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)

Length, Perimeter and Area

Worked Exercise

1. Tracy used a piece of wire m long to support tomato plants in the garden. The wire was cut into pieces of 28cm long. How many complete pieces were obtained?
   1. 85
   2. 30
   3. 20
   4. 30.10
      Working
      1 M = 100cm
      8½m = ?
      8½ x 100 = 850cm
      1 piece = 28 cm
                ? = 850cm
      = ⁸⁵⁰/₂₈
      = 30 complete pieces remainder 10cm
2. The figure below represents a flower garden
   
   What is the perimeter of the garden?
   1. 25m
   2. 38.5m
   3. 11m
   4. 44m
      Working
      P = ¼П d + r + r
      = ( ¼ x ²²/₇ x 14) + (7+7)
      = 11 + 14
      = 25 m
      The correct answer is A (25)
3. The parallel sides of a trapezium measure 10cm by 18cm respectively. If the distance between the parallel sides is 8cm, what is the area of the trapezium in cm²?
   1. 224
   2. 112
   3. 108
   4. 84
      Working
      Area of a trapezium = ½h (a + b)
      = ½ x 8 x (10+18)
      = ½ x 8 x 28
      = 112cm²
4. The figure below shows vegetable garden.
   
   What is the perimeter?
   1. 0.526m
   2. 5.26m
   3. 52.6m
   4. 526m
      Working
      Perimeter of semi-circle
      = ½П d(Circumference only)
      =½ x 2 x ²²/₇ x 7
      = 22m
      To get DC = √ 25 – √ 16
      = √ 9
      = 3m
      Length DE = AB – ED
      = 12.8 – 7
      = 5.8m
      Total length 12.8+ 5 + 3 + 5.8 + 22 + 4
      = 52.6 m
      The correct answer is (52.6)
5. What is the perimeter of the following shape?
   
   
   1. 88cm
   2. 44cm
   3. 176cm
   4. 56cm
      Working
      P = circumference of a circle of radius 7cm
      = 2Π r
      = 2 x ²²/₇ x 7
      = (44 cm)
6. The figure below shows a right angled triangle LMN in which LM = 7.5cm and LN = 19.5cm
   
   What is the area of the triangle in cm²?
   
   1. 18
   2. 67.5
   3. 27
   4. 34.5
      Working
      Apply Pythagoras relation in triangle LMN
      LN² = LM² + NM²
      Nm² = LN² – LN²
      = 19.5² – 7.5²
      = 380.25 – 56.25
      = 324
      NM = √ 324
      = 18 cm
      Area of triangle LMN
      = Base x height
      = ½ X 18 X 7.5
      = 67.5cm²
      The correct answer is B (67.5cm²)
7. The area of a right-angled triangle is 84cm². If the height of the triangle is 7cm, what is the length of the longest side?
   1. 25cm
   2. 24cm 
   3. 19cm
   4. 12cm
      Working
      
      The Pythagoras relationship states that
      H² = b² + h²
      But Area = ½bh
      84 =½ x b x 7
      84 x 2 = 7b
      24 = b
      H² = 24² + 7²
      H² = 576 + 49
      H² = 625
      H = 25
      Therefore the correct answer is 25cm (A)
8. What is the surface area of an open cylinder whose radius is 6.3cm and height of 25cm.
   1. 114.74cm²
   2. 1239.48cm²
   3. 3118.50cm²
   4. 619cm²
      Working
      Total surface area = Πr²+Πdh
      = ( ²²/₇x 6.3 x 6.3) + 2 x ²²/₇ x 6.3 x 25
      = 124.74 + 990
      = 1114.74 cm²
      The correct answer is 1114.74 cm² (A)
9. A Welder made a door with a design as shown below.
   
   What is its area? (Take Π =²²/₇ )
   1. 15.12m²
   2. 12.04m²
   3. 13.36m²
   4. 21.28m²
      Working
      Area of the semi- circle = ½Π r²
      = ½ x ²²/₇ x 1.4 x 1.4
      = 3.08m²
      Area of the rectangle = L x w
      = 3.2 x 2.8
      = 8.96 m²
      Total area = (3.08 + 8.96 )m²
      = 12.04 m²
      The correct answer is B (12.04m²)
10. The diagram below represents a plot with a diameter of 28 meters.
    
