HP Board 8th Class Model Test Paper 2024 Math

24 (8th) File -10
MODEL TEST PAPER −5
Additive inverse of is
CLASS - 8th 9
5 9
SUBJECT - Mathematics (i) (ii)
9 −5
Time : 3 hours M.M. : 100
9
(iii)
v. ‚÷Ë ¬˝‡ÔŸ •ÁŸflÊÿ¸ „Ò¥ – 5
All question are compulsory w. ‚◊Ë∑ ⁄áÊ y+3 = 10 ◊ð¥ ø⁄ „Ò
w. ¬˝‡ÔŸ ¬òÊ ∑ Ù z πá«Ù¥ ◊ð¥ Áfl÷ÊÁ¡Ã Á∑ ÿÊ ªÿÊ „Ò – πá« ‘•’ ◊ð¥ (i) 3 (ii) 10
xÆ ’„È Áfl∑ À¬Ëÿ ¬˝‡ÔŸ „Ò¥ ¬˝àÿð∑ ¬˝‡ÔŸ v– •¢∑ ∑ Ê „Ò – πáÔ« - (iii) y
‘’’ ◊ð¥ vÆ Á⁄ÄÔà SÕÊŸ „Ò ¬˝àÿð∑ ¬˝‡ÔŸ v •¢∑ ∑ Ê „Ò – πá« ‘π’ In the equation y+3 = 10 the variable is
◊ð¥ vÆ ¬˝‡ÔŸ „Ò¥ ¬˝àÿð∑ w •¢∑ ∑ Ê „Ò – πá«- Œ ◊ð¥ vÆ ¬˝‡ÔŸ „Ò¥ (i) 3 (ii) 10
¬˝àÿð∑ ¬˝‡ÔŸ x •¢∑ ∑ Ê „Ò – πá«-߸ ◊ð¥ ∑È ‹ w ¬˝‡ÔŸ „Ò¥ ¬˝àÿð∑ (iii) y
¬˝‡ÔŸ z •¢∑ ∑ Ê „Ò – x. Á∑ ‚Ë ’„È ÷È¡ ∑ð ’Ê±Ê ∑ ÙáÊÙ¥ ∑ Ê ÿÙª „ÙÃÊ „Ò –
Question Paper is divided into 5 sections Section A (i) 180° (ii) 360°
consists of 30 multiplicative choice question each carry
(iii) 120°
1 mark each. Section B has 10 fill ups each carry 1 marks
each Section C has 10 question each carry 2 marks The Sum of measures of the external angles of any
Section D has 10 question each carry 3 marks. Section polygon is
E consists of 2 question. Each carry 5 marks. (i) 180° (ii) 360°
Section-A (πá«-•) (iii) 120°
’„È Áfl∑ À¬Ëÿ ¬˝‡ÔŸ (Mutiple choice question) y. ‚◊Ê¢Ã⁄ øÃÈ÷ȸ¡ ∑ð Áfl∑ áʸ ∞∑ ŒÍ‚⁄ð ∑ Ù ........... ∑ ⁄Ãð „Ò¥
−5 (i) ∞∑ ŒÍ‚⁄ð ¬⁄ ‹ê’ (ii) ‚◊Ám÷ÊÁ¡Ã
v. ∑ Ê ÿÙÖÿ ¬˝ÁËÙ◊ „Ò –
9 (iii) ¬˝ÁÃë¿ð Œ
5 9 Diagonals of a parallelogram ...........each other.
(i) (ii)
9 −5 (i) perpendicular to one another
9 (ii) bisect each other
(iii)
5 (iii) intersect

