Sample CS exam
From Compsci1
SAMPLE PAPER
SECTION A
1. What is the mid point between (3,5) and (1,3)?
2. What is the slope of the following line? 2x + 3y -6 = 0
3. Find the slope of a line perpendicular to 2x + 3y -8 = 0
4. Find the midpoint of the line joining the points (0,7) and (-1,4).
5. Find the length of the line segment joining (-2,3) and (2,-4).
6. Find the slope of the line joining the two points (3,1) and (-4,-2).
7. Find dy/dx of the equation: y = 4x3-3x2+2x + 1
8. Find the local minimum of the curve y = 2x2 + 3x -1.
9. Find the local maximum of the curve: y = -2x2 +3x +4
10. Differentiate (x2+2x+1)(x2+5x+3)
11. Differentiate (3x+5)/(2x+1).
12. Find the turning points of the curve: y = x3 -3x2 – 9x +15
13. Find the amplitude, period and phase of 4 sin 2x, 5 cos (x/2 + 6).
14. Calculate the length of side a of the triangle
10cm a
450
15. Calculate the length of side a of the triangle
12cm a
5 cm
16. Draw a graph of y = 3 sin 2x between x = 0 and x = 7200
17. Draw a graph of y = 2 cos 4x between x = 0 and x = 1800
18. Convert the following numbers from binary to decimal: 1011110, 1000111, 10101101
19. Convert the following numbers from decimal to binary: 99, 123, 64
20. Convert the following numbers from binary to hexadecimal: 11001101011011, 11101111110110
21. Convert the following numbers from hexadecimal to decimal: FE46, 67CB
22. Convert the following numbers from hexadecimal to binary: C7FE, D18A
23. Why is hexadecimal used in computing?
24. Write the truth tables and draw the diagrams for AND, OR, NOT, NOR and NAND gates.
25. Using truth tables prove the following equivalence laws: De Morgan’s Laws: ~ (p v q) ≡ ~p ^ ~q ~ (p ^ q) ≡ ~ p v ~ q Commutative Law : p ^ q ≡ q ^ p
26. Calculate the length of side a of the triangle
3cm a
4 cm
27. Calculate the length of side a of the triangle
a 10 cm
0
7 cm
28. Define a megabyte.
29. Define a gigabyte.
30. What is the probability of throwing a 6 on a roll of a fair dice?
31. What is the probability of throwing an even number on a rollof a fiar dice?
32. What is the probability of throwing a 2 or a 3 on a roll of a fair dice?
33. If there are 3 balls in a bag – a red, green and blue. When a fair dice is rolled a ball is also take from the bag. Find the probability of red ball from the bag and a 6 on the dice.
34. What is the mode of the following set of data: 12 10 11 12 13 17 10 14 10 11 14 18 16 10 19 16 18 17 15 19
35. What is the mean of the following set of data: 12 10 11 12 13 17 10 14 10 11 14 18 16 10 19 16 18 17 15 19
36. Find the standard deviation for the following set of data: 12 10 11 12 13 17 10 14 10 11 14 18 16 10 19 16 18 17 15 19
