• Living The Christian Faith
• The Meaning of Prayer
• Private and Public Prayers
• Answers to Prayers
• Difference Between Prayer and Magicians
• The Relationship Between Fasting And Prayer
• Self-Denial in Service to Others
• Faith in Daily Actions
• The Meaning of Living Faith

Living The Christian Faith

The Meaning of Prayer

• Prayer is communicating withy God
• There are two types of prayers namely:
  1. Private prayer
  2. Public prayer
• During prayer Christians hold a conversation with God. 4. In prayer, one talks to god and also listens to Him.
• There are four elements of prayers
  1.  Adoration
  2. Confession
  3. Thanksgiving
  4. Supplication
• Adoration involves praise and worship
• Supplication involves petition and intercession
• Petition is a prayer on behalf of oneself.
• Intercession is a prayer on behalf of others.
• Prayers should be made in faith and humility.

Quiz

1. Confession should be accompanied by
2. The parable of teaches about humility in prayer.

Private and Public Prayers

• Prayer is a conversation with God.
• There are public and private prayers
• Private prayer is when one converses with God
• It is called individual or solo prayer
• Public prayer is made in a group
• It is also called communal or corporate prayer
• Public prayer is made aloud
• Such prayers are made in schools, homes or churches
• Public prayers are also made during occasions such as
  1. Church services
  2.  Weddings
  3. National holidays
  4. Christian holidays
• God answers public and private prayers

Quiz

1. State the meaning of the following Christian groups abbreviations
   1. C U
   2.  YMCA
   3. YWCA
   4. CA
2.  Acts 2:42 says________________

Answers to Prayers

• God listens to and answers prayers
• We know God has answered our prayers when what we pray for happens
• Christians expect answers to both public and private prayers
• God can answer prayers in three ways namely:-
  1. Yes
  2. No
  3. Wait
• God answers prayers according to his will
• When God answers “no” it might be that we prayed for something that can harm you
• God answers “wait” when the time is not appropriate for our requests.
• Saul consulted a medium at Endor when God failed to answer his prayers.
• God was angry with Saul because of his disobedience.
•  We should obey God so that our prayers get answered.

Quiz

1. Write a prayer before exams
2. State four elements of prayers

Difference Between Prayer and Magicians

1. Magic is manipulating forces in the universe to achieve results.
2. It can be used for good or evil purposes
3. Consulting magicians comes from lack of trust in God.
4. Traditional Africans used magic to produce :-
   1. Wealth
   2. Luck
   3. Success
   4. Good health.
5. Magic creates dependence on magicians who may control victims to their detriment.
6. Prayer, unlike magic has positive effects on a Christian.
7. It is guided by the free will of a Christian
8. Christian prayers lead to peace and reconciliation with God, oneself and others
9. Simon of Samaria used magic to do wonders.
10. He tried to buy the Holy Spirit using money which offended God.

Quiz

1. The words magician utter are called_________________
2. Magicians cast__________________ on their victims.

The Relationship Between Fasting And Prayer

• Fasting and prayer are Christians practices.
• Fasting is voluntarily denying oneself food and spend time in prayer.
• It involves self denial and disciplined commitment
• Fasting intensifies the effects of prayers
• Jesus taught his disciples to be humble when praying and fasting.
• He taught that fasting should not be done for a public show.
• One can fast to pray for personal or individual needs.
• Fasting can also be done to intercede for others.
• Genuine fasting is rewarded by God.
• Prayer and fasting brings one nearer to God.

Quiz

1. State three bible personalities who went without food for forty day
   1. _____________________
   2. _____________________
   3. _____________________
2. Jesus taught that prayer and fasting should be done in_____________________

Self-Denial in Service to Others

• Self-denial is depriving oneself of certain things so as to serve others
• Fasting is an example of self-denial in order to pray.
• Christians also sacrifices money and other resources to serve God.
• Christians also sacrifice their time to serve
  1. The aged
  2. Destitute children
  3. Prisoners
  4. People living with HIV/AIDS
• Jesus taught that following Him is about self denial
• He taught that Christians must put the interest of others before their own
• Following Jesus involves carrying the cross daily.
• The cross is a symbol of suffering.

Quiz

1. List five ways through which Christians demonstrates self-denial
   1. _______________
   2. _______________
   3. _______________
   4. _______________
   5. _______________
2. Celibacy means______________

Faith in Daily Actions

• Christians face many challenges that require them to demonstrate their faith
• A committed Christian should trust in God even in difficult circumstances
• Christians can demonstrate their faith by :-
  1. Obeying God’s commandments
  2. Observing set rules and regulations
  3. Reporting crime to lawful authorities.
  4. Being role models
  5. Helping the needy.
  6. Self-denial
  7. Practicing honesty and integrity.
• The bible teaches that Christians should offer themselves as a living sacrifice.
• They should dedicate themselves to God’s service
• Christians should please God in all they do.
• They should allow God to transform them inwardly to be like Him
• We should emulate the example of patriarchs who had total faith in God.

Quiz

1. ________________was considered blameless and walked with God
2. God called a man after my own heart.

The Meaning of Living Faith

• Living faith involves actions dictated by gospel values.
• Gospel values include :-
  1. Honesty
  2. Integrity
  3. Love
  4. Mutual caring
  5. Sharing
• Apostle James teaches that Christian’sfaith should be meaningful
• Living faith is accompanied by actions
• It involves practically showing concern for the needy.
• Faith without action is dead.
• James also taught that Christiansshould confess their sins to one another
• A prayer made in faith by a righteous person has power to heal.
• Jesus taught that it is more blessed to give than to receive.
• We should demonstrate living faith in all we do.

