Maths Unit Test
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NAME__________________________________
PEARL ACADEMY Anjali Apartment Near Sapna Hall Makarpura road Vadodara-390 009 Cell:-9825283326 9426765811
MATHS Unit Test l Total marks – 90
Total Time 2.5 hours
___________________________________________________________________________________
Q-1.Express the following in the form i. ii. iii. iv. v.
p q
[5]
0.7 18.48 0.23 0.67 32.1235
Q-2.Represent 2 , 3 and
6 on a number line.
[6]
Q-3.Draw the graph of linear equation 4x + y + 1 = 0.
[2]
Q-4.Draw the graph of linear equation x + 3y – 8 = 0
[2]
[2] Q-5.What is the name of the horizontal and the vertical lines draw to determine the position of any point in the Cartesian plane? What is the name of each part of the plane formed by these two lines? Also write the name of the point where these two lines intersect. Q-6.Explain, how irrational numbers differ from rational numbers? Q-7.Prove that Q-8.Rationalize
3 − 2 is irrational number? 5 3− 5
,
Q-9.Simplify the following
1 7+ 3
and
7 3 10 + 3
−
2 Q-11.If x +
[2]
2 3− 5
[6]
2 2 +3 3 2 5 6+ 5
Q-10.Determine “a” and “b” in the following
[2]
−
7+ 5 7− 5
3 2
[3]
15 + 3 2 −
7− 5 7++ 5
1 1 1 = 27, find the value of x + and x − 2 x x x
= a + 7 5b
[3]
[4]
Q-12.If x +
1 1 1 1 = 5 then find the value of x 2 + 2 and x 4 + 4 and x 3 + 3 x x x x
[6]
Q-13.Expand (9x + 2y + z)2
[2]
Q-14.Solve (a + b)3 – (a – b)3 and (4x + 2y)3 + (4x – 2y)3
[3]
Q-15.Find the value of (1002)2 using the identity
[2]
(a 2 − b 2 ) 3 + (b 2 − c 2 ) 3 + (c 2 − a 2 ) 3 Q-16.Simplify the following ( a − b ) 3 + (b − c ) 3 + ( c − a ) 3
[3]
Q-17.Factorize x4+4 and x4 + 4x2+3
[4]
Q-18.Factorize x12 – y12
[3] [2]
Q-19.For what values of a is 2x3 + ax2 + 11x + a +3 is exactly divisible by (2x-1) [2] Q-20.Two supplementary angles are in the ratio of 4 : 5. find the angles Q-21.If the angles ( 2x – 10) and (x -5) are complementary angles, find x.
[2]
[4] Q-22.If OP bisects angle BOC and OQ bisects angle AOC. Show that angle POA = 900 Q
C P
A
O
B
Q-23.If two parallel lines are intersected by a transversal then each pair of corresponding angles are __________ [2] Q-24.Give an example in each case. i. ii. iii.
[6]
Difference of two irrational numbers is a rational number Difference of two irrational numbers is an irrational number Difference of one rational and one irrational number is always irrational number iv. Sum of one rational and one irrational number is always irrational number. v. Sum of two irrational numbers is a rational number vi. Sum of two irrational numbers is an irrational number [4] Q-25. In the figure below BM and DN are both perpendiculars to the segments AC and BM=DN. Prove that AC bisects BD.
B
A N O M
C Q-26.Show that
D
2 and 3 3 is not a rational number.
[7]
PEARL ACADEMY Anjali Apartment Near Sapna Hall Makarpura road Vadodara-390 009 Cell:-9825283326 9426765811
MATHS Unit Test l Total marks – 90
Total Time 2.5 hours
___________________________________________________________________________________
Q-1.Express the following in the form i. ii. iii. iv. v.
p q
[5]
0.7 18.48 0.23 0.67 32.1235
Q-2.Represent 2 , 3 and
6 on a number line.
[6]
Q-3.Draw the graph of linear equation 4x + y + 1 = 0.
[2]
Q-4.Draw the graph of linear equation x + 3y – 8 = 0
[2]
[2] Q-5.What is the name of the horizontal and the vertical lines draw to determine the position of any point in the Cartesian plane? What is the name of each part of the plane formed by these two lines? Also write the name of the point where these two lines intersect. Q-6.Explain, how irrational numbers differ from rational numbers? Q-7.Prove that Q-8.Rationalize
3 − 2 is irrational number? 5 3− 5
,
Q-9.Simplify the following
1 7+ 3
and
7 3 10 + 3
−
2 Q-11.If x +
[2]
2 3− 5
[6]
2 2 +3 3 2 5 6+ 5
Q-10.Determine “a” and “b” in the following
[2]
−
7+ 5 7− 5
3 2
[3]
15 + 3 2 −
7− 5 7++ 5
1 1 1 = 27, find the value of x + and x − 2 x x x
= a + 7 5b
[3]
[4]
Q-12.If x +
1 1 1 1 = 5 then find the value of x 2 + 2 and x 4 + 4 and x 3 + 3 x x x x
[6]
Q-13.Expand (9x + 2y + z)2
[2]
Q-14.Solve (a + b)3 – (a – b)3 and (4x + 2y)3 + (4x – 2y)3
[3]
Q-15.Find the value of (1002)2 using the identity
[2]
(a 2 − b 2 ) 3 + (b 2 − c 2 ) 3 + (c 2 − a 2 ) 3 Q-16.Simplify the following ( a − b ) 3 + (b − c ) 3 + ( c − a ) 3
[3]
Q-17.Factorize x4+4 and x4 + 4x2+3
[4]
Q-18.Factorize x12 – y12
[3] [2]
Q-19.For what values of a is 2x3 + ax2 + 11x + a +3 is exactly divisible by (2x-1) [2] Q-20.Two supplementary angles are in the ratio of 4 : 5. find the angles Q-21.If the angles ( 2x – 10) and (x -5) are complementary angles, find x.
[2]
[4] Q-22.If OP bisects angle BOC and OQ bisects angle AOC. Show that angle POA = 900 Q
C P
A
O
B
Q-23.If two parallel lines are intersected by a transversal then each pair of corresponding angles are __________ [2] Q-24.Give an example in each case. i. ii. iii.
[6]
Difference of two irrational numbers is a rational number Difference of two irrational numbers is an irrational number Difference of one rational and one irrational number is always irrational number iv. Sum of one rational and one irrational number is always irrational number. v. Sum of two irrational numbers is a rational number vi. Sum of two irrational numbers is an irrational number [4] Q-25. In the figure below BM and DN are both perpendiculars to the segments AC and BM=DN. Prove that AC bisects BD.
B
A N O M
C Q-26.Show that
D
2 and 3 3 is not a rational number.
[7]
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