    The plot was fenced by erecting posts 4m apart. How many posts were used ? (Π = ²²/₇)
    1. 12
    2. 17
    3. 18
    4. 19
       Working
       Perimeter =½ П d + d
       = (½ x ²²/₇ x 28 + 28)
       = 72
       No of posts = ^Perimeter/_Interval
       =⁷²/₄
       = 18 posts
       The correct answer is C (18)

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)

• General Geometric Shapes
  • Square
  • Rectangle
  • Parallelogram
  • Rhombus
  • Trapezium
  • Right-angled Triangle
  • Equilateral Traingle
  • Isosceles Triangle
• Properties of Triangles and Parallel Lines
  • Triangle
  • Parallel Lines and Transversal
• Speed,Distance and Time

General Geometric Shapes

Square

• All sides are equal
• Opposite sides are parallel
• Each interior angle is a right angle (90º)
• The interior angles total up to 360º
• Diagonals bisect each other at right angles.
• Diagonals measure the same length and bisect interior angles.

Rectangle

• Each interior angle is 90º and they all add up to 360º
• Diagonals are equal
• Diagonals bisect each other but NOT at right angles

Parallelogram

• Opposite sides are equal and parallel
• Opposite angles are equal
• Diagonals bisect each other
• Diagonals are not equal
• Adjacent angles are supplementary (add up to 180º)

Rhombus

• All sides are equal
• Opposite sides are parallel
• Opposite angles are equal
• Diagonals bisect each other at 90º
• Diagonals bisect the interior angles

Trapezium

• The sum of the interior angles is 360º
• Has a pair of parallel lines which are not of the same length
• Has a perpendicular height joining the two parallel lines

Right-angled Triangle (Pythagorean relationship)

• H2 = b2 + h2
• b2 = H2 – h2
• H2 = H2 - b2
  Examples of relationships
  

  Base	Height	Hypotenuse
  3	4	5
  6	8	10
  5	12	13
  7	24	25
  8	15	17
  9	40	41

Properties of Triangles and Parallel Lines

Triangle

Exterior angles & interior angles

• Angles x, y, and z are exterior angles while a, b, and c are interior angles.
• Exterior angles add up to 360º while interior angles add up to 180º.
• Angles x, a; b, z; and c, y; are adjacent to each other and they add up to 180º (supplementary angles)

Parallel Lines and Transversal

1. Angles at a point e.g. a + b+ c + d = 360º
2. Vertically opposite e.g. a/d, b/c, f/g, e/h. They are equal
3. Corresponding angles e.g. b/f, a/e, c/g, d/h. They are equal
4. Alternate angles e.g. c/f, d/e are always equal.
5. Co-interior angles e.g. c/e, d/f, are always equal.
6. Co-interior/allied angles e.g. c/e, d/f are formed by parallel lines. They are supplementary.

Speed, Distance and Time

The formulae related to speed, distance and time can be derived from the following triangle.

• Length
• Mass
• Volume And Capacity
• Time
• Area
  • Rectangle
  • Square
  • Parallelogram
  • Rhombus
  • Triangle
  • Trapezium
  • Circle, half circle, quarter circle
• Surface Area
  • Surface area of a Cylinder
  • Surface area of a Cube
  • Surface area of a Cuboid
  • Surface area of a Triangular Prism
• Volume of Cylinder and Rectangular Shapes
  • Volume of a Cylinder
  • Volume of a Rectangular Shape
• Perimeter
  • Perimeter of a Rectangle
  • Perimeter of a Square
  • Perimeter of a Circle
  • Perimeter of a Half a Circle
• Expressing areas of Large Shapes

Length

The units of length that are used include the following:

• millimetre (mm)
• centimetre (cm)
• decimetre (dm)
• Metre (m)
• Dekametre (Dm)
• Hectometre (Hm)
• Kilometre (Km)
  
  
  

From the illustration:

• 10mm = 1cm
• 10cm = 1dm
• 10dm = 1m
• 10m = 1 Dm
• 10Dm = 1Hm
• 10 Hm = 1Km

The relationship between the units of lengths may be clearly seen if the units are written with a 10 between them.