Quiz

1. The crippled beggar at the Beautiful gate was healed by _______________ and ______________
2. State three reasons for fasting
   
   1. ______________________
   2. ______________________
   3. ______________________

• Jesus Christ's Victory Over Pain and Suffering
• Causes of Suffering
• Pain and Suffering
  • Varieties of Mental Suffering
  • Varieties of Physical Suffering
  • Varieties of Emotional Suffering
• Jesus Christ Triumphs Over Pain and Suffering
• The Purpose of Suffering
• Martyrdom
• Christian Suffering Today

Jesus Christ's Victory Over Pain and Suffering

Causes of Suffering

• Suffering is the feeling of pain, sorrow or discomfort.
• All people experience suffering in different ways
• Suffering is caused by:-
  1. Natural calamities
  2. Negligence
  3. Sickness and death
  4. Irresponsible sexual behavior
  5. Armed attacks e.g. by robbers
  6. War and ethnic clashes
  7. Violence in homes, at school
  8. Drug substance abuse.
  9. Jesus taught that suffering can be caused by sins
  10. He forgave the sins of the paralyzed man and took away his suffering.
• Suffering can also come so that God’s glory may be seen
• Jesus took away the suffering of the blind man when He sent him to the pool of Siloam.
• We should trust in God to overcome all forms of suffering.

QUIZ

1. The Word Siloam means?
2. Write three examples of natural calamities.

Pain and Suffering

• Pain and suffering are the same or related
• There are three main types of suffering:
  
  1. Physical suffering
  2. Emotional suffering
  3. Mental suffering
• Physical suffering involves inflicting pain on the body.
• Emotional suffering involves feelings such as guilt, sadness or joy.
• Mental suffering relates to the mind
• Job suffered mentally, emotionally and physically
• He suffered physically because he got sores all over his body.
• He suffered emotionally because he lost the children he loved
• Job also suffered mentally when he lost everything he owned.
• We should remain faithful to God who helps us overcome suffering.

Quiz

1. State three types of suffering each with a valid example
2. Name another person in the bible other than Job who suffered physically.
3. Job 2:10 says_____________________

Varieties of Mental Suffering

• Any problem that affects the mind causes mental suffering
• Not all people who suffer mentally are mad
• Some people may be depressed while others are retarded.
• Mental suffering can be caused by:-
  1. Diseases
  2. Injury to the brain
  3. Disturbing experiences
  4. Being naturally born in such a state
  5. Drug and substance abuse.
• Jesus healed a man who suffered mentally in Gerasa territory.
• The man had an evil spirit which made him mad.
• He was called legion or mob because the demons in him were many
• Jesus has the power to heal those who suffer mentally.

Quiz

1. The evil spirits in legion begged Jesus not to__________
2. Mad people are also called_____________
3.  To be possessed means__________________

Varieties of Physical Suffering

• Physical suffering occurs when pain is inflicted in the body.
• Physical suffering can be caused by :-
  1. Injury
  2. Deprivation
  3. diseases
  4. Brutality
  5. War
  6. Poverty
  7. injustice
• Jesus taught the parable of the rich man and Lazarus.
• The rich man lived in great luxury and comfort
• Lazarus had sores on his body and no food to eat
• The rich man did not show love and concern for Lazarus.
•  Lazarus competed with dogs for left over’s from the rich man’s table
• Lazarus trusted in God and ended up being rewarded in paradise.

Quiz

1. List down four examples of suffering
2. The _____________of _________________, the first Christian martyr made him suffer physically.

Varieties of Emotional Suffering

• People suffer emotionally when they feel rejected or unloved.
• Other cause of emotional suffering may include :-
  1. Conflict between friends or relatives
  2. Failure in exams
  3. Harassment and bullying
  4. Loss of loved ones
  5. Breakdown in relationship
  6. Unemployment or loss of a job.
  7. Poverty.
• When people suffer emotionally they cry or weep.
• Emotional suffering can be overcome through prayer and moral support.
• It can also be dealt with through guidance and counseling.
• Jesus was tried both by Pirate and Sanhedrin.
• He suffered emotionally because of the false accusations brought up against Him
• Like Jesus, we should always trust in God to help us overcome suffering.

QUIZ

1. Which actions of the soldiers made Jesus suffer emotionally?
   1. ______________________
   2. ______________________
2. Jesus persevered because his suffering had_____________________

Jesus Christ Triumphs Over Pain and Suffering

• Jesus underwent pain and suffering
• He persevered suffering in humility and silence
• He accepted his suffering to save mankind from sin.
• Jesus was the final sacrifice for the deliverance of man
• He suffered to accomplish a mission which was the will of God.
• Prophet Isaiah referred to Jesus as the suffering servant.
• While on the cross Jesus said the following things
  1. Eloi Eloi Lama Sabachthani
  2. Father forgive them for they do not know what they are doing.
  3. Behold your mother, behold your son.
  4. Today you will be with me in paradise
  5. I am thirsty
  6. Father, into your hands I place my spirit.
  7. It is done it is finished.
• Christians remember Jesus victory over pain and suffering during Easter.

Quiz

1. The man who repented after he was crucified with Jesus was________________
2. After Jesus’ death, the centurion said__________________

The Purpose of Suffering

1. Suffering is worthwhile when it has a purpose
2. Africans suffered as they fought for independence
3. Jesus died in order to save us from our sins
4. Jesus died physically but resurrected from the dead.
5. Christians share the experience of Jesus through baptism.
6. We share the privilege of Noah, who together with his family was saved from the flood.
7. When we suffer because we are Christians, we shall be rewarded. Christians should not suffer for immoral things.
8. Apostle peter taught that those who suffer for Christ glorify God.
9.  In suffering Christians should trust God because He keeps His promises.

