Model questions for SA-1

1.      A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data.

Number

of cars        0-10      10-20      20-30      30-40      40-50   50-60     60-70      70-80

             Frequency      7           14            13             12            20          11           15               8

2.      A frequency distribution of the life times of 400 T.V. picture tubes tested in a company is given below. Find the average life of a tube.

Life time (in hours)	Frequency
300-399	14
400-499	46
500-599	58
600-699	76
700-799	68
800-899	62
900-999	48
1000-1099	22
1099-1199	6

3.      If the median of the distribution given below is 28.5, find the value of x and y.

class	freq
0-10	5
10-20	X
20-30	20
30-40	15
40-50	Y
50-60	5

4.      Check graphically whether the pair of linear equation 4x – y – 8 = 0 and 2x – 3y + 6 = 0 is consistent. Also, find the vertices of the triangle formed by these lines with the x-axis.

5.      Use Euclid’s division algorithm to find the HCF of 196 and 38220.

6.      Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5, where q is some integer.

7.      Prove that square of any positive integer is of the form

8.      Draw an ogive and the cumulative frequency polygon for the following frequency

distribution by more than method.

class	freq
0-10	7
10-20	10
20-30	23
30-40	51
40-50	6
50-60	3

9.      Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.

t ² – 3;      2t⁴ + 3t³ – 2t² – 9t – 12

10.  A rhombus of side 20 cm has two angles of 60° each. Find the length of the diagonals.

11.  Obtain all the zeros of the polynomial  x⁴ +2 x³ – 7x² – 2x + 24, if two of its zeros are 1 and 2, find other zeros.

12.  What is Euclid lemma? Use euclid’s division algorithm to find the HCF of 10224 and 9648.

13.  Divide 15x3 – 20x2 + 13x – 12 by 2 – 2x + x2 and verify the result by division algorithm.

14.  In ΔABC, right-angled at B. AB = 3 cm and AC = 6 cm. Find ÐA and ÐC.

15.  Evaluate sin230° cos245°+ 4tan230° + ½  sin290° - 2cos290° + 1/24

16.  In a right angled triangle one acute angle is thrice than the measure of other angle. Find the acute angles.

17.  In a right angled triangle one acute angle is 20 more  than the measure of other angle. Find the acute angles.

18.  Smaller of two complimentary angle is 26 less than the larger one . Find the measure of angles.

19.  Verify the given sides are the sides of a right angled triangle. 15, 20,26

20.  If q is an acute angle such that cos q = ¾ then find sin q tan q - 1

                                                                                                             2tan²  q

    21. Simplify:  sin³ q+cos³ q

                           Sin q+cosq

    22. If sinq= 3/5  find all trigonometric ratios.