So to find how many small units are equivalent to another, multiply the number of tens between the units, hence:

• Km 1
• Hm 10
• Dm 100
• M 1000
• dm 10000
• mm 1000000

Mass

• 1000 g = 1Kg
• 1000 Kg = 1Tonne
• 1000000 g = 1Tonne

Volume and Capacity

• 1 cm³ = 1 Ml (millilitre)
• 1000 cm³ = 1 L (litre)
• 100 cm³ = 1 dl (decilitre)
• 1 m³ = 1000 litre
• 1000000 cm³ = 1 m³
• 10 dl = 1 Litre
• 1000ml = 1 Litre

Time

• 60 Seconds = 1 Minute
• 60 Minutes = 1Hour
• 3600 Seconds = 1 Hour
• 24 Hours = 1 day
• 7 Days = 1 Week

Area

Rectangle

Area = Length x Width
A = L X W

Square

Area = Side x Side
A = S x S
A = S²

Parallelogram

A = base x Height
A = b x h

Rhombus

Area = base x height
A = b x h

Triangle

Area = base x height
A = b x h

Trapezium

Area = x sum of parallel lines x height
A = (a + b) x h
A = h (a + b)

Circle, half circle, quarter circle

Circle

Area = П x radius x radius

A = П x r x r

A = Пr2

Half circle

Area = Area of a full circle ÷ 2

A = П r2
       2

A =½ Пr2

Quarter circle

A = Area of the full circle ÷ 4

A = Пr2 ÷ 4

A = ¼Пr2

Note: П = 22/7 or 3.14 or 3 1/7

Surface Area

Surface Area of  a Cylinder

T.S.A = Area of circular ends + area of the curved surface

=2Пr2 + Пdh ( if closed both ends)

T.S.A = Пr2 + Пdh (if open one end )

T.S.A = Пdh (if open both ends/pipe)

Surface Area of  a Cube

T.S.A = Total area of all the six faces

= 6 x L x L

= 6L2 (if closed)

or

= 5L2 (if open one end)

Surface Area of  a Cuboid

T.S.A = Total area for the six faces

= 2 (L x w) + 2 (L x h) + 2 (w x h)

or

= (L x w) + 2 (L x h) + 2(w x h) ( if open on top)

Surface Area of  a Triangular prism

T.S.A = Area of all the 5 faces of the prism

Volume of Cylinder and Rectangular Shapes

Volume of a Cylinder

Volume = Base area x height

= Пr2 x height

= Пr2h

Volume of a Rectangular shape

Volume = Base area x height

V = L x w x h

Note: Depending on the cross-section, the volume of any shape / solid is given by.

V = Area of cross-section x height/length

Perimeter

Perimeter of a Rectangle

P = Length + Length + Width + Width

= L + L + W + W

= 2L + 2W or 2(L + W)

Perimeter of a Square

P = L + L + L + L

= 4L

Perimeter of a Circle

C = П x diameter

= Пd or 2Пr

Note: Perimeter of a full circle is called circumference

Perimeter of a Half a Circle

Perimeter = circumference + diameter

P = ½Пd + d

Note: For triangles and irregular shapes, JUST ADD THE DISTANCE ALL ROUND.

Expressing area of large shape

Hectare – A shape that measures 100m by 100m

Therefore 1ha = (100 x 100)m2

1 ha = 10000m2

Are – a piece / shape that measures 10m by 10m

Therefore 1 are = 10 x 10

1 are = 100m2

Hence:

1 ha = 10000m21are = 100m2

1ha = 100ares

STANDARD 8, END OF TERM 1
MATHEMATICS
NAME....................................................SCHOOL...............................

1. What is 8 346 524 in words?
   1. Eight million three hundred and forty six thousand, five hundred and twenty four.
   2. Eighty three million forty six thousand five hundred and twenty four
   3. Eight hundred and thirty four thousand six hundred and fifty two and four tenth.
   4. Eighty three million four hundred and six thousand and twenty four.
2. What is the value of
   
   1. 1
   2. 9
   3. 12
   4. 60
3. What is 4 899.84 rounded off the nearest whole number?
   1. 4899
   2. 4 899.8
   3. 7890
   4. 4 900
4. What is the LCM of 18, 24 and 36?
   1. 6
   2. 72
   3. 144
   4. 108
5. What is the sum of the total values of digit 2 and digit 7 in the number 4 265 785?
   1. 200 000
   2. 700
   3. 200 700
   4. 265 700
6. Hassan bought the following items from a shop.
   3 packets of maize flour at sh. 110
   2kg rice for sh. 210 1 ¹/₂kg of ndengu at Sh. 140
   2 loaves of bread at sh. 55
   If he paid using 2-500 shilling notes, how much balance did he get?
   1. Sh. 140
   2. Sh. 860
   3. Sh. 199
   4. Sh. 805
7. What is the value of x in the equation?
   