25 (8th) File -10

z. }v ∑ Ê flª¸◊Í‹ „Ò¥ – ~. ‹Ê÷ % = ‹Ê÷ × vÆÆ
(i) | (ii) vv ?
(iii) ~ (i) Áfl∑˝ ÿ ◊ÍÀÿ (ii) ∑˝ ÿ◊ÍÀÿ
The square root of 81 is (iii) ◊Í ‹ œŸ
(i) 7 (ii) 11 Profit % = Profit × 100
(iii) 9 ?
{. ‚¢ÅÿÊ z ∑ Ê ÉÊŸ „Ò – (i) Selling Price (ii) Cost Price
(i) vwz (ii) vz (iii) Principal
(iii) wz vÆ. ∞ð‚Ë ¬Á⁄◊ðÿ ‚¢ÅÿÊ Á‹Áπ∞ Á¡‚∑ Ê ∑ Ù߸ √ÿÈà∑˝ ◊ Ÿ„Ë¥ „Ò –
The cube of 5 is
(i) Æ (ii) v
(i) 125 (ii) 15
(iii) -v
(iii) 25
The rational number that does not have a reciprocal.
|. v Á∑ .◊Ë. = ............ ◊Ë≈⁄
(i) 0 (ii) 1
(i) vÆÆ (ii) vÆ
(iii) –1
(iii) vÆÆÆ
1 km. = ............ metre
vv. ∞∑ øÃÈ÷ȸ¡ ∑ Ê ŸÊ◊ Á‹Áπ∞ Á¡‚∑ð Áfl∑ áʸ ’⁄Ê’⁄ „Ò
(i) 100 (ii) 10 (i) ‚◊øÃÈ÷È¡¸ (ii) ¬Ã¢ª
(iii) 1000 (iii) •ÊÿÃ
}. S z ∑ Ê S vÆ ‚𠕟ȬÊà „Ò – The name of quadrilateral Whose diagonals are equal
(i) v— w (ii) w—v (i) Rhombus (ii) Kite
(iii) v— x (iii) Rectangle
The ratio between Rs 5 to Rs 10 is vw. y •ı⁄ | p ∑ Ê ªÈáÊŸ» ‹ „Ò –
(i) 1:2 (ii) 2:1 (i) w} p (ii) y| p
(iii) 1:3
(iii) vv p

26 (8th) File -10
Product of 4 and 7 p is v|. flÎà ∑ð ˇÊðòÊ» ‹ ∑ Ê ‚ÍòÊ „Ò
(i) 28 p (ii) 47 p (i) 2π
πr (ii) π r2
(iii) 11 p 1
(iii) πr
vx. xy, yz, zx ∑ Ê ªÈáÊŸ» ‹ „Ò – 2
(i) 2xyz (ii) x2yz The formula of Area of circle is
(iii) x2 y2 z2 (i) 2π
πr (ii) π r2
Product of xy, yz and zx is
1
(i) 2xyz (ii) x2yz (iii) πr
2
(iii) x2 y2 z2 v}. ÿÁŒ ÉÊŸ ∑ Ë ÷È¡Ê 4 cm „Ò ÃÙ ÉÊŸ ∑ Ê •Êÿß „Ò –
vy. 1+ x+x2 ◊ð¥ x2 ∑ Ê ªÈáÊÊ¢∑ „Ò – (i) 16 cm2 (ii) 8 cm2
(i) w (ii) v (iii) 64 cm3
(iii) Æ Find the volume of a cube whose side is 4 cm.
The co-efficient of x2 in 1+x+x2 is (i) 16 cm2 (ii) 8 cm2
(i) 2 (ii) 1 (iii) 64 cm3
(iii) 0 v~. 3–2 ∑ Ê ◊ÊŸ „Ò –
1 1
am
(i) (ii)
9 3
vz. =?
an 1
(iii)
(i) a m–n (ii) am+n 6
The value of 3–2 is
(iii) a mn 1 1
(i) (ii)
v{. •Êÿ‹⁄ ‚ÍòÊ „Ò – 9 3
(i) F+V=E+2 (ii) F–V=E+2 1
(iii)
6
(iii) F+V=E-2
Which one of the folling is Euler’s Formula wÆ. a 2 – b2 ∑ð ªÈáÊŸπ¢« „Ò
(i) F+V=E+2 (ii) F–V=E+2 (i) (a – b) (a – b) (ii) (a + b) (a – b)
(iii) (a + b) (a + b)
(iii) F+V=E–2

27 (8th) File -10
Factor of a2 – b2 is The factors of 7a2+14a are
(i) (a – b) (a – b) (ii) (a + b) (a – b) (i) 7a(a+7) (ii) 7a (a+2)
(iii) (a + b) (a + b) (iii) 7a2(1+2)
wv. 12x •ı⁄ 36 ∑ Ê ‚Êfl¸ ªÈáÊŸπ¢« „Ò – wz. ab-bc, bc-ca, ca-ab ∑ Ê ÿÙª» ‹ „Ò–
(i) 6 (ii) 12 (i) 0 (ii) abc
(iii) 9 (iii) 2abc
Common factor of 12x and 36 is Sumn of ab-bc, bc-ca and ca-ab is
(i) 6 (ii) 12 (i) 0 (ii) abc
(iii) 9 (iii) 2abc
ww. ÉÊŸ ∑ Ê ¬ÎDÔ Ëÿ ˇÊðòÊ» ‹ w{. a 2 × 2a22 × 4a 26 ∑ Ê ªÈáÊŸ» ‹ „Ò –
(i) 3 l (ii) 6 l
(i) 8a 48 (ii) 8a 50
(iii) 6 l2
(iii) 20a50
Surface area of a cube is
The product of a 2 × 22 × 4a26 is
(i) 3l (ii) 6l
(i) 8a 48 (ii) 8a 50
(iii) 6l2
wx. ÿÁŒ ‚◊øÃÈ÷ȸ¡ ∑ð Áfl∑ áʸ 7cm •ı⁄ 12cm „Ò¥ ÃÙ ß‚∑ Ê ˇÊðòÊ» ‹ (iii) 20a50
„Ò – −13
w|. ∑ Ê ªÈáÊÊà◊∑ ¬˝ÁËÙ◊
(i) 42cm2 (ii) 45cm2 19