Quiz

1.  A martyr is________________
2. _________________was the first Christian martyr
3. Jesus sweat blood in the_______________ of ______________

Martyrdom

• A martyr is a person who suffers or dies for their faith.
• Throught history, many people have died or suffered because they refused to denounce their faith.
• Kabaka Mwanga’s rule in the Buganda kingdom led to the death of many Christian
• Among those who died were Charles Lwanga, Joseph Mukasa kizito and Mathias Mulumb
• There is a shrine dedicated to the martyr at Namugongo
• Stephen was the first Christians martyr
• He was one of the seven deacons
• The seven deacons were
  1. Philip
  2. Nicanor
  3. Prochorus
  4. Nicolaus
  5. Permenas
  6. Timon
  7. Stephen
•  Stephen was opposed by the Libertines, the synagogue of Freedmen.
• Jesus promised us the holy spirit to help endure suffering.

Quiz

1. Mention tha North African Martyrs
2. Acts 7:60 says_________________

Christian Suffering Today

• Some Christians suffer rejection from their friends and relatives
• They are considered traitors because of forsaking their traditional way of life
• Some people are sent away from home after responding to the call for salvation.
• Persistent prayer and faith in God strengthens one’s resolve to follow Christ
• The bible teaches that Christians should share in Christ suffering.
• God rewards those who remain faithful even when persecuted.
• God also saves people from danger and provides them with their needs.
• We should pray for Christians undergoing persecution.

Quiz

1. State three types of suffering
2. The words spoken by Stephen similar to those spoken by Jesus were_______________________

Ratio And Proportion

Worked Exercise

1. Muraya and Dan each made 126kg of a mixture of maize and beans. Muraya mixed maize and beans in the ratio 4:3 while Dan mixed maize and beans in the ratio 4:3 while Dan mixed maize and beans in the ratio of 5:4. How many more kilograms?
   
   1. 2
   2. 3
   3. 4
   4. 6
      Working
      In Muraya’s mixture, maize: beans = 4:3
      maize = ^{Ratio of maize}/_{Total ratio} x No of kg
      =4/₇ x 126
      72kg
      In Dan’s mixture, maize: beans = 5: 4
      Maize = ^{Ratio of maize}/_{Total ratio} x No of kg
      =⁵/₇ x 126
      = 70kg
      Difference = ( 72 - 70 )kg
      = 2kg
      The correct answer is A (2kg)
2. A rectangular plot measures 12m by 10m.The length of the plot is increased in the ratio 3:2 , while the width is decreased in the ratio 4;5.By what ratio is the area of the plot decreased?
   1. 4:3
   2. 5:4
   3. 6:5
   4. 3:2
      Working
      New length after increase
      ³/₂ x 12 = 18m
      New width after decrease
      ⁴/₅ x 10 = 8m
      Original area before the increase/decrease
      = (12 x 10) m²
      = 120m²
      New area = (18 x 8) m²
      = 144 m²
      New ratio = 144: 120
      = 6 : 5
      The correct answer is C (6: 5).
3. Gladys keeps hens, ducks, and turkeys. The ratio of hens to ducks is 5:2. The number of turkeys is 35 less than the number of hens. How many turkeys are there if there are 30 ducks?
   1. 105
   2. 40
   3. 75 
   4. 65
      Working
      Hens : ducks = 5 : 2
      Total ratio = 7
      Ducks = ²/₅
      Hens = ⁵/₇ of x
      Therefore ²/₇ of x = 30
      x = 30 x  ⁷/₂
      x = 105 (Total hens and ducks)
      Hens =⁵/₇ x 105
      = 75
      Turkeys = (75 – 35)
      The correct answer is B (40)
4. Elijah and Paul shared some money in the ratio 5:8.Elijah got sh120 less than Paul. How much money did Paul get?
   1. Sh520
   2. Sh320
   3. Sh200
   4. Sh192
      Working
      Let the amount Paul got be t
      Therefore Elijah got (t-120)
      Therefore t -120 : t = 5 : 8
      ^{t – 120}/_t = ⁵/₈
      8t – 960 = 5t
      8t – 5t = 960
      3t = 960
      t = sh320
      Therefore Paul got = sh 320
      The correct answer is B (sh320)
5. A contractor employed 60 men to complete a piece of work in 150 days. How many more days would 50 men take to complete the same work?
   1. 180
   2. 30
   3. 40 
   4. 50
      Working
      60 men take 150 days
      1 man take (150x60) days
      Therefore 50 men will take ^{150 x 60}/₅₀ days
      = 180 days
      How many more? (180 – 150) days
      = 30 days
      The correct answer is B (30 days)
6. Eighteen men can finish to dig a piece of land in 45 days. How many days would 15 men take to finish the same piece of land?
   1. 54
   2. 2
   3. 7½
   4. 9
      Working
      18 men take 45 days
      1 man takes (45 x 18) days
      Therefore 15 men will take ^{45 x 18}/₁₅
      = 54 days
      The correct answer is A (54 days)