   1. 4  
   2. 2
   3. 3
   4. 1
8. The area of a square is 3 364m². What is the length of one side of the square?
   1. 1 682
   2. 58
   3. 841
   4. 52
9. What is the CORRECT order of writing the fractions ²/₃, ¹/₂, ³/₅, ⁴/₇ from the smallest to the largest? 
   1.  ²/₃ , ³/₅ , ⁴/₇ , ¹/₂ 
   2.  ¹/₂ , ²/₃ , ³/₅ ,⁴/₇
   3.  ¹/₂ ,⁴/₇  , ³/₅ ,²/₃
   4.  ⁴/₇ ,³/₅   , ²/₃ ,¹/₂
10. In the triangle ABC below, draw a bisector of angle ABC and angle BCD. Join the two bisectors and let them meet at x. Let point x be the centre of the circle and draw a circle touching the sides ABC. What is the length of the radius?
    
    
    1. 2.5cm
    2. 5c
    3. 42cm
    4. 8.4c
11. A rectangular picce of land measures 215m by 65m. Fencing posts are put at an interval of 5m. How many posts are required to fence?
    1. 56
    2. 280
    3. 560
    4. 112
12. Okello bought a jacket for sh. 1 350 after getting a 10% discount. What was the marked price of the jacket?
    1. Sh. 1 215
    2. Sh. 1 650
    3. Sh. 1 500
    4. Sh. 1 800
13. The table below shows the number of crates of a soda delivered in a depot for six days.
    

    Days	Mon	Tue	Wed	Thur	Fri	Sat
    No of crates	24	32	18	25	27	33

    
    What was the median sale in that week?
    1. 27
    2. 18
    3. 33
    4. 26
14. Nyar Gem and Jar Kisumu shared some money in the ratio 2:3. How much more money did Jar Kisumu get than Nyar Gem if they shared Sh. 8 400 in total?
    1. Sh. 3 360
    2. Sh. 1 680
    3. Sh. 5 040
    4. Sh. 4 200
15. What is the value of 0.6+0.4+0.25
                                            0.2
    1. 2.2
    2. 4.4
    3. 11
    4. 3.6
16. Which of the following statement is NOT TRUE about a square?
    1. All sides are equal.
    2. Has two pairs of parallel sides.
    3. All interior angles are equal.
    4. Diagonals are not equal.
17. Kamau had the following denominations of money.
    2 - 1000 shillings notes
    12- 500 shilling notes
    8 - 200 shilling notes.
    12 - 100 shilling notes
    He decided to change all the money into fifty shilling notes How many notes did he get in total?
    1. 408
    2. 216
    3. 10 800
    4. 108
18. On a map a road of 12km is represented by 6cm. What is the scale used?
    1. 1:2 00
    2. B. 1: 20 000
    3. 1:200 000
    4. 1:2 000 000
19. What is the simplest form of
    
    1.  8x +2y
    2. 6x
    3. 4.x + 2y
    4. 8x
20. A rectangular plot has a diagonal of 170m. If the lenth is 150m, how long is the width?
    1. 120m
    2. 160m
    3. 80m
    4. 270m
21. The triangle PQR below is drawn to scale.
    
    What is the size of angle QPR?
    1. 55°
    2. 74°
    3. 68°
    4. 52°
22. Ogello is paid sh. 14 375 after working for 25 day's How much does he carn for working 12 days?
    1. Sh. 575
    2. Sh. 6000
    3. Sh 11 500
    4. SHS 750
23. A meeting was attended by 600 people. Out of these 0.14 were men, 0.2 were women and the rest were youth How many youths were there?
    1. 84
    2. 204
    3. 120
    4. 396
24. Terry is twice as old as Tracy but eight years younger than Iriza, If Tracy is y years old. what will be the sum of their ages in 6 years lo come?
    1. 5y +26
    2. 5y + 8
    3. 4y + 26
    4. 4y + 18
25. A family uses 2 - 500ml packets of milk daily. How many litres of milk does the family consume in the month of January. February and March of a leap year?
    1. 92 litres
    2. 90 litres
    3. 89 litres
    4. 91 litres
26. What is the square root of 0.0016?
    1. 0.0004
    2. 0.004 
    3. 0.04
    4. 04
27. Kiprono ran round the track 7 times.
    