(iii) 21cm2 19 19
(i) (ii)
If the diagonals of rhombus are 7cm and 12 cm then its 13 −13
area is
13
(i) 42cm2 (ii) 45cm2 (iii)
19
(iii) 21cm2
−13
wy. 7a2+14a ∑ð ªÈáÊŸπ¢« „Ò¥ – Mutiplication inverse of is
19
(i) 7a(a+7) (ii) 7a (a+2)
(iii) 7a2(1+2)

28 (8th) File -10

19 19 2 4 3
(i) (ii) (i) (ii) (iii)
13 −13 7 7 7

13 The probability of finding a red apple
(iii)
19 2 4 3
(i) (ii) (iii)
w}. ÿÁŒ 6x=12 „Ò ÃÙ x ∑ Ê ◊ÊŸ „Ò – 7 7 7
(i) 4 (ii) 3 Section - B( πá« - B)
(iii) 2 w. Á⁄ÄÔà SÕÊŸ ÷⁄Ù¥
If 6x=12 then the value of Fill in the blanks 1×10=10
(i) 4 (ii) 3 v. ‡ÊÈãÿ ∑ Ê √ÿÈà∑˝ ◊ ............. „Ò
(iii) 2
Zero has ........... receprocal
w~. ߟ◊𥠂ð ∑ ıŸ ‚Ë ¬Íáʸ flª¸ Ÿ„Ë¥ „Ò – t
(i) 64 (ii) 81 w. ÿÁŒ ‚◊Ë∑ ⁄áÊ = 12 „Ò ÃÙ ∑ Ê ◊ÊŸ ........... „Ò
5
(iii) 45 t
If an equation is = 12 then the value of t is ...........
Which of the following is not a perfect square. 5
(i) 64 (ii) 81 x. ÃËŸ ÷È¡Ê•Ù¥ flÊ‹Ë ‚◊ ’„È÷È¡ ∑ Ù ............ ∑ „Ãð „Ò
(iii) 45 a regular Polygon of 3 sides 3 is known as ..........
xÆ. •Ê∑Î Áà ◊𥠋ʢ’ ‚ð’ ôÊÊà ∑ ⁄Ÿð ∑ Ë ¬˝Áÿ∑ ÃÊ ôÊÊà ∑ ËÁ¡∞–
y. 64 =............

64 = ............
z. {y ∑ Ê ÉÊŸ◊Í‹ 3 64 = ........... „Ò
Cuberoot of 64, ie 3 64 = ............
{. a m × an = a ..........
a m × an = a ..........
|. Á∑ ‚Ë flSÃÈ ∑ð •¢Á∑ à ◊ÍÀÿ ◊ð¥ ŒË ¡ÊŸð flÊ‹Ë ÉÊÍ„ ∑ Ù ............
∑ „Ãð „Ò –