Scale Drawing

Worked Exercise

1. The distance between two villages is 6.4KM. On the map of the region this distance is represented by a line 1.6 cm long. What is the scale of the map?
   1. 1: 400000
   2. 1: 40000
   3. 1: 4000 
   4. 1: 4
      Working
      Actual distance = 6.4 km
      Drawing length = 1.6cm
      1 cm on the map = ^6.4/_1.6
      = 4km on the ground
      But 1 km = (1000 x 100) cm
      4km = 4 x 1000 x 100
      = 400000cm
      Therefore scale = 1: 400000
      The correct answer is A (1: 400000)
2. A rectangular field measures 105 m. On a scale drawing of the field, the longer side is 7cm.What is the measurement of the width on this scale drawing?
   1. 5 cm
   2. 50 cm
   3. 500 cm
   4. 7.35cm
      Working
      7 cm represents 105 m
      1 cm represents (105 ÷ 7)
      Scale used,
      1 cm represents 15m
             ?                  75m
      = ^{(75 x 1)}/₁₅
      5cm
      The correct answer is 5cm (A)
3. The scale on a plan is 1:20. How many cm will represent 1m on this plan?
   1. 50 cm
   2. 50 cm
   3. 5 cm
   4. 2 cm
      Working
      1 : 20 scale means 1 cm on a drawing represents 20 cm on the ground.
      1 cm represents 20cm
         ?                      100cm
      =¹⁰⁰/₂₀
      = 5cm
      The correct answer is C (5cm)
4. A rectangular field measuring 720m by 550m is to be represented on a scale drawing using the scale 1: 10,000. What is the perimeter of the drawing in centimetres?
   1. 0.254
   2. 2.54
   3. 25.4
   4. 254
      Working
      1: 10000 means 1 cm on the map represents 10000 cm on the ground
      If 1 cm = 10,0000cm
      ? = 72,000cm
      = (⁷²⁰⁰⁰/₁₀₀₀₀) cm
      = 7.2cm
      If 1cm = 10,000cm
      = 55,000cm
      = ( ^55,000/_10,000 ) cm
      = 5.5cm
      Perimeter
      
      P = 2(L+W)
      = 2 (7.2 + 5.5)
      = 25.4 cm
      The correct answer is (C)
5. The scale of a map is 1: 50000. What is the length of this map of a road 20km long?
   1. 40cm 
   2. 400 cm 
   3. 4000 cm
   4. 4 cm
      Working
      Scale 1 : 50000 means 1cm on the map represents 50000 cm on the ground.
      20 km = 20 x 1000 x 100
      = 2000000 cm
      50,000cm represents = 1 cm
      2,000,000 represents = 2,000,000 ÷ 50,000
      = 40cm
      The correct answer is A (40 cm)

Algebra

Worked Exercise

1. What is the value of x in the equation?
   2(3x – 2) = 3x + 8
   1. 12 
   2. 3
   3. 5
   4. 4
      Working 2 (3x – 2 ) = 3x + 8
      Step 1: Open brackets 6x – 4 = 3x + 8
      Step 2: Collect like terms and simplify 6x – 3x = 8 + 4 3x = 12 x = 4
      The correct answer is D (4)
2. Francis has r shillings. John has s shillings. Ouma has sh.150 less than the total money of both Francis and John. Which one of the following expressions gives the total amount of money do the three men have?
   1. 2r + 2s – 150
   2. r + s – 150
   3. 2r + 2s + 300
   4. r + s + 300
      Working
      Francis = r
      John = s
      Ouma = r + s - 150
      Total money = r + s + r + s – 150
      = 2 r + 2s – 150
      The correct answer is A (2r + 2s – 150)
3. If x = 2, y = z - x and z = 3, What is the value of
   3x – 4y + 2z  
   2 (x + 2y – z)
   1. 8
   2. 5
   3. 7
   4. 4
      Working
      Substitute the values of x, y, and z
      = (3x2) – (4x1) + (2x3)
             2 (2+2 x 1 - 3)
      = ⁸/₂ = 4
      The correct answer is D (4)
4. In a meeting there were 30 women than men and three times as many men as children.If there were 1,360 people altogether. What was the number of children in the meeting?
   1. 220
   2. 190
   3. 600
   4. 570
      Working Men 3x
      Children x
      Women 3x + 30
      Total 7x + 30 = 1360
      7x = 1360- 30
      7x = 1330
      x = 190
      Children are 190
      The correct answer is B (190)
5. What is the value of p in the equation?
   ¾(8p- 4) = 4p +7
   1. 2
   2. 5 
   3. 5½
   4. 2 ³/₈
      Working
      ¾(8p - 4) = 4p +7
      6p – 3 = 4p + 7 (opening brackets)
      6p – 4p = 7 + 3 (collecting like terms)
      2p = 10
      p = 5 (Simplifying)
      The correct answer is B (5) 
6. Omammo is two years older than Temo and three years younger than Mbeti. The sum of their ages is 64 years. If Omamo’s age is m, which of the following equations below can be used to find Omamo’s age?
   1. 3m + 1 = 64 
   2. 3m – 1 = 64
   3. 3m – 5 = 64
   4. 3m + 5 = 64
      Working
      Omamo = m
      Temo = m- 2
      Mbeti = m + 3
      Total age = 64
      X + m – 2 + m + 3 = 64
      m + m + m – 2 + 3 = 64
      3m + 1 = 64
      The correct answer is A (3m + 1 ) = 64
7. What is the simplified form of 5x + (8x – 2y)
   1. 37x – 8y
   2. 7x –
   3. 28x – 2y
   4. 7x – 2y
      Working
      5x + ¼(8x – 2y ) open brackets
      5x + 2x – ½y simplify
      = 7x – ½y
      The correct answer is B (7x – ½y)

Geometry

Worked Exercise

1. Find the value of x in the following.
   
   Working
   X+45+50=1800 (Angles on a straight lines are supplementary i.e. add up to 180º )
   X+95=180º
   X=85º
   The value of x =85º
2. Find the sum of angle “a” and angle “b” in the figure below.
   
   Working
   Lines AB and C D are transversals  are Therefore 90+b = 1800
   Co-interior angles - supplementally
   Therefore b=180-90
   B = 90º
   Angle a = 120º - (Corresponding angles)
   Therefore a = 120º
   Sum of a and b
   =120 + 90
   = 210º
3. Find the size of angle marked A B D in the figure below.
   
