TEST PAPER (EXPANSION/FACTORIZATION)
1) Evaluate: (6x²- x +8)(x²-3).
2) If x - 1/x =4, find a) x²+ 1/x² b) x⁴ + 1/x⁴.
3) Evaluate: (83)² - (17)² with the formula.
4) Factorise:
a) x³- 3x² + x -3.
b) 63x²y² -7
c) 1- 6x + 9x².
d) 7x²- 19x - 6
5) ab - a - b +1=?
a) (1- a)(1- b) b) (1- a)(b- 1) c) (a- 1)(b - 1) d) (a- 1)(1- b)
6) 3+ 23x - 8x²= ?
a) (1- 8x)(3+ x)
b) (1+ 8x)(3 - x)
c) (1- 8x)(3- x) d) none
7) 7x²- 19x - 6=?
a) (x -3)(7x +2)
b) (x + 3)(7x - 2)
c) (x -3)(7x -2)
d) (7x -3)(x +2)
8) 12x²+ 60x +75=?
a) (2x +5)(6x +5)
b) (3x + 5)²
c) 3(2x +5)² d) none
9) 10p²+ 11p +3=?
a) (2p +3)(5p + 1)
b) (5p + 3)(2p +1)
c) (5p -3)(2p -1) d) none
10) 8x³- 2x =?
a) (4x -1)(2x -1)x
b) (2x² + 1)(2x - 1)
c) 2x(2x -1)(2x +1) d) none
Fill in the blanks
11) x²- 18x +81= (___)
12) 4- 36x²= (___)(___)(___)
13) x²- 14x +13= (__)(___)
14) 9z²- x² - 4y²+ 4xy = (___)(___)
15) abc - ab - c +1= (__)(__)
Test Paper-2
Section - A (10 x 1=10)
1) In the given figure,
angle BPC=19°, arc AB= arc BC= arc CD. Then, measure of angle APD is
a) 38° b) 59° c) 57° d) 76°
2) The given figures show two congruent circles with centre O and O'.
Arc AXB subtends an angle of 75° at the centre and arc A'YB' subtends an angle of 25° at the centre O'. Then , the ratio of arc AXB to A'YB' is
a) 3:1 b) 1:3 c) 2 : 1 d) 1:2
3) Greatest chord of a circle is called its
a) radius b) diameter c) chord d) secant
4) In the given figure,
if OA = 5cm, AB= 8cm and OD is perpendicular to AB, then CD is equals to
a) 2 cm b) 3 cm c) 4cm d) 5 cm
5) If a straight line APQB is drawn to cut two concentric circles,
then
a) AP> BQ b) AP= BQ c) AP< BQ d) AQ> PB
6) The radius of a circle is 5cm and the length of one chord is 8cm. The distance of the chord from the centre.
a) 4cm b) 3cm c) 5cm d) 6cm
7) In a quadrilateral ABCD, AB|| DC and AD= BC= 5.5cm, and one of the angles is 80°, then the other angles are
a) 90,90,100 b) 120,80,80 c) 80,100,100 d) 110,85,85
8) Which of the following is not true for a parallelogram ?
a) opposite sides are equal
b) opposite angles are always bisected by the diagonals
d) diagonals bisect each other.
9) ABCD is a rhombus
in which angle BCD= 100, then (x + y) equals to
a) 40 b) 60 c) 80 d) 70
10) Given a trapezium PQRS such that PQ= 12cm, RS= 5cm, PQ|| SR, PS= QR= 8cm, If Ang R = 130°, then angle P is
a) 130 b) 50 c) 150 d) 120
Section - B
(13x4= 52)
11) The given figure 
show the circumcircle of an equilateral triangle. If the radius of the circumcircle is 20cm, find the length of each side of the equilateral triangle.
12) In a circle of radius 7.5cm, AB and BC are two equal chords, 
each of length 9cm. Find the length of the chord AC.
13) Two circles of radii 17cm and 10cm intersect at two points and the length of the common chord is 16cm. Find the distance between their centres.
14) In the given figure,
the straight lines l, m and n are parallel to each other and G is the midpoint of CD. Calculate
a) BG, if AD= 7cm
b) CF, if GE= 2.5cm
c) AB, if AC= 9cm.
d) ED, if FE= 4cm.
15) ABCD is a quadrilateral P,Q,R, S are the midpoints of AB, BC, CD and DA respectively.
If AC= 6cm, BD= 8.6cm, calculate PQ, QR, SR and PS.
16) ABCD and AEFG are two parallelogram.
If Angle C= 58, determine angle F.
17) In the given figure, ABCD is a parallelogram,
AX and CY are respectively the bisectors of opposite angle A and C. If Angle DCB= 80, find the measure of angle DAX.
18) In the given figure ABCD is a parallelogram. E is the midpoint of CD and through D a line is drawn parallel to EB to meet CB produced at G and it cuts AB at F.
Show that
a) AD= (1/2) GC
b) DG= 2EB
OR
Prove that the line segment joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides and equal to half their difference.
19) PQRS is a parallelogram. PO and QO are respectively the angle bisectors of angle P and Q. Line LOM is drawn parallel to PQ.
Prove that
a) PL= QM
b) LO= OM.
20) The base of a right angled triangle is 24cm and its hypotenuse is 25cm. Find the area of the triangle.
21) The area of a triangle is 216cm² and its sides are in the ratio 3:4:5. Find the perimeter of the triangle.
22) If the length and breadth of a rectangular room are each increased by 1m, then the area of floor is increased by 21m². If the length is increased by 1m and breadth is decreased by 1m, then the area is decreased by 7m². Find the perimeter of the floor.
