02 SEPTEMBER 2014
Mathematics Mock Test
Summative Assessment 1
Prepared according to CBSE guidelines
MM 90
Mathematics Mock Test Class IX SA1 2014
Time 3 hours
Questions 1- 4 carry 1 mark each, 5 - 10 carry 2 marks each, 11 - 20 carry
3 marks each and 21 - 31 carry 4 marks each.
Section A
1
1.
Write rationalisation factor of
2.
Find all real zeroes of x2 + 1
3.
In ΔABC, ∠ A + ∠ B = 95° and ∠ C + ∠ B = 105°. Find ∠ B
4.
Write abscissa of all points on y axis.
6− 5
Section B
5.
Represent 4.113 as a vulgar fraction.
6.
Factorise 25a2 – 9b2 – 5a – 3b
7.
C is midpoint of line segment AB and D is midpoint of line segment XY. If
AC = XD, using Euclid’s axiom show AB = XY.
8.
X and Y are points on sides AB and BC of ΔABC respectively. If AX = CY and
AB = BC, show using Euclid’s axiom BX = BY.
9.
Sides of a triangle are in ratio 2:3:4 and its perimeter is 180 cm. Find its area.
10.
Find area of a rhombus whose one side is 80 cm and one diagonal is 96 cm.
or
Find area of an equilateral triangle of side a using Heron’s formula.
Section C
11.
If 125x =
25
. Find x
5x
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MM 90
12.
Write
Mathematics Mock Test Class IX SA1 2014
3
Time 3 hours
4, 3, 4 6 in ascending order.
Or
Represent
13.
6 on number line.
Show that x + 1 and 2x – 3 are factors of 2x3 – 9x2 + x + 12. Also find the
remaining factor.
14.
If the polynomial x3 + mx2 + nx + 6 has x – 2 as a factor and leaves remainder 3,
when divided by x – 3, find the value of m and n.
15.
PQR is a triangle in which PQ = PR. S is any point on the side PQ. Through S a line
is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
16.
In figure, PQ ll RS, angle PAB = 70° and angle ACS = 100°. Determine angles ABC
and BAC.
17.
In figure, transversal EF cuts two lines AB and CD at E and F respectively. EG and
FH are the bisectors of ∠ AEF and ∠ DFE respectively. If ∠ AEG= ∠ HFD, Show
that EG ll FH and AB ll CD.
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MM 90
18.
Mathematics Mock Test Class IX SA1 2014
Time 3 hours
Plot points A(0.25, 0), B(- 0.75, 0) and C(2, 200) on graph using appropriate
scale. Also find area of figure formed.
19.
O is a point in the interior of ΔABC, show that AB + AC > OB + OC
or
In figure, ∠ 3 and ∠ 4 are exterior angles of quadrilateral ABCD at point B and D.
If ∠ A = ∠ 2, ∠ C = ∠ 1. Prove that ∠ 3 + ∠ 4= ∠ 1 + ∠ 2.
20.
An umbrella is made by stitching 10 triangular pieces of cloth, each piece
measuring 20cm, 50cm and 50cm. Find the cloth required for the umbrella.
(Take 6 =2.45)
Section D
21.
Ravi was facing some difficulty in finding the value of a +
1
1
, given a =
. His
a
7−4 3
classmate Priya gave him a clue to rationalise the denominator. Ravi evaluated
a+
1
1
and thanked Priya for this goodwill. How Ravi evaluate a + ? What value
a
a
does it indicate?
22.
1
 xa  ab
Prove that  b 
x 


1
1
 xb bc  xc  ca
.  c  .  a  = 1
x 
x 


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MM 90
23.
Mathematics Mock Test Class IX SA1 2014
Time 3 hours
Factorise 27p3(4q – 2r)3 + 64q3(2r – 3p)3 + 8r3(3p – 4q)3
or
Factorise 4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
24.
Find the quotient and remainder if the 3x4 – 4x3 – 3x – 1 is divided by x – 1.
25.
Factorise using factor theorem: x3 – 3x2 + 3x – 1
26.
Factorise:
27.
Show that the perimeter of a Δ is greater than the sum of its three medians.
28.
In figure OA =OD and ∠ 1 = ∠ 2. Prove that ΔOCB is an isosceles triangle.
29.
If two parallel lines are intersected by a transversal, prove that the bisectors of
a3 −
1
2
− 2a + .
3
a
a
two pairs of interior angles enclose a rectangle.
30.
If two lines intersect, the vertically opposite angles are equal. Prove it.
Or
ΔABC and ΔDBE are equilateral and E lies on BC. Show that AE = CD.
31.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles,
calculate the angles of the triangle.
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