   X+4x+x+30=180º (angles on a straight line are supplementary)
   = 6x+30=180
   6x=180-30
   6x = 150
   X = 25
   Angle A B D =x + 4X
   But x = 25
   Therefore 25 + (4 x 25)
   = 25 + 100
   = 125º
4. Draw an equilateral triangle A B C where Line AB = 6cm.
   Draw a circle touching the 3 vertices of the triangle. What is the radius of the circle?
   Working
   Steps:
   1. Draw line A B = 6cm
   2. With A as the Centre with the same radius 6cm, mark off an arc above line A B.
   3. With B as the Centre with the same radius 6cm, mark off an arc above line A B to meet the arc in (II) above. Call the point of intersection point C
   4. Join C to A and C to B
   5.  Bisect line A B and B C and let the bisectors meet at point X.
   6. With X as the Centre, draw a circle passing through points A, B and C.
   7. Measure the radius of the circle.
      
5. Construct a triangle P Q R in which Q P = 6cm. Q R = 4cm and P R =8cm. Draw a circle that touches the 3 sides of the triangle, measure the radius of the circle.
   Working
   1. Draw line Q P 6cm
   2. With Centre Q, make an arc 4cm above line Q P.
   3. With Centre P, make an arc 8cm above line Q P and let the arc meet the one in (II) above. Label the point of intersection as R.
   4. Join R to P and R to Q.
   5. Bisect any two angles and let the bisectors meet at point Y.
   6. With Y as the Centre, draw a circle that touches the 3 sides of the triangle.
      
      Construction
      R = 3.5cm
6. A rectangle measures 6cm by 2½ cm. What is the length of the diagonal?
   Working
   
   AC² = AB² + BC² [ Pythagoras Theorem]
   AC² = 6² + 2 ½²
   AC² = 36 + 6.25
   AC² = 42.25
   AC = √42.25
   = 6.5 or 6 ½
   NB: The Pythagoras theorem states
   H² =B² +h²
   h² = H² – b²
   b² = H² –h²
7. In the figure below, A B C is a straight line and B C D E is a quadrilateral. Angle CBD = 620 and lines EB = BD = DC. Line EB is parallel to DC.
   
   What is the size of angle BDE?
   Working
   Consider triangle BCD (isosceles triangle)
   Therefore base angles are equal
   CBD = 62º
   BCD = 62º
   Therefore, BDC = 180 – 124 = 56º
   Angle CDB = angle EBD [Alternate triangle]
   Therefore EBD = 56º
   Angle BDE =^{180 - 56}/₂
   = 62º
   Therefore, BDE = 62º
8. Find the size of the largest angle from the following triangle.
   
   Working
   4X – 10 + x – 20 + 3x + 10 = 180 [Angle sum of a triangle]
   8x – 20 = 180
   8x = 200
   X = 25
   4x – 10 = (100 – 10)º
   = 90º largest angle.

Time, Speed and Temperature

Worked Exercise

1. An airplane took 4½ hours to fly from Cairo to Zambia. If it landed in Nairobi at Nairobi at 0215 h on Saturday, when did it take off from Cairo?
   1. Friday 2145 h
   2. Saturday 2245h 
   3. Friday 2245h
   4. Saturday 2145 h
      Working
      The time the aeroplane took from midnight to 0215h of Saturday = 2h 15min
      The difference (4h 30min – 2h 15min) is the time the aero plane took on Friday night.
      Time on Friday night
        h         min
        4         30
      - 2         15
        2         15
      = 2h 15min before midnight
      Time of takeoff from Cairo
      h      min
      24     00
      - 2     15
      21     45 on Friday
      The correct answer is A (Friday 2145 h)
2. A train let Mombasa on Monday at 2125 h and took sixteen and half hours to reach
   Kisauni. When did the train reach Kisumu?
   1. Tuesday 1.55 a.m
   2. Tuesday 1.55 p.m
   3. Wednesday 1.55 p.m
   4. Monday 1:55 a.m
      Working
      Monday: from 2125h to midnight = 2400h - 2125h
      = 2h 35min
      Tuesday: Number of hours traveled from midnight
      = 16h 30min - 2h 35 min
      = 13h 55min
      The train arrived at Kisumu on Tuesday at 1355h
      This is the same as 1.55p.m
      The correct answer is B (Tuesday 1.55pm)
3. A meeting started at quarter to noon. If the meeting lasted for 2 h 35min, what time in 24-h clock system did the meeting end?
   1. 1320h 
   2. 1420h
   3. 1310h
   4. 1410h
      Working
      The meeting started at 11.45
      Add the meeting time
         h       min
        11       45
      + 2       35  
        14      20  
      The meeting ended at 1420h
      The correct answer is B (1420 h)
4. A wall clock gains 3 seconds every one hour. The clock was set correct at 1pm on Tuesday. What time was it showing at 1pm on Friday on the following week?
   Working
   The number of days from Tuesday 1 pm to Friday 1pm the following week = 10days.
   Number of hours = (24 x 10) = 240 hrs.
   The clock gains 3 seconds after every hour in ten days.
   240 x 3 = 720 seconds
   Min = ⁷²⁰/₆₀ = 12 min
   Hence it will show 1 p.m. + 12 min = 1.12 pm
   In 24 h clock system
   = 1312h
   The correct answer is B (1312h)
5. A cyclist traveled from Nairobi to Nyeri for 4h 30min at a speed of 80km/h. He drove back to Nairobi taking 4 hours. What is his speed, in km/h?
   1. 90
   2. 72
   3. 80
   4. 100
      Working
      Distance = speed x time
      = 80 x 4½
      = 360 km
      From Nyeri - Nairobi distance = 360km
      Time taken = 4hrs
      Therefore speed = ^Distance/_Time
      = 90km/h
      The correct answer is A (90km/hr)
6. A motorist crosses a bridge at a speed of 25m/s. What is his speed in km/hr?
   1. 80
   2. 90
   3. 60
   4. 30
      Working
      When working out this kind of question we use a relationship,
      If 10 m/s = 36 km/h
      25m/s = ?
      = ( x 36) km/h
      = 90 km/h
      The correct answer is B (90km/h)
7. The distance between Mombasa and Mtito Andei is 290km. A bus left Mombasa at 1035h and traveled to Mtito Andei at a speed of 50km/h. At what time did it arrive at Mtito Andei?
   1. 1623h
   2. 1523h
   3. 1423h
   4. 1723h
      Working
      Time = ^Distance/_Speed
      = ²⁹⁰/₅₀
      = 5 ⁴/₅hours or 5h 48min
      Arrival time = Departure time = Time taken + Time taken
       h       min
      10      35
       +5     48
      16      23
      The arrival time 1623 h
      The correct answer is A (1623h)
8. Kamau drove from town M to town N a distance of 150 km. He started at 9.30 am and arrived at town N at 11.00 am. He stayed in town for one hour and 50 minutes. He drove back reaching town M at 2.30pm. Calculate Kamau’s average speed for the whole journey.
   1. 90km/h
   2. 100km/h
   3. 60km/h
   4. 150 km/h
      Working
      Total distance from M to N and back
      = 150 x 2
      = 300 km
      Total time taken
      From 9.30 - 11.00 = 1 h 30 min
      Time spent in town
      = 1 h 50 min
      Time taken from N to M
      = 1430h – 1250h
      = 1h 40min
      Total time = 5 hours
      Average speed = ^{Total distance}/_{Total time taken}
      =(60km/h)
      The correct answer is C (60km/h)
9. The temperature of an object was 20º C below the freezing point. It was warmed until there was a rise of 40º in temperature. What is the reading in the thermometer?
   1. 60 Cº
   2. 40Cº
   3. 20Cº
   4. 20Cº
      Working
      Below freezing point means; - 20
      Rose by 40º
      Therefore - 20º + 40 = 20 C
      The correct answer is C (20º C)

