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Name........................................................... no. .........................., adm no........................: ..................................: .................................., mathematics alt. a, time: 2Β½ hours, lugulu girls high school, april, holiday 2023.

For examinerβs use only.

Section I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total

Section II 17 18 19 20 21 22 23 24 Total

• Evaluate 84 7 3 5

## 4 ( 4 15 5 3 4 2 )

β of β +β οΈ +β β οΈ (3 mks)

• Simplify 3 x 2 x 1
• Solve the following inequality and state the integral solutions. (3 marks)

## 21 ( 24 β 4 x)&gt; 6 ( 3 x β 34 )ο³β 32 ( 42 + 3 x)

The position vector of P is OP = 2i β 3j and M is the mid β point of PQ. Given OM = i + 4j, Obtain the vector PQ. (3 marks)

In the figure below O is the centre of the circle. &lt;BCA =80 0 and &lt;CBO = 10 0. Determine the size of &lt;CAB. (3 mks)

In a bookstore, books packed in cartons are arranged in rows such that there are 50 cartons in the first row, 48 cartons in the next row, 46cartons in next and so on.

(a) How many cartons will be there in 8th row. (2 mks)

(b) If there are 20 rows in total, find the total number of cartons in the books store. (2 mks)

• Find the value of x if. (3 mks)

The image of a point K(1,2) after translation is K 1 (-1,2). What is the coordinate of the point R whose image is R 1 (-3,3) after undergoing the same translation? (3 mks)

The figure below is a velocity time graph for a car.

(a) Find the total distance travelled by the car (2 mks)

(b) Calculate the deceleration of the car. (2 mks)

• Security light poles have been erected along both sides of a street in Bahati town. The poles are 50m apart along the left-handside of the road while they are 80m apart along the right-hand side. At one end of the road the poles are directly opposite each other. How many poles will be erected by time the poles are directly opposite each other at end of the road? (3 mks)
• Nakuru county government is to construct a floor of an open wholesale market whose area is 800m 2. The floor is to be covered with a slab of uniform thickness of 200mm. In order to make the slab, sand, cement and ballast are to be mixed such that their masses are in the ratio 3:2:3 respectively. The mass of dry mass of dry slab of volume 1m 3 is 200kg.

(a) Calculate

(i) The volume of the slab. (2 mks)

(ii) The mass of the dry slab. (2 mks)

(iii) The mass of cement to be used. (2 mks)

(b) If one bag of cement is 50kg, find the number of bags to be purchased. (1 mk)

(c) If a lorry carries 10 tonnes of ballast, calculate the number of lories of ballast to be purchased. (3 mks)

• Paul is a sales executive earning sh 20,000 and a commission of 8% for the sales in excess of 100,000. In January 2014 he earned a total of 48000 in salaries and commissions.

(a) Determine the amount of sales he made in that month. (4 mks)

(b) If the total sales in the month of February and march increased by 18% and then dropped by 25% respectively. Calculate.

(i) Paul`s commission in the month of February. (3 mks)

(b) His total earnings in the month of March. (3 mks)

• The vertices of a triangle ABC are A (2,5) B (4,3) and C (2,3). It rotates half-turn about the origin.

(a) Draw triangle ABC and A 1 B 1 C 1 under it. (4 mks)

(b) Theimage AβBβC is mapped onto AββBββCββ under a reflection R in the line x=0 followed

by a translation T = ο·ο· οΈ

. Find the coordinates of AββBββ and Cββ and AβββBβββCβββ. Hence draw triangle

AβββBβββCβββ. (4 mks)

(c) Find the area of the triangle AββBββCββ. (2 mks)

• Ombati owns a farm that is triangular in shape as shown below.

(a) Calculate the size of angle BAC. (2 mks)

(b) Find the area of the farm in hectares. (3 mks)

(c) Ombati wishes to irrigate his farm using a sprinkler machine in the farm such that it is equidistant from points A. B and C.