29 (8th) File -10

Reduction given on the marked price of the article is called Section C (πáÔ« ) ‚
........... x. ŒÙ •¢∑ Ù¥ flÊ‹ð ¬˝‡ÔŸ
}. ¡’ éÿÊ¡ flÊÁ·¸∑ ‚¢ÿÙÁ¡Ã „ÙÃÊ „Ò ÃÙ Each question carry 2 marks. 2×10=20
7
.... n v. ∑ Ù ‚ÅÿÊ ⁄ð πÊ ¬⁄ ÁŸM Á¬Ã ∑ ËÁ¡∞
∑È ‹ ⁄ÊÁ‡Ê A = P(1 + ) 4
100 7
Amount when Intereset is compounded annually Represent an number line.
4
.... n w. –20x4 ÷10x2 ∑ Ê Áfl÷Ê¡Ÿ ∑ ËÁ¡∞
A = P(1 + )
100
Divide –20x4 ÷10x2
~. x. ÄÿÊ Á∑ ‚Ë ’„È » ‹∑ ∑ð vÆ » ‹∑ wÆ Á∑ ŸÊ⁄ð •ı⁄ vz ‡ÊË·¸ „Ù
‚∑ Ãð „Ò
Can a Polyhedron have 10 faces, 20 edges and 15 vertix?
y. ªÈáÊŸ» ‹ ôÊÊà ∑ ËÁ¡∞
–4p, 7pq
Find the product of –4p, 7pq
z. ‚Ù„Ÿ Ÿð ∞∑ ¬È⁄ ÊŸÊ ⁄ð Á»˝ ¡⁄ð ≈ ⁄ M wzÆÆ ◊ð¥ π⁄ËŒÊ •ı⁄ ©‚ð
M xxÆÆ ◊𥠒ðø ÁŒÿÊ– ©‚∑ Ê ‹Ê÷ ÿÊ „ÊÁŸ ¬˝ÁÇÊà ôÊÊà ∑ ËÁ¡∞
Sohan bought a second hand refrigerator for Rs 2500
and sold it for Rs 3300 Find his loss or gain Percent.
{. ∞∑ √ÿÁÄÔà ∑ð flðß ◊ð¥ vÆ % flÎÁh „ÙÃË „Ò – ÿÁŒ ©‚∑ Ê ŸÿÊ
flðß v,zy,ÆÆÆ „Ò ÃÙ ©‚∑ Ê ◊Í‹ flðß ôÊÊà ∑ ËÁ¡∞
A man got 10% increase in his salary if his new salary is
Rs 1,54,000. Find his orginal salary
|. ‚◊Ë∑ ⁄áÊ ∑ Ù „‹ ∑ ËÁ¡∞
vÆ. √ÿ¢¡∑ 7x - 42 ∑ð ªÈáÊŸπá« ............. „Ò¥
Factor of 7x - 42 is ........... 7 3
5x + = x−4
2 2

30 (8th) File -10

7 3 Find A and B in
Solve 5 x + = x − 4 1 2 A
2 2
+6 A B
}. •÷ÊÖÿ ªÈáÊŸ πáÔ« ÁflÁœ ‚ð vx}wy ∑ Ê ÉÊŸ◊Í‹ ôÊÊà ∑ ËÁ¡∞
A 0 9
Find the cube root of 13824 by Prime factorisation
method. y. „‹ ∑ ËÁ¡∞ — (y2 + 7y + 10) ÷ (y + 5)
~. ∞∑ ∞ð‚ð ÉÊŸÊfl ∑ Ë ™ øÊ߸ ôÊÊà ∑ ËÁ¡∞ Á¡‚∑ Ê •Ê¬ÃŸ w|zcm 3 Solve : (y 2 + 7y + 10) ÷ (y + 5)
•ı⁄ •ÊœÊ⁄ ∑ Ê ˇÊðòÊ» ‹ 25cm2 „Ò z. ∞∑ »Ò Ä‚ ∑ Ù ∑È ¿ flSÃÈ∞° {x ÁŒŸ ◊𥠒ŸÊŸð ∑ð Á‹∞ yw ◊‡ÊËŸÙ¥
Find the height of cuboid whose volume is 275cm3 and ∑ Ë •Êfl‡ÿ∑ ÃÊ „ÙÃË „Ò – ©ÃŸË „Ë flSÃÈ∞¢ zy ÁŒŸ ◊𥠒ŸÊŸð ∑ð
base area is 25cm2 Á‹∞ ◊‡ÊËŸÙ ∑ Ë •Êfl‡ÿ∑ ÃÊ „٪˖
vÆ. ÷ʪ ∑ Ë ÁflÁœ ‚ð vx{~ ∑ Ê flª¸◊Í‹ ôÊÊà ∑ ËÁ¡∞ A factory requires 42 machines to produces a given
Find the square root of 1369 by division method number of articles in 63 days. How many machines would
Section D πá« Œ be required to produce the same number of articles in
y. ÃËŸ •∑ Ù¥ flÊ‹ð ¬˝‡ÔŸ 54 days.
Each question carry 3 marks 3×10=30 {. P(p – q), q(q – r) ∞∑ r(r – p) ∑ Ù ¡ÙÁ«∞
v. ∞∑ øÃÈ÷ȸ¡ PQRS ∑ Ë ⁄øŸÊ ∑ ËÁ¡∞ Á¡‚◊ð¥ PQ=4cm QR Add P(p – q), q(q – r) and r(r – p)
= 6cm, Rs = 5cm, PS = 5cm •ı⁄ PR = 7cm „Ù |. ∞∑ ÉÊŸÊ◊ ∑ Ë Áfl÷Ê∞° 60cm × 54cm × 30cm „Ò – ß‚ ÉÊŸÊ÷
Construct a quardrilateral PQRS Where PQ=4cm QR ∑ð •¢Œ⁄ 6cm ÷È¡Ê flÊ‹ð Á∑ ßð ¿Ù≈ð ÉÊŸ ⁄πð ¡Ê ‚∑ Ãð „Ò¥ –
= 5cm, RS 5cm, PS 5 Cm and PR=7cm. A cuboides of dimension 60cm × 54cm × 30cm. How
w. vÆ,}ÆÆ ¬⁄ x fl·¸ ∑ð Á‹∞ vw½% flÊÁ·¸∑ Œ⁄ ‚ð flÊÁ·¸∑ M ¬ ◊ð¥ many small cubes with side 6cm can be placed in the
‚ÿÙÁ¡Ã ∑ ⁄Ÿð ¬⁄ ø∑˝ flÎÁh √ÿÊ¡ ¡Êà ∑ ËÁ¡∞ given cube.
Find compound interest of Rs 10800 for 3 year at 12½% }. 3m 2+9m+6 ∑ð ªÈáÊŸπ¢« ôÊÊà ∑ ËÁ¡∞
per annum compounded annually Find the factor of 3m2+9m+6
x. A •ı⁄ B ∑ Ê ◊ÊŸ ôÊÊà ∑ ËÁ¡∞ ~. ∞∑ ∞ð‚ð flð‹Ÿ ∑ Ë ™ øÊ߸ ôÊÊà ∑ ËÁ¡∞ Á¡‚∑ Ë ÁòÊÖÿÊ 7cm •ı⁄
1 2 A ∑È ‹ ¬Îc∆Ëÿ ˇÊðòÊ» ‹ ~{}Cm 2 „Ò–
+6 A B Find the height of a cyclinder whose radius is 7cm and
A 0 9 total surface area is 986cm2