Money

Worked Exercise

1. Mutiso paid sh.330 for an item after the shopkeeper gave him a 12% discount. What was the marked price of the radio?
   1. sh300
   2. sh369.60
   3. sh375
   4. sh350
      Working
      Marked price = 100%
      Discount = 12%
      S.P = 100% - 12%
      = 88%
      If 88 % = 330
      100% = ?
      ^{100 x 300}/₈₈ = Sh375
      The correct answer is C (375)
2. Olang’ borrowed sh.54000 from a bank which charged interest at the rate of 18% p.a. He repaid the whole loan after 8 months .How much did he pay back?
   1. sh6480
   2. sh60, 480
   3. sh14580
   4. sh77760
      Working
      I = ^PRT/₁₀₀
      = ^{54000 x 18 x 8}/_{100 x 12}
      = sh6480
      Amount = P + I
      = (54,000 + 6,480) shillings
      = Ksh 60, 480
      The correct answer is B
3. The cash price of a microwave is sh. 18000. The hire purchase price of the microwave is 20% more than the cash price. Bernice bought it on hire purchase terms by paying 40% of the hire purchase price as the deposit and the balance equal monthly installments of sh1620. How many installments did she pay?
   1. 12
   2. 10
   3. 9
   4. 8
      Working
      Let the cash price be 100%
      Hire purchase = 100% + 20%
      = 120% of the cash price
      = ¹²⁰/₁₀₀ x 1800
      = sh.21, 600
      Deposit = 40% of HPP
      = ⁴⁰/₁₀₀ x 21,600
      = sh.8, 640
      HPP = D + MI
      I = ^{HPP - D}/_MI
      = ^{21600 – 8640}/₁₆₂₀
   5. = 8 Months
      The correct answer is D (8)
4. Salim deposited sh25000 in a bank which paid compound interest at the rate of 10% per annum. If he withdraws all his money after years, how much interest did his money gain?
   1. sh5250
   2. sh2500
   3. sh1375
   4. sh387
      Working
      Interest for year 1
      I = ^PRT/₁₀₀
      = ^{25000 x 10 x 1}/₁₀₀
      = Sh2500
      Amount = 25000 + 2500
      = 27,500
      Interest for 2nd year
      I = ^PRT/₁₀₀
      = ^{27,500 x 10 x ½}/₁₀₀
      = Sh13775
      Total interest (2,500 + 1,375)
      = Sh3875
      The correct answer is D (Sh 3875)
5. Kamaru bought bananas in groups of 20 at sh20 per group. He grouped them into smaller groups of 5 bananas each and sold them at sh10 per group. What percentage profit did he make?
   1. 40%
   2. 50% 
   3. 60 %
   4. 70%
      Working
      For every 20 bananas = sh 25
      One group produces 4 smaller groups of 5 bananas each
      S. P = 4x 10
      = sh40
      B.P price = sh25
      Profit = 40 – 25
      = sh15
      % profit = ^P/_BP x 100
      = 60%
      The correct answer is C (60).
6. A shopkeeper bought 3 trays of eggs at sh 150 per tray. On the way to the shop, he realized 20% of the eggs were broken. He sold the rest at sh 72 per dozen. How much loss did he make?
   1. sh450
   2. sh432
   3. sh18 
   4. sh28
      Working
      B.P for 3 trays = 3 x 150
      = sh450
      Number of eggs = 3 x 30
      = 90 eggs
      20% eggs broke = ²⁰/₁₀₀ x 90
      = 18 eggs broken
      Therefore remained = (90 - 18) eggs
      = 72 eggs
      1 dozen = 12 eggs
                 ? = 72 eggs
      = 6 dozens
      1 dozen = sh.72
      6 dozens = ?
      Loss = B.P – S.P
      = 450 - 432
      sh18
      The correct answer is C (sh18)
7. A Salesperson earns a basic salary of sh7500 per month. He is also paid a 5% commission on all sales above sh30, 000. In a certain month his total earnings were sh.14250. What was his total sales for that month?
   1. sh135000
   2. sh285000
   3. sh165000
   4. sh315000
      Working
      Commission = sh14250 – sh7500
      = sh6750
      5% = sh6750
      100% = ?
      = ¹⁰⁰/₅ x 6750
      = Sh. 135,000
      Total sales = (135,000 + 30,000)
      = sh165000
      The correct answer is C (sh 165,000)
8. Shiku bought the following items from a shop
   6kg of sugar @ sh45
   ½ of tea for sh90
   3 kg of rice @ sh30
   2kg of fat @ sh70
   If she used one thousand shillings to pay for the items, what balance did she receive
   1. sh410
   2. sh455
   3. sh590
   4. sh765
      Working
      Shiku’s Bill
      