    How many kilometres did he cover?
    1. 3
    2. 30
    3. 300
    4. 3 000
28. Wanjala bought a cow at Sh. 14 000. During the dry season he sold-it making a 15% loss. At what price did he sell the cow?
    1. Sh 11 900
    2. Sh. 16 100
    3. Sh. 2 100
    4. Sh. 12 150
29. A wheel of radius 28cm makes 2 000 revolutions. How many kilometres docsit cover?
    1. 325 000km
    2. 3 520km
    3. 352km
    4. 3.52km
30. What is the value of
    ¹/₂ + ¹/₂(¹/₃ - ¹/₆) of ²/₃ ÷ ¹/₄?
    
    
    1. ¹³/₁₈
    2. ⁵/₁₈
    3. ¹³/₂₄
    4. ¹²/₁₇
31. Kawira bought 60 mangoes @ sh. 5 each. She spent sh. 100 on transport. During transportaion, 10 mangoes got spoilt and sold the rest at sh 12 each. How much profit did she make?
    1. Sh. 300
    2. Sh. 200
    3. Sh. 150
    4. Sh. 400
32. Line AB below is part of a Rhombus. Angle ABC 65° Complete the Rhombus. What is the length of diagonal BD?
    
    
    
    
    
    
    
    1. 5.8cm
    2. 4cm
    3. 10.3cm
    4. 8.6cm
33. A bus left Mombasa on Tuesday at 8:30pm. It took 8 hours 45min to reach Nairobi. On what day and time did it get to Nairobi?
    1. Wednesday 0515hrs
    2. Wednesday 1715hrs
    3. Tuesday 1515hrs
    4. Tuesday 0315hrs
34. The pie chart below shows how Mkulima spent his sh. 36 000 salary
    
    How much did he save?
    1. 6 000
    2. 4 000
    3. 2 000
    4. 24 000
35. A car travelled a distance of 216km in 3 hours hours and later covered another 144km in 2 hours. What was the average speed in km per hour.
    1. 72km/h
    2. 60km/h
    3. 80km/h
    4. 90km/h
36. The diagram below shows a cuboid.
    
    Calculate the surface area.
    1. 220cm² 
    2. 196cm² 
    3. 168cm² 
    4. 112cm² 
37. A carton contains 36 - 500g tins of blueband. How many tonnes does such 12 cartons carry?
    1. 216
    2. 21.6
    3. 2.16
    4. 0.216
38. The diagram below sows a Trapezium ABCD
    
    What is the area of the trapezium?
    1. 840cm² 
    2. 420cm²
    3. 510cm² 
    4. 255cm² 
39. A tank had water upto 4 full. When 120 litres of water were drawn from the tank, it became ¹/₂ full. What was the capacity of the tank?
    1. 160 litres
    2. 480 litres
    3. 360 litres
    4. 340 litres
40. At a prayer rally 2 800 men attended. The number of women was 1 800 more than that of men but 3 200 less than that of children. How many people attended the rally?
    1. 15 200
    2. 10 600
    3. 7 400
    4. 7800
41. In the figure below ABCDE is a rhombus and BCD is a triangle. Angle BDC = 54° and line BD = line BC.
    
    What is the size of angle DEA?
    1. 63º
    2. 68°
    3. 117°
    4. 78°
42. The table below shows the charges of sending money via money order.
    

    Range	Charged
    upto - 1000	110
    1001 - 2500	165
    2501 - 5000	225
    5001 - 10000	285
    10001 - 20000	355

    
    Njagi sent two money orders one of sh. 12 000 and another one of sh. 7 500. How much money in total did he pay at the post office?
    1. Sh. 19 500
    2. Sh.20 040
    3. Sh. 640
    4. Sh. 20 140
43. Kirinkai is paid a basic salary of sh. 18 000 and a commission of 4% on all the sales he makes. How much money did he earn in a month he sold goods worth sh. 480 000
    1. Sh. 19 200
    2. Sh. 18 000
    3. Sh. 37 200 
    4. Sh. 19 920
44. What is the sixth number in the pattern
    1, 4, 9, 16,_____?
    1. 25
    2. 36
    3. 49
    4. 29
45. The marked price of a generator is sh. 36 000 but a discount of 20% is given on cash payment. On hire purchase a deposit of sh. 6 000 and monthly instalment of sh. 3 000 for 12 months. How much more is the hirepurchase price than cash price?
    1. Sh. 42 000
    2. Sh. 28 800
    3. Sh. 12 000 
    4. Sh. 13 200
46. The table mat below is made up of rectangular cloth joined to a semi-circular ones.
    