(i) The sprinkler rotates in a circular motion so that the maximum point reached by the water jets is the vertices A, B and C. Calculate the area outside the farm that will be irrigated. (5 mks)

• Town B is 102km on the bearing of 122 0 from town A. Town C is 94 km on bearing of 062 0 from B. Town D is on a bearing of 073 0 from A and 336 0 C.

(a) Using a scale of 1cm to represent 20km, draw a scale diagram to show the relative positions of town A, B, C and D. (4 mks)

(i) The bearing B from D. (1 mk)

(ii) The bearing of A from C. (1 mk)

(iii) The distance from town A to D. (1 mk)

(iv) The distance from town B and D. (1 mk)

• The table below gives some of the values of x and y for the functions y= Β½x 2 +22x + 1 in the

## interval 0 ο£ x ο£ 6.

(a) Complete the values in the table above. (1 mk) (b) Use the values in the table to draw the graph of function on the grid provided below. (2 mks)

(b) Using the graph and the mid-ordinate rule with 6 stripes, estimate the area bounded by the curve, the x-axis, the y-axis and the line x=6. (3 mks)

(d) Using integration, calculate the exact area and hence find percentage error made when mid-ordinate rule is used. Give your answer correct to 2. (4 mks)

x 0 1 2 3 4 5 6

University : maseno university.

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Highschool Kenya Revision Material: 2023 Notes, Free Exams with Marking Schemes

## By Dean of Studies

Check the questions here.

END TERM 3 – 2022

MATHEMATICS.

MARKING SCHEME

Instructions.

Answer all questions in the spaces provided.

• Express the following numbers in words.                                                                  (2mks)

Fourteen million six hundred and thirty three thousand and one.

Thirty million and ten.

• A matatu charges sh. 120 as fare from town A to town B. It has a capacity of  18 passangers. How much money does it make in one day covering 10 trips with full capacity.                                                                                                              (3mks)

120 x 18 = 2160

1 trip = 2160

10 trips = 2160 x 10

= shs. 21,600

• Use the divisibility test of 11 to check whether the following numbers are divisible by 11.                                                                                                                                    (2mks)

( 1 + 4 + 5 + 4 ) β (0 + 8 + 6)

14 β 14 = 0

( 1 + 2 + 0 + 4 ) β ( 1 + 0 + 4)

Not divisible

• Use Bodmas to evaluate.                                                                                            (3mks)

Β½        3 / 5 + ΒΌ  ( 7 / 3 β 3 / 7 ) of 1 Β½ Γ· 5

3 5 / 7

Β½ ( 3 / 5 + ( 40 / 21 ) of 1 Β½ Γ· 5)

Β½ ( 3 / 5 + 10 / 21 x 3 / 2 x 1 / 5 )

Β½ ( 3 / 5 + 1 / 7 )

Β½ ( 26 / 35 ) = 13 / 35

13 / 35 Γ· 3 5 / 7

13 / 35 x 7 / 26

• Victoria spent  ΒΌ  of his net January salary on school fees. She spent ΒΌ  of the remainder on electricity and water bills. She then spent 1 / 9 of what was left on transport. If she finally had sh. 3400. What was her net January salary.                                                (3mks)

School fees= ΒΌ

Electricity =  ΒΌ x ΒΎ = 3 / 16

Transport = 1 / 9 x 9 / 16 = 1 / 16

Β½ = 3400

Total salary = shs. 6800

• Using mathematical tables evaluate.
• 7340 2                                                                                                                (1mk)

7.340 x 10 3

53.88 x 10 6

5.388 x 10 7

• 14.5 2 + 0.714 2                                                                                                  (2mks)

7.14 x 10 -10 = 50.98 x10 -2

210.3 + 0.5098

• Given that a:b = 1:2 and b:c = 3:4. Find a:b:c                                                            (1mk)

a:b:c                            (1×3)                (2 x 3)              (2 x 4)

1:2                               a:                     b:                     c

3:4                               3                      6                      8

• Three bells ring at intervals 30mins, 35mins and 50 mins. If they ring together at 11:25 p.m on Monday at what time and day will they next ring together.                           (3mks)