31 (8th) File -10

vÆ. (x+a) (x+b) = x2 + (a+b) x+ab ∑ Ê ¬˝ÿÙª ∑ ⁄∑ð {. ÁŸêŸ ÁflãŒÈ•Ù¥ ∑ Ù flªÊ¸Á∑ à ∑ ʪ¡ ¬≈ •¢Á∑ à ∑ ËÁ¡∞ •ı⁄
501× 502 ∑ Ù „‹ ∑ ⁄𥠌ðÁπ∞ Á∑ ÄÿÊ flð ‚÷Ë ∞∑ „Ë ‚⁄‹ ⁄ð πÊ ◊ð¥ „Ò – •ª⁄ „Ò ÃÙ ©‚
by using identify (x+a) (x+b) = x2 + (a+b) x+ab ⁄ð πÊ ∑ Ù ŸÊ◊ ŒËÁ¡∞
Solve 501× 502 (Æ, w), (Æ, z) , (Æ, {) (Æ, x.z)
Section - E πá« - (߸) Plot the following points and verify if they lie on a line if
they lie on a line name it.
z •∑ Ù¥ flÊ‹ð ¬˝‡ÔŸ
(0, 2) (0, 5) (0, 6) (0, 3.5)
Each question carry 5 marks 2×5=10
z. ÁŸêÔŸ Á‹Áπà ‚ÍøŸÊ ∑ Ù Œ‡ÊʸŸð flÊ‹Ê ∞∑ ¬Ê߸ øÊ≈¸ πËÁø∞– ÿ„
‚Ê⁄áÊË √ÿÁÄÔÃÿÙ¥ ∑ð ∞∑ ‚◊Í„ mÊ⁄Ê ¬‚¢Œ Á∑ ∞ ¡ÊŸð flÊ‹ð ⁄ªÙ¥
∑ Ù Œ‡ÊʸÃË „Ò –
⁄¢ ª √ÿÁÄÔÃÿÙ¥ ∑ Ë ‚¢ÅÿÊ
ŸË‹Ê v}
„⁄Ê ~
‹Ê‹ {
¬Ë‹Ê x
ÿÙª x{
Draw a pie chart showing the following information. The
table shows the colours prefred by a group of peoples.
Colours No. of peoples
Blue 18
Green 9
Red 6
Yellow 3
Total 36