    What is the area of the table mat?
    1. 12 712cm² 
    2. 8808cm² 
    3. 4 704cm² 
    4. 8 710cm² 
47. The table below shows the number of crates of broad sold by a supplier.
    

    DAY	MON	TUE	WED	THUR	FRI	SAT	SUN
    No. of crates sold	16	15	7	6	13	8	12

    
    If a crate holds 15 breads, how many breads did he sell that week?
    1. 77
    2. 1155
    3. 1005
    4. 67
48. The mass of an empty lorry is 7.2 tonnes. When loaded with 60 bags of maize each with a mass of 90kg and 45 bags of rice each of mass 50kg. What is the mass of loaded lorry in tonnes?
    1. 14.85 tonnes
    2. 7650 tonnes
    3. 7.65 tonnes
    4. 14 850 tonnes
49. The number of road accidents recorded in the country in the year 2019 was 17 000.In the year 2020 the number decreased to 14 450. What was the percentage decrease?
    1. 1712%
    2. 85%
    3. 15%
    4. 20
50. The graph below shows the journey by Kipkewewe from Kapchorua to Kiplagich and back.
    
    What was the average speed for the whole journey?
    1. 12km/h
    2. 30km/h
    3. 24km/h 
    4. 40km/h

MARKING SCHEME

1. A
2. B
3. D
4. B
5. C
6. A
7. D
8. B
9. C
10. A
11. D
12. C
13. D
14. B
15. C
16. D
17. B
18. C
19. D
20. C
21. A
22. B
23. D
24. A
25. D
26. B
27. D
28. A
29. D
30. A
31. B
32. B
33. A
34. B
35. A
36. A
37. D
38. B
39. B
40. A
41. C
42. D
43. C
44. B
45. D
46. A
47. B
48. D
49. C
50. C

1. What is nine million one hundred and nine thousand and nine written in symbols?
   1. 9100909
   2. 9109009
   3. 9019009
   4. 9010909
2. In a polling station the number of registered voters was 679495. What was the number rounded off to the nearest ten thousands?
   1. 680000
   2. 679000
   3. 700000
   4. 679500
3. What is the sum of the total values of digits 6 and 2 in the number 864280?
   1. 6020
   2. 60200
   3. 860200
   4. 62000
4. What is the value of 96120 divided by 24?
   1. 4005
   2. 405
   3. 45
   4. 40005
5. What is the value of ¹/₈ + (¹/₃ ÷ ¹/₆) ?
   
   1. 2¹/₆ 
   2. 4¹/₂₄
   3. 2¹/₈
   4. ⁵/₈
6. What is the place value of digit 4 in the number 58.3948?
   1. Thousandths
   2. Hundredths
   3. Ten thousandths
   4. Tens
7. What is the circumference of the circle drawn below?
   
   
   1. 220m
   2. 290m
   3. 110m
   4. 255m
8. A hotel buys 41.5 litres of milk every day. How many litres of milk did the hotel buy in the month of January, February and March year 2021?
   1. 3776.51
   2. 37351
   3. 38181
   4. 3776.251
9. The figure below shows angles formed by two intersecting lines.
   