      Item	Sh	ct
      6kg sugar @ sh45	270	00
      ½ kg tea for sh90	90	00
      3kg rice @ sh30	90	00
      2kg fat @ sh70	140	00
      Total	590	00

      Total expenditure = sh590
      Balance = sh1000 – sh590
      The correct answer is = sh410 (A)
9. Maranga paid sh4, 400 for a bicycle after he was given a 12% discount. James bought the same item from a different shop and was given a 15%. How much more than James did Maranga pay for the bicycle?
   1. sh250
   2. sh300
   3. sh750
   4. sh150
      Working
      Maranga B.P = 100% - 12%
      = 88%
      ⁴⁴⁰⁰/₈₈ x 100 = sh5000
      James B.P = 100% - 15%
      = 85%
      ^{85 x 100}/₄₄₀₀ = sh4,250
      How much more? = (5000-4250) shillings
      = sh750
      The correct answer is C (750)
10. The table below shows postal charges for sending letters;
    

    Mass of letter	Sh	ct
    Up to 20g	25	00
    Over 20g up to 50g	30	00
    Over 50g up to 100g	35	00
    Over 100g up to 250g	50	00
    Over 250g up to 500g	85	00
    Over 500g up to 1kg	135	00
    Over 1kg up to 2kg	190	00

    
    Namu posted two letters each weighing 95g and another one weighing 450g. How much did he pay at the post office?
    1. sh120
    2. sh135
    3. sh155
    4. sh240
       Working
       Two letters
       95g → Sh35.00
       95g → Sh35 .00
       Another 450g → Sh85.00
       The correct answer is C (sh155)

Volume, Capacity and Mass

Worked Exercises

1. A Jerry can contains 5 litres of juice. This juice is used to fill 3 containers each of radius 7 cm and height of 10cm. How many milliliters of juice are left in the jerry can?
   1. 38
   2. 480 
   3. 400
   4. 420
      Working
      Volume of container: = Πr² h
      =²²/₇ x 7 x 7 x 10
      = 1540 cm³
      Volume of 3 such containers
      = (1540x3) cm³
      = 4620 cm³
      Volume of juice in jerry can = (5 x 1000)
      = 5000cm³
      Volume of juice left = (5000-4620) cm3
      = 380 cm³
      = 380 ml
      The correct answer is A (380ml)
2. The diagram below represents a solid whose dimensions are shown.
   
   What is the volume in cm³?
   1. .30000
   2. 300000
   3. 3000
   4. 3000000
      Working
      Volume = Area of the Cross-section x length
      Volume of the top = (20 x 10 x 150)
      = 30,000cm³
      Volume of the bottom = 60 x 30 x150
      = 270,000cm³
      Whole solid = top + bottom
      = 30,000 + 270,000
      = 300,000cm³
      The correct answer is B (300 000)
3. In the month of October, a farmer delivered 48750kg of maize to a miller. In November the amount of maize delivered was 1850kg more than that of October. The amount delivered in December was 2450kg less than that of November. What was the total mass, in tonnes, was delivered by the farmer in the 3 months?
   1. 145.65
   2. 147.5
   3. 152.4
   4. 150.55
      Working
      October = 48750 kg
      November = (48750+1850) kg
      = 50,600 kg
      December = 50,600-2,450) kg
      = 48,150 kg
      Total mass = 48750+50600 +48150
      = (147500/1000) tonnes
      = 147.5 tonnes.
      The correct answer is B (147.5)
4. A rectangular tank measures 1.2m by 80cm by 50cm. water is poured into the tank to a height of 15cm. How many more liters of water are needed to fill the tank?
   1. 144
   2. 14.4
   3. 33.6
   4. 336
      Working
      Capacity of the tank = 120 x 80 x 50
      = 480,000cm³
      Convert to litres = ^480,000/¹⁰⁰⁰
      = 480litres
      Volume of the water poured = 120 x 80 x 50
      = 144000cm³
      Convert to litres = ¹⁴⁴⁰⁰⁰/₁₀₀₀
      = 144 litres
      Volume of water needed = 480 – 144 = 366litres.
      The correct answer is D (366)
5. The diagram below represents a solid triangular prism.
   