23) A rectangular lawn 60m by 40m has two roads, each 5m wide, running in the middle of it, and parallel to length and the other parallel to breadth. Find the cost of gravelling them at Rs3.60 per m²
24) Find the area of a trapezium ABCD in which AB|| DC, AB= 77cm, BC= 25cm, CD= 60cm and DA= 26cm
TEST PAPER - 1
(Full marks- 80)
1) Attempt all the questions (1 x 10= 10)
a) After rationalising the denominator of 7/(3√3 - 2√2), we get the denominator as
i) 13 ii) 19 iii) 5 iv) 35
b) The compound interest on 1000 at 10% per compounded annually for 2 years is
i) Rs190 ii) Rs200 iii) Rs210 iv) Rs1210
c) Factorization of 63x²- 112y² is
i) 63(x - 2y)(x +2y) ii) 7(3x + 2y)(3x -2y)
d) If x = 3, y = k is a solution of the equation 3x - 4y=-7 then the value of k is
i) 16 ii) - 16 iii) 4 iv) - 4
e) The roots of the quadratic equation x²- 3x -4=0 are
i) -4,1 ii) 4, -1 iii) 4,1 iv) -4, -1
f) The value of (log8 - log2)/log32 is
a) 2/5 b) 1/4 c) -2/5 d) 1/3
g) Three angles of a quadrilateral are 75° ,90° and 75°. The fourth angle is
i) 90° ii) 95° iii) 105° iv) 120°
h) Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is
i) 1:2 ii) 1:1 iii) 2:1 iv) 3:1
i) if d is the diameter of a circle, then its area is
i) πd² ii) πd²/2 iii) πd²/4 iv) 2πd²
j) The distance between the points (0,5) and (-5,0) is
i) 5 units ii) 5√2 units iii) 2√5 units iv) 10 units
2) Any 10 (2 x 10=20)
a) Find the amount of the compound interest on Rs8000 at 5% per annum for 2 years.
b) Find the co-efficient of x² and x in the product of (x -5)(x +3)(x+7).
c) If x - y= 8 and xy= 5, find x²+ y².
d) Solve for x and y: 3x + 4y=10; 2x - 2y=2.
e) The sum of two number is 43. If the larger is doubled and the smaller is tripled, the difference is 36, Find the two numbers.
f) Solve: 2x²- 5x = 0.
g) Evaluate : [(64)²⁾³ (2)⁻² + 8⁰]⁻¹⁾²
h) Evaluate: 2 log 5 + log 8 - (1/2) log 4.
i) in ∆ABC, AB= AC and D is point on AB such that AD = DC= BC. Show that angle BAC = 36.
j) If the sides of a triangle are in the ratio 3:4:5, prove that it is right angled triangle.
k) A chord of length 16cm is drawn in a circle of a diameter 20cm. calculate its distance from the centre of the circle.
3) Any 10 (2 x 10= 20)
a) If the area of an equilateral triangle is 81√3 cm², find its perimeter.
b) Find the area of a quadrilateral whose diagonals are of length 18 cm and 12 cm, and they interesect each other at right angles.
c) Find the radius and circumference of a circle whose area is 144π cm².
d) The volume of a cube is 729 cm³. Find its surface area and the length of a diagonal.
e) if sin x = 5/13 and x is acute angle, find the value of tan x + 1/cos x.
f) Evaluate: 2√2 cos45 cos 60 + 2√3 sin 30 tan 60 - cos 0.
g) Evaluate: cos²26+ cos64 sin 26 + tan36/cot54.
h) Find points on the x-axis which are at a distance of 5 units from the point (5,-4).
i) The mean of 5 numbers is 20. If one number is excluded, mean of the remaining numbers becomes 23. Find the excluded number.
j) Explain the meaning of class mark.
k) In a right angled triangle, if hypotenuse is 20cm and the ratio of the other two sides is 4:3, find the sides.
l) In ∆ ABC, AB= AC, Angle A= (5x + 20)°and each of the base angle is 2/5 th of Angle A. Find the measure of Angle A.
4) The compound interest on a sum of money for 2 years is Rs410 and the simple interest on the same sum for the same and at the same rate is R400. Find the sum and the rate of interest
Or
On what sum will the difference between the simple and compound interest for 3 years at 10% p.a. is Rs232.50? (4)
5) Constrct a histogram for the following data:
Weekly earnings (in Rs) No of workers
150-165 8
165-180 14
180-195 22
195-210 12
210-225 15
225-240 6 (4)
6) a) Constuct a rectangle ABCD with AB= 5 cm and AD= 3 cm. (2)
b) Draw the graphs : 2x + y + 3= 0. (2)
7) If AD, BE, CF are medians of ∆ABC, prove that 3(AB²+ BC²+ CA²)= 4(AD²+ BE²+ CF²).
OR
Prove that each angle of a rectangle is 90°.
a) If the diagonals of a rhombus are equal, prove that it is a square.
b) If the angle of a quadrilateral are equal, prove that it is a rectangle. (4)
7) Two Cubes, each with 12 cm edge, are joined end to end. Find the surface area of the resulting cuboid. (4)
8) If log {(x+ y)/2)}= (1/2) (logx + logy), show that x²+ y²= 6xy. (4)
9) a) If an angle of a parallelogram is two-thirds of its adjacent angle, find the angle of the parallelogram. (2)
b) If 2ˣ = 3ʸ = 6⁻ᶻ, show that 1/x + 1/y + 1/z = 0. (2)
10) Factorize: x⁴+ 9x²y²+ 81y⁴
Or
Factorize: x²+ x⁵. (2)
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