   Which of the following pair of angles are vertically opposites?
   1. f and h
   2. gandh
   3. f and g
   4. e andf
10. What is the next number in the series
    12, 14, 17, 22, 29 _____ ?
    1. 38
    2. 42
    3. 40
    4. 46
11. What is the actual length of a road in kilometres that measures 4cm on a map drawn to a scale of 1:400000?
    1. 160km
    2. 1.6km
    3. 16kom
    4. 0.16 km
12. A sales lady salary of sh 4000 was increased by 16%. What was the new salary of the sales lady?
    1. sh. 640
    2. sh. 3360
    3. sh. 4640
    4. sh. 10460
13. A dairy company donated 60 carton of milk to a pre-school. If each carton contained 80-2dl packet of milk, how many litres of milk was donated?
    1. 9.6
    2. 9600
    3. 96
    4. 960
14. The perimeter of a square plot of land is 216m. What is the area of the plot quare metres?
    1. 2816²
    2. 864m²
    3. 2916m²
    4. 46656m²
15. Muli bought the following items from a supermarket.
    1kg sugar @sh. 115
    ½kg rice @sh. 110
    2kg maize flour for sh. 130
    2 loaves of bread @sh. 45
    If he paid using sh. 1000 note, how much balance did he get back?
    1. sh. 725
    2. sh. 610
    3. sh. 275
    4. sh. 390
16. Which of the following statement is incorrect about an equilateral triangle?
    1. All sides are equal
    2. Sum of angles add upto 180°
    3. All angles are equal
    4. Base angles are equal
17. A train left Nairobi at 6.15pm and took 2¼ hrs to reach Mombasa. At what time in 12 hour clock system did it reach Mombasa?
    1. 8.30am
    2. 7.45pm
    3. 8.30pm
    4. 7.45am
18.  A motorist drove from Nakuru to Naivasha town a distance of 360km taking 4 hours. What was the average speed in kilometres per hour for the joumey?
    1. 9km/hr
    2. 20km/hr
    3. 90km/hr
    4. 80km/hr
19. What is the L.C.M of 30, 40 and 60?
    
    1. 10
    2. 120
    3. 240
    4. 180
20. The table below shows number of eggs sold by a vendor in a week.
    

    Days	Mon	Tue	Wed	Thur	Fri	Sat	Sun
    No. sold	22	16	22	17	24	20	26

    What is the mean number of eggs sold in the week?
    1. 22
    2. 17
    3. 21
    4.  20
21. Using a ruler and a pair of compass construct triangle XYZ such that line XY=8cm, YZ=7cm and XZ = 6.5cm. Measure the size of angle YZX.
    1. 58°
    2. 105°
    3. 75°
    4. 47°
22. Which of the following is the correct order ³/₅, ⁵/₈, ⁷/₁₀, and ½ of arranging from the largest to the smallest?
    1. ½, ³/₅,⁵/₈, ⁷/₁₀
    2. ³/₅, ⁷/₁₀, ⁵/₈, ½
    3. ½, ⁷/₁₀, ⁵/₈, ³/₅
    4. ⁷/₁₀, ⁵/₈, ³/₅, ½
23. The table below show time table of a bus between different towns
    

    Town	Arrival time	Departure time
    Nairobi   Naivasha   Gilgil  Nakuru  Eldoret	_________  10.25pm  12.10pm  1.50pm  2.45pm	9.10am  10.40am  12.25pm    2.10pm   __________

    How long did the bus take to travel from Naivasha town to Nakuru?
    1. 3¹/₆ hrs
    2. 1⁵/₆ hrs
    3. 3½ hrs
    4. 2¾hrs
24. What is the difference between the L.C.M of 15, 20 and 25 and the G.C.D of 45, 75 and 90?
    1. 315
    2. 10
    3. 85
    4. 285
25. A lorry is carrying 90 cartons each holding 40 tins of cooking fat. If each tin weighs 500g, what was the total mass of tins in kilograms?
    1. 1.8kg
    2. 180kg
    3. 1800kg
    4.  0.18kg
26. In a class the number of boys is ¹/₃ and the rest are girls. If there were 40 girls in the class, how many pupils were there in total/
    1. 60
    2. 35
    3. 75
    4. 90
27. A lady sold milk from 12^th January to 9^th March 2020. For how many days did she sell the milk?
    1. 58
    2. 59
    3. 57
    4. 56.
28. The figure below represents a stack made of cuboids.
    
    How many cuboids are used to make the stack drawn above?
    1. 33
    2. 32
    3. 30
    4. 27
29. Using a ruler and a pair of compass construct triangle MNT such that line MN=5cm, NT=4 cm and angle MNT=120°. Bisect angle MNT and let the bisector meet line MT at S Measure the length of line MS.
    1. 4.3cm
    2. 7.8cm
    3. 2.3cm
    4. 3.4cm
30. The figure below shows a school ground.
    
