Maths club

Happy new year 2023 pals

We will be back with More revision materials,stay tuned.

It's my birthday TODAY.
Thanking Almighty God for His Grace in my life over the years.
Thanks for being part of that journey too.
Where's the cake?..😁

Today we are learning about equivalent fractions,How to arrange in ascending order and vice versa,Hope this one helps you.🖌️🖌️
Enjoy your day wadau.🖊️

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SECTION I

1. Without using a calculator, evaluate
5 x 6 + (-76)  4 + 27  3
( -15)  3 x ( -4) ( 3 marks )

2. Simplify m + 2 - m – 1 - m – 3
3 5 4 ( 2 marks )

3 . Draw a line AB = 12cm long. Using ruler and pair of compasses only, construct the point
X which divides the line AB internally in the ratio 5 : 3. Measure AX. ( 4 marks )

2
4. The size of each interior angle of a regular polygon is x0 and each exterior angle is x - 36 0 .
Calculate the sum of interior angles in the polygon. 3
( 4 marks )

5. The scale 1 : 50,000 is used on a drawing. An area of a thicket on the drawing is found
to be 20cm2. Calculate the area of the thicket on the actual ground in hectares. ( 3 marks )

6. The gradient of a line T through points A (2x, 4) and B (-1, x) is 1/7. Find the equation
of a line perpendicular to T through B. ( 3 marks )

3
7. The volumes of two similar containers are 625cm3 and 1080cm3 respectively. If the base
area of the smaller container is 75cm2, find the base area of the bigger container. ( 3 marks )

8. Find the range of values of x which satisfy the following inequalities simultaneously
and represent them on a number line. ( 4 marks )

9. Simplify 1252/5  34 ( 3 marks )
243 -3/5

4
10. Solve for x if log ( x + 2 ) = 1 + log ( 4x – 3 ) ( 3 marks )

11. A liquid chemical mass 800g is packed in a cylindrical container of internal radius 10cm.
Given that the density of the liquid is 0.85g/cm3, calculate to one decimal place the height of the
liquid in the container. ( 3 marks )

12. Mueni bought eight pair of shoes and ten pair of socks which costed sh. 3400. Ndinda
bought five pair of shoes and three pair of socks in the same shop which costed sh. 1,800.
Find the cost of each pair of shoes and socks. ( 3 marks )

5
13. A motorbike moving at a speed of 20km/hr leaves town A at 10.00 am. One hour later a car
moving at 45km/hr leaves town A to catch up with the motorbike. What time will it catch up the
motorbike? ( 3 marks )

14. A classroom measures ( x + 2) m by ( x – 5)m. If the area of the classroom is 60m2.
Find its length. ( 3 marks )

6
15. The proceeds of a certain harambee was distributed among three secondary schools A, B
and C. A received 1/3 of the total amount realized, B received 1/3 of the remainder while C received
4/5 of what B received. If the difference of what remained and B’s share was sh. 25,000, determine
how much the harambee realized. ( 4 marks )

16. In a Mathematical experiment it was derived that Tan 1440 = 1 - 3 , determine the value
of Tan 540 from this results leaving your answer in the form a + c where a, b and c are integers.
b ( 3 marks )

7

SECTION II ( 50 MARKS )

17. In the figure below, ABCD is a cyclic quadrilateral and that angle ABD = 420, angle
BAC = 580 and angle DBC = 360.

C

D

360
42 B

580

A
Giving reasons, find the values of;
(a) Angle DAC ( 2 marks )

(b) Angle ADB ( 2 marks )

(c) Angle ACD ( 2 marks )

(d) Angle CDB ( 2 marks )

(e) Angle CEB ( 2 marks )

8
18. (a) Complete the table below for the function y = 3x2 – 2x – 1 for -3  x  4. ( 2 marks )

X -3 -2 -1 0 1 2 3 4
3x2 3 27
-2x 6 -8
-1
Y 15 7

(b) Draw the graph of y = 3x2 – 2x – 1. (3 marks )

(c ) Draw the line y =3x + 1 on the same axis hence find the values of x for which
y = 3x + 1 and y = 3x2 – 2x – 1 are equal. ( 3 marks )

(d) Write down the simplified quadratic equation whose roots are the solution of the
simultaneous equations in (c ) above. ( 2 marks )

Pg 10. graph paper

9.
19. A cross country route has five sections AB, BC, CD, DE and EA. B is 2km on a bearing of 0500
from A. C is 5km from B. The bearing of B from C is 3000. D is 4km on a bearing 2300 from C. E
is 2.5km on a bearing 0250 from D. Use the scale 1cm for 0.5km to draw the diagram representing
the cross country route. From the diagram determine. (6 marks )

(i) The distance in km of A from E. ( 2 marks )

(ii) The bearing of E from A. ( 2 marks )

11
20. The table below shows the marks scored by 40 students in a test.

Marks 10 – 19 20 – 24 25 – 29 30 – 34 35 – 39 40 - 49
Frequently 3 4 7 10 9 7

(a) Calculate the mean mark. (3 marks )

(b) Calculate the median mark. ( 3 marks )

(c ) Calculate the standard deviation. ( 4 marks )

12
21. A cold water tap can fill a bath in 3 minutes while a hot tap can fill in 5 minutes. The drain pipe can
empty the bath in 3 ¾ minutes. The two taps and the drain pipe are fully open for 2 minutes, after
which the drain pipe is closed.

(a) What fraction of the bath is filled after the first two minutes. ( 3 marks )

(b) How many more seconds are required for the bath to be completely filled? ( 3 marks )

(c ) Given that the cold water tap delivers water at the rate of 200cm3/s, determine:
(i) The capacity of the bath in litres. (2 marks )

(ii) The rate of flow of the hot water tap. ( 2 marks )

13
22. (a) Use a ruler and pair of compasses only for all the construction in this question.
(i) Construct the parallelogram ABCD such that AB = 8cm,BC =7cm and angle
ABC = 1050. Measure AC. ( 4 marks )
(ii) Drop the perpendicular from point D to meet AC at X. Measure DX. (2 marks )
(iii) Hence or otherwise, determine the area of the parallelogram ABCD. (4 marks )

14
23. Draw the quadrilateral with vertices at A = (-6, -1), B ( -6, -4), C (3, -7) and D ( 3, 2 ).

(a) On the same grid draw the image of ABCD under enlargement centre (0, -1), scale factor 1/3. Label the image A1B1C1D1. (3 marks)

(b) Draw A11B11C11D11 th e image of A1B1C1D1 under rotation of +900 about (1, 0). (2 marks )

(c) Draw A111B111C111D111 the image of A11B11C11D11 under reflection in the line y – x = 0.
( 2 marks )

(d) Draw AIVBIVCIVDIV, the image of A111B111C111D111 under translation -2
and write the coordinates of the final image. 3 (3 marks )

15
24. A particle moves along a straight line such that its displacement s metres from a given
point is s = t3 – 5t2 + 3t + 4 where t is time in seconds.

Find:
(a) The displacement of the particle at t = 8. ( 2 marks )

(b) The velocity of the particle when t = 10. (3 marks )

(c ) The values of t when the particle is momentarily at rest. ( 3 marks )

(d) The acceleration of the particle when t = 3. (2 marks )

16.

Rule of algebra.

Just to serve as a reminder mathematicians