th class mathematics paper

3 Show that the points mCe oy B(S,~5), C(3,-8} and D(~6, ~8) are the vertices of a rectangle.

_ Find the length of its diagonals. Are they equal?

— Q.4 — Prove that if in the correspondence of the two right-angled triangles, the hypotenuse and one side of one

_ triangle are congruent to the hypotenuse and the corresponding side of the other, then the triangles are congruent.

Q.5 — Prove that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Q.6 — Prove that in a right angled triangle, the square of the tength of hypotenuse is equal to the sum of the squares of

™ the length of the other two sides.

—- ar Construct the tiangle XYZ. Draw its three medians and show that they are concurrent.

mXY =5em, m¥Z=6cem, mi¥ = 60°

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