    An athletee run all round the field two times, how many metres did he cover? (Take π=²²/₇)
    1. 400m
    2. 526m
    3. 800m
    4. 1052m
31. What is 7.5% written as a fraction to its simplest from possible.
    1. ¹⁵/₂
    2. ¾
    3. 7½
    4. ³/₄₀
32. The table below shows postal rates for sending money order. 
    

    Order value in shs.	Commission
    Not exceeding 500 500 - 1000 1001 -3000 3001 - 5000 5001 - 10000 10001 - 20000 20001 - 30000	sh. 42   sh. 144   sh. 174   sh. 209   sh. 295    sh. 441   sh. 617

    
    A father sent school fees for his two children as follows sh. 10500 and sh. 17400 respectively. How much commission did he pay at the post office?
    1. sh. 617
    2. sh. 1058
    3. sh. 736
    4. sh. 882
33. What is the value of   
    
    
    1. 6²/₃
    2. 4
    3. 3
    4. 2
34. What is the value of   16.42 − (3.16 + 8.4)  
                                                   2.43
    1. 0.2
    2. 200
    3. 2
    4. 20
35. A staff meeting ended at 5.00pm after taking 5 hours 55 minutes. At what time did the meeting started? 
    1. 12.55pm
    2. 11.05am
    3. 12.05pm
    4. 11.55am
36. The figure below shows a rectangular tank.
    
    If the tank is to be filled with water using 50 litres container, how many containers will be required to fill the tank?
    1. 240
    2. 160
    3. 480
    4. 320
37. A square garden has an area of 10.24m². What is the length of each side in centimetres?
    1. 3.2cm
    2. 3200cm
    3. 320cm
    4. 32cm
38. Work out the value of 2²/₃ × 3½?
    1. 6¹/₃
    2. 6²/₃
    3. 9¹/₃
    4. 3¹/₉
39. In a harambee there were 850 adults and 457 children. If each adult contributed sh. 200 and each child contributed sh. 100, how much money was collected altogether?
    1. sh. 215700
    2. sh. 176400
    3. sh. 91400 
    4. sh. 21750
40. What is the value of 5(3y - 2x) - 13y + 6x to its simplest form possible?
    1. 28y + 4x
    2. 2y + 4x
    3. 2y − 4x
    4. 28y + 16x
41. The pie chart below shows how a lady spent her salary.
    
    If her salary was sh. 56000, how much money did she spent on rent?
    1. sh. 21000
    2. sh. 14000
    3. sh. 28000
    4. sh. 32000
42. What is the area of the triangle drawn below.
    
    
    1. 720m²
    2. 270m²
    3. 432m²
    4. 216m²
43. Joel got 80% of the total marks in the end term examination. If the total marks was 500, how many marks did he lose on the examination?
    1. 100
    2. 140
    3. 400
    4. 360
44. What is the value of t in the equation
    4t − 6 + 36t = 60?
    1. 1¾
    2. 1¹⁷/₂₀
    3. 1³/₅
    4. 1¹³/₂₀
45. The price of a text book is sh. 600. If the price was decreased by 15%, what was the new price of the book? 
    1. sh. 570
    2. sh. 690
    3. sh. 450
    4. sh. 510
46. The diagram below shows a cuboid whose length is 0.48m and a width of 0.25m.
    
    If its volume is 0.042m³, what is the length of its height (h) in centimetres?
    1. 55cm
    2. 38cm
    3. 35cm
    4. 28cm
47. A vendor sold 2500 copies of daily nation news paper at sh. 70 each. If the vendor got 8% of the total sales, how much money did the vendor receive from the sales?
    1. sh. 50000
    2. sh. 14000
    3. sh. 35000
    4. sh. 70000
48. In the figure below line AB = AC, angle ABC=50°, angle ECA=15° and angle BAD= angle DAC.
    
    What is the size of angle AEC?
    1. 30°
    2. 25°
    3. 15°
    4. 20°
49. In the figure drawn below, the radius of the circle is 35cm with a centre O.
    Take π = ²²/₇
    
    What is the area of the shaded part?
    1. 3850cm² 
    2. 2450cm²
    3. 1400cm²
    4. 700cm²
50. The bar graph drawn below shows amount of rainfall recorded in a week.
    
    What was the amount of rainfall recorded in the last four days of the week?
    1. 1055mm
    2. 2250mm
    3. 1100mm
    4. 1150mm