   What is the volume in cm³?
   1. 2400
   2. 2000
   3. 5200
   4. 576
      Working
      Apply Pythagorean relation in triangle ABC
      BC =√26² -10²
      =√576
      = 24cm
      Volume = Area of the Cross section x length
      = ½ x 24 x 10x 20
      = 2400cm³
      The correct answer is A (2400cm³)
6. A cylindrical tank has a radius of 2m and a height of 1.5m. The tank was filled with water to a depth of 0.5M. What is the volume of water in the tank, in litres? (П = 3.14)
   1. 6280
   2. 628 
   3. 9240
   4. 18840
      Working
      Volume = П r ²h
      = 3.14 x 2 x 2 x 0.5
      = 6.28 m³
      In litres = (6.28 x1000) litres
      = 6280 litres
      The correct answer A (6280)
7. When processed, 7kg of coffee beans produce 1kg of processed coffee. Processed coffee is then packed in 50kg bags. A farmer delivered 5.6 tonnes of coffee berries in one month. How many bags were obtained?
   1. 12
   2. 16
   3. 40
   4. 20
      Working
      Mass of coffee berries = 5.6tonnes
      = 5.6x1000
      = 5600kg
      Mass obtained = ⁵⁶⁰⁰/₇
      = 800kg
      Number of bags = 800 ÷ 50
      = 16 bags
      The correct answer is B (16)
8. A rectangular container whose base measures 40cm by 60cm has 30 liters of water when full. Find the height of the container in cm.
   
   1. 0125
   2. 1.25
   3. 12.5
   4. 125
      Working
      V = base area x height
      Height = ^volume/_{base area}
      Volume = 30 litres
      = 30x1000
      = 30,000cm³
      Height = ^30,000/₂₄₀₀
      = 12.5cm
      The correct answer is C (12.5)
9. A shopkeeper had 43 litres sand 5 litres and 5 dl of paraffin. He packed all the paraffin in 7.5 dl-containers. How many containers did he fill?
   1. 58
   2. 5.8
   3. 6
   4. 60
      Working
      Convert decilitres into litres
      1 dl =1/10 litres
      5 dl =5/10 litres
      7.5 dl =7.5/10 litres = 0.75 litres
      Hence 43 litres 5dl = 43.5 litres
      No of containers = ^43.5/_0.75 = 58 containers
      The correct answer is 58 (A)
10. The figure below shows a cylindrical solid of diameter 28cm and length 20 cm. A square hole of side 1.5 cm has been removed. What is the volume of the material in the solid, in 3cm³?
    
    1. 12320
    2. 4500
    3. 8400
    4. 7820
       Working
       
       Volume of solid = volume of a cylinder - volume of the square hole
       = ( x 14 x 14x 20) - (15 x 15 x 20)
       = 12320 - 4500
       = 7,820 cm³
       The correct answer is D (7,820cm³)

In this section you will need the following hints to solve the exercises:

• Place value of whole numbers
• Total value of whole numbers
• Multiplication of whole numbers/tables
• BODMAS
• LCM and GCD

Worked Exercise

1. What is four million seventy thousand and five hundred and thirty three?
   1. 4,070,353
   2. 4,070,533
   3. 4,007,533
   4. 4,700,533
      
      Working
      Using the place value table, the question can be solved as follows:
      

      Millions	Hundred Thousands	Ten thousands	Thousands	Hundreds	tens	Ones
      4	0	7	0	5	3	3

      The correct answer is B (4070533)
2. What is the square root of 7 ⁹/16
   1. 7 ¾
   2. 2 ¾ 
   3. 1 ³/₈
   4. ²¹/₁₆
      Working
      Step 1: Change the mixed fraction to improper Find the square root of both numerator and denominator.
      Step 2: Find the square root of both numerator and denominator
      = √121
          √16
      =¹¹/₄
      Step 3: Change the improper fraction to mixed fraction
      = 2¾
      The correct answer is B
3. What is 25% as a fraction?
   1. ¹/₅
   2. ¾
   3. ½
   4. ¼
      Working
      Step1: Express the percentage with 100 as a denominator.
      =²⁵/₁₀₀
      Step 2: Simplify
      =¼  correct answer is D
4. What is the value of of ¹/₃ of(½ + ¹/₉) ÷¹/₆
   1. ¹¹/₃₂₄
   2. ¹/₉₉
   3. 1²/₉
   4. ⁴/₁₁
      Working
      Step1: Using the order of operation, BODMAS, solve the brackets first.
      ¹/₂ + ¹/₉ = ¹¹/₁₈
      Step 2: Open brackets and calculate ‘of ‘
      =¹/₃ of (¹¹/1₈) ÷ ¹/₆
      =¹/₃ x (¹¹/₁₈) ÷ ¹/₆
      =¹¹/₅₄ ÷ ¹/₆
      Step3: Calculate the division part
      =¹¹/₅₄ ÷ ¹/₆
      =¹¹/₅₄ x ⁶/₁(multiply by the reciprocal of ¹/₆)
      =¹¹/₉
      Step 4: Change the improper fraction to mixed fraction.
      = 1 ²/₉
      The correct answer is C.
5. The price of radio is Sh1800. The price was reduced by 15% during an auction. How much is the price after the reduction?
   1. Sh270
   2. Sh2070
   3. sh1530
   4. sh1785
      Working
      Marked price = Sh1800
      Percentage decrease = 15%
      New price
      85% of Sh1800 (100% - 15%)
      = ^{85 x 1800}/₁₀₀
      = Sh1, 530
      The correct answer is Sh 1530 (C)
6. In a certain year a tea factory produced 2500 tonnes of tea leaves. The following year the tonnes increased to 4000. What is the percentage increase?
   1. 160%
   2. 62½ %
   3. 60%
   4. 37½ %
      Working
      First year = 2500 tonnes
      Second year = 4000 tonnes
      Increase = 1500 tonnes (4000-2500)
      % Increase = ^{Increase x 100}/<sub>Original
      
      = 60%</sub>
      The correct answer is C (60%)
7. What is the next number in the sequence below.
   6, 10, 19, 35, …..
8. 60
9. 84 
10. 71
11. 51
    Working
    
    The next difference is 5² = 25
    The next number is 35 + 25 = 60
    The correct answer is A (60)