## CHECK THE QUESTIONS HERE

**END TERM 3 – 2022**

**FORM 1**

**MATHEMATICS.**

**MARKING SCHEME**

__Instructions.__

**Answer all questions in the spaces provided.**

- Express the following numbers in words. (2mks)
- 14633001

*Fourteen million six hundred and thirty three thousand and one.*

- 30000010

*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)
- 1048564

*( 1 + 4 + 5 + 4 ) – (0 + 8 + 6)*

*14 – 14 = 0*

*Divisible.*

- 1120043

*( 1 + 2 + 0 + 4 ) – ( 1 + 0 + 4)*

*7 – 5 = 2*

*Not divisible*

- Use Bodmas to evaluate. (3mks)

½ ^{3}/_{5} + ¼ (^{7}/_{3} – ^{3}/_{7} ) of 1 ½ ÷ 5

3 ^{5}/_{7}

* ½ ( ^{3}/_{5} + (^{40}/_{21}) of 1 ½ ÷ 5)*

* ½ ( ^{3}/_{5} + ^{10}/_{21} x ^{3}/_{2} x ^{1}/_{5})*

* ½ ( ^{3}/_{5} + ^{1}/_{7})*

* ½ ( ^{26}/_{35}) = ^{13}/_{35}*

^{13}*/ _{35}÷ 3^{5}/_{7}*

^{13}*/ _{35} x ^{7}/_{26}*

*= ^{1}/_{10}*

- Victoria spent ¼ of his net January salary on school fees. She spent ¼ 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= ¼*

*Electricity = ¼ x ¾ = ^{3}/_{16}*

*Transport = ^{1}/_{9} x ^{9}/_{16}=^{1}/_{16}*

*Total = ½*

* ½ = 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*

*= 210.8098*

- 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 | 30 | 35 | 50 |

5 | 15 | 35 | 25 |

3 | 3 | 7 | 5 |

5 | 1 | 7 | 5 |

7 | 1 | 7 | 1 |

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

*7hr 30mins*

*2325 6:50 a.m*

* 730*

*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 π=^{22}/_{7}) (3mks)

*A= Ѳ x πr ^{2}*

* 360*

*4.8 = Ѳ x ^{22}/_{7} x 3.5^{2}*

* 360*

* Ѳ = 44.88 ^{O}*

- Express the following as a single fraction.

- x-1 + x+2 + x (3mks)

2 4 5

*10 (x – 1) + 5 (x +2) + 4 (x)*

* 20*

*10x – 0 + 5x + 10 + 4x*

* 20*

^{19}*/ _{20}x*

- ax – ay + bx –by (2mks)

a+b

*a(x-y) + b (x – 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*

*24 x10*

* = 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=6000*

*19 = ?*

*=19 x 6000*

* 3*

*= shs 38000*

- Use bodmas to evaluate: (4mks)

5×6-76÷4+27÷3

4-2×4+36÷4

* 30 – 19 + 9 4 – 8 + 9*

* 20 5*

* = ^{20}/_{5}*

* = 4*

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

Buying (ksh) | Selling (ksh) | |

1 us dollar | 95.34 | 95.87 |

1 uk pound | 124.65 | 125.13 |

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

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

*15000 x 124.65*

*= 1869750*

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

*1867950*

* -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*

*= 512*

*Volume cube = L x L x L*

*= 512cm ^{3}*

*Length = 3√512*

*= 8 cm*

- 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*

*a= 4.031*

- Below is a travel timetable for a vehicle operating between towns A and D 70 km apart.

Town | Arrival | Departure |

A | 10.10 am | |

B | 10.30am | 10.40 am |

C | 11.00 am | 11.05 am |

D | 11.20am |

- At what time does the vehicle depart from town A? (1mk)

*10.10 am*

- How long does it take to travel from town A to town B? (1mk)

*20 mins*

- For how long does it stay in town B? (1mk)

*10 mins*

- At what time does it arrive in town D? (1mk)

*11:20 a.m*

- What is the average speed of the whole journey? (1mk)

*S= D = 70*

* T 1 ^{1}/_{6}*

*= 60km/hr*

- 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*

*16:30*

* 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*

*= 0.6 km*

- Its area in m
^{2}. (2mks)

*= 100 x 200*

*= 20,000m ^{2}*

- Its area in ha. (2mks)

*20000 = 2ha*

*10000*

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

*= 10000 x 20000*

* 100 100*

*= 100 x 200*

*= 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*

*= 500,000*