MATHS 2ND C.A TEST

SECOND CONTINUOUS ASSESSMENT TEST CLASS : SS TWO SUBJECT: MATHEMATICS TIME: 50 MINS TOPIC 1: TRIGONOMETRY 1( SINE RULE) 1.) Find the values of θ lying between 0° and 360° for each of the following: a) cos θ= 0.2874 b) tan θ = -2.106 2.) In Δ ABC, a= 7.1cm, b = 9.5cm and B =63°18'. solve the triangle completely. ( Hint: sketch the diagram) 3.) Use trigonometrical tables to find the values of the following; i) tan 118° ii) cos 305° iii) sin 241.6° iv) tan(-280)° 4.) Find the remaining angles of ∆ABC in which a= 12.5cm, c= 17.7cm and C= 116°.

5.) A man walks due east for 4km. He then changes direction and walks on a bearing of 197° until he is south- west of his starting point. How far is he then from his starting point?

6.) A tree is on a bearing S36°W from a point X and S78°E from a point Y. If X is 200m due east of Y, calculate the distance of the tree from Y to the nearest metre.

TOPIC 2: TRIGONOMETRY 2(COSINE RULE) 7.) In ∆ABC, c=8.44km, a=7.92km and B= 151.3°, calculate /AC/.

8.) Three towns A, B, and C are situated so that /AB/= 60km and /AC/ = 100km. The bearing of B from A is 060° and the bearing of C from A is 290°. Calculate the distance /BC/.

9.) From a point on the edge of the sea, one ship is 5km away on a bearing S50°E and another is 2km away on a bearing of S60°W. Are far apart are the ships?

10.) City A is 300km due east of city B. city C is 200km on a bearing of 123° from city B. How far is it from C to A? 11.) Calculate the largest angle in a triangle with sides 4.1cm, 5.9cm and 7.7cm.

12.) The sides of a parallelogram are 7cm and 10cm and its longer diagonal is 15cm. Use the cosine formular to find the length of the other ( shorter) diagonal.

TOPIC 3: GEOMETRICAL RATIOS 13(a) Define intercept theorem 13(b) list the four(4) intercept theorem and state each of them.

14.) In the figure below, /OX/ = 4cm, /XR/ =6cm, /RZ/ =2cm and <XQR= < XZY. Calculate /YQ/.

15.) In the diagram below, LP, NR and MQ are parallel lines. If /LN/ : /LM/ = 1 : 2, calculate /NR/.

16.) In the figure below, /QL/ = 2cm, /LM/= 3cm and /PR/= 4cm, calculate /QR/.

17.) In the diagram below, if /XA/ = 9cm, /AB/= 15cm, /AP/= 10cm and /XP/= 12cm. Calculate; (i) /BQ/; (ii) /PQ/;

18.) In the diagram below, <PQX = < XZY, /PQ/ =2cm, /XP/= 3cm, /XQ/=4cm and /QY/ =2cm.

Calculate/YZ/.

TOPIC 4: SIMULTANEOUS EQUATION 19.) Solve the simultaneous equations; 2x + 5y = 1, 3x = 30 + 2y 20.) Solve the equations;

21.) A two - digit number is such that the sum of its digits is 11. The number is 27 greater than the number obtained by interchanging the digits. Find the number.

22.) A woman's age and her son's age add up to 45years. Five years ago, the woman was six times as old as her son. How old was the woman when the son was born?

23.) A cyclist cycles for x hours at 12km/h and y hours at 18km/h. Altogether she cycles 78km in 5 hours.

Find x and y.

24.) Solve the equation; 3x + y = 10, 2x² + y² = 19 TOPIC 5: STATISTICS 1( MEASURES OF CENTRAL TENDENCY) 25.) Five children have an average age of 7 years 11months. If the youngest child is not included, the average age increase to 8year 4 months. Find the age of the youngest child.

26.) In an examination, the pass mark was 45. The mean mark of eight students was 53, but two of them failed. What is the lowest possible mean mark for the six students that passed? ( Assume that the marks are whole numbers) 27.) A mother has seven children. The mean age of the children is 13years 2months. If the mother's age is included, the mean age rises to 17years 7 months. Find the age of the youngest child.

28.) A die was rolled 50 times with the results given in the table below: Score

1

2

3

4

5

6

Frequency

5

9

7

11

8

10

a) calculate the mean; b) find the median; c) what is the mode?

29.) Students at a teacher training college are grouped by ages as given in the table below; Age( years)

20

21

22

23

24

25

Frequency

4

5

10

16

12

3

(a) find the modal age; (b) find the median age; (c) calculate the mean age of the students; 30.) The number of beans in some cocoa pods is shown below: number of beans

30

31

32

33

34

35

36

number of cocoa pods

2

1

3

4

2

1

1

(a) How many pods are there? (b) calculate the mean number of beans per cocoa pods? (c) find the median number of beans per cocoa pods?