Section A (Each question carries 2 marks)
Q.1: Simplify the expression and evaluate it as directed:
x (x – 3) + 2 for x = 1
Q.2: An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions.
Q.3: Express 0.0000000000025 in standard form.
Q.4: Factorise: 12x + 36
Q.5: Name any two three dimensional shapes.
Section B (Each question carries 3 marks)
Q.6: Plot the following points on a graph paper. Verify if they lie on a lie.
A(1,1), B(2,2), C(3,3), D(4,4)
Q.7: There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group ?
Evaluate: (5/8) (-7) x (8/5) (-4)
Q.8: Using the Euler’s formula find the vertices, if faces are 5 and edges are 9.
Q.9: Multiply: ( a2 + 2b2 ) ( 5a – 3b )
Q.10: Using suitable identity find the product of (6x – 7) (6x + 7)
Section C (Each question carries 5 marks)
Q.11: Find the value of:
i) (1/2) (-2) + (1/3) (-2) + (1/4) (-2)
ii) (-3) 4 x (5/3) 4
Q.12: A factory requires 42 machines to produce a given number of articles in 63 days.
i) How many machines would be required to produce the same number of articles in 54 days ?
ii) How many days would it take to produce the same number of articles in 21 days ?
Q.13: Factorise the following:
i) 121b2 – 88bc + 16c2
ii) q2 – 10q + 21