2 x 5 x 3 x 5 x 3 = 450 mins

7hr                  30mins

2325                6:50 a.m

2050                Tuesday

•  The length of minute hand of a clock is 3.5cm. Find the angle it turns through if it sweeps an area of 4.8cm 2 . (take Ο= 22 / 7 )                                                               (3mks)

A= Ρ² x Οr 2

360

4.8 = Ρ² x 22 / 7 x 3.5 2

360

Ρ² = 44.88 O

•  Express the following as a single fraction.
• x-1  + x+2   + x                                                                                               (3mks)

2           4        5

10 (x β 1) + 5 (x +2) + 4 (x)

20

10x β 0 + 5x + 10 + 4x

• ax β ay + bx βby                                                                                             (2mks)

a+b

a(x-y) + b (x β y)

a+b

(a+b) (x-y) = x-y

a+b

• Fifteen tractors each working eight hours a day takes eight days to plough a piece of land. How long would it take 24 tractors each working 10 hours a day to plough the same piece of land.                                                                                                                (3mks)

Tractors                               hours                                     Days

15                                           8                                              8

24                                           10                                           ?

15x 8 x 8

= 4 days

• Use factor tree to decompose 256 into prime factors.                                                (2mks)

256 = 2×128                        2 x 8

2 x 64                         2 x 4

2 x 32                         2 x 2

2 x 16                           2x 2 x2 x 2 x 2 x 2 x2

= 2 7

• Juma, Ali and Hassan share the profit of their business in the ratios 3:7:9 respectively. If Juma receives sh. 6000. How much profit did the business yield.                          (3mks)

3

= shs 38000

• Use bodmas to evaluate:                                                                                             (4mks)

5×6-76Γ·4+27Γ·3

4-2×4+36Γ·4

30 β 19 + 9                          4 β 8 + 9

20                                       5

= 20 / 5

= 4

• A Kenyan bank buys and sells foreign currency as shown in the table below.

A tourist arrived in Kenya with 15000 pounds which he converted in kshs.

• How much kshs did he receive?                                                                                 (2mks)

15000 x 124.65

• He later spend sh. 125340 while in Kenya. He converted the remainder in dollars. How many dollars did he receive?                                                                                                (3mks)

-125340

1,744,410

= 1744410

125.13

= 13940.78 dollars

• A metallic cuboid measuring 16cm by 8cm by 4cm was melted. The material was used to make a cube. What is the length of the cube?                                                             (3mks)

V = L x W x h

= 18 x 8 x 4

Volume cube = L x L x L

Length = 3β512

•  Find a if a 2 = b 2 + c 2 given that b=2 c=3.5.                                                               (2mks)

a 2 = 2 2 + 3.5 2

a 2 = 16.25

• Below is a travel timetable for a vehicle operating between towns A and D 70 km apart.
• At what time does the vehicle depart from town A?                                      (1mk)
• How long does it take to travel from town A to town B?                              (1mk)
• For how long does it stay in town B?                                                             (1mk)
• At what time does it arrive in town D?                                                          (1mk)
• What is the average speed of the whole journey?                                           (1mk)

S= D  = 70

T       1 1 / 6

• A football match lasts 90 minutes with a break of 15 minutes at half time. If a referee allows five minutes extra for injuries and stoppages, what time does a match which kicks off at 4:30 pm end?                                                          (3mks)

90 + 15 + 5 = 1 hr 50 mins

1 :50

14:40 hrs

2:40p.m

• A rectangular plot measures 100m by 200m. Determine:
• Its perimeter in km.                                                                                         (2mks)

= 2 (100+200)

1000

• Its area in m 2 .                                                                                                  (2mks)

= 100 x 200

= 20,000m 2

• Its area in ha.                                                                                                   (2mks)

20000  = 2ha

• Square tiles of 100cm by 100cm are use to cover the floor. How many tiles are used?                                                                                                                    (2mks)

= 10000 x 20000

100        100

= 20,000 tiles

• If the cost of 1 tile is sh. 25. How much money will be spent on tiles.          (2mks)

20,000 x 25

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