Grade 8 Distinction Assessment Study Guide: Mathematics, Science, Agriculture & Pre-Tech
Grade 8 Assessment Study Guide: Mathematics, Integrated Science, Agriculture & Pre-Technical Studies
Mathematics Assessment Study Notes
Strand: Numbers
Problem 1: Integer Addition and Subtraction on a Number Line
Problem Statement: Solve using a number line.
Methodology & Explanation:
Step 1: Begin at on the number line. Move steps to the left to reach .
Step 2: From , move steps to the right (addition of positive integer) to reach .
Step 3: From , move steps to the left (subtraction of positive integer) to reach .
Final Answer:
Problem 2: Capacity and Least Common Multiple (LCM)
Problem Statement: Maria wanted to fill containers with capacities of , , and respectively without a remainder. Find the least capacity of a tank she can use.
Methodology & Solution:
Determine the Least Common Multiple (LCM) of , , and .
Prime factorization:
Final Answer:
Problem 3: Area of a Square Farm Using Mathematical Tables
Problem Statement: Johana has a square farm of sides . Find the area of the square farm using a mathematical table.
Methodology & Solution:
Reading squares from mathematical tables for gives
Final Answer:
Problem 5: Decimal Conversion of Mixed Fractions
Problem Statement: During a drought, the government purchased of maize flour. Express this mass in decimal form.
Methodology & Solution:
Convert the fractional part:
Combine with the whole number:
Final Answer:
Problem 7: Fraction Subtraction and Word Problem
Problem Statement: Madam Ann bought of maize flour for her visitors. She then gave each of her five visitors of flour. Determine the amount of maize flour Madam Ann remained with.
Methodology & Solution:
Total flour given out =
Initial flour bought =
Remaining flour =
Final Answer: (or )
Problem 8: Recurring Decimals
Problem Statement: Express the following fractions as decimals indicating the recurring digits:
a)
b)
Methodology & Solution:
a) (recurring digits are and )
b) (recurring digit is )
Problem 11: Multi-Variable Whole Number Word Problem
Problem Statement: In a county hall meeting there were men. The number of women was twice the number of boys, while the number of girls was more than the number of men but less than the number of boys. Find the total number of people who attended the town hall meeting.
Methodology & Solution:
Men () =
Girls () =
Since Girls () is less than Boys ():
Women () =
Total Attendance =
Final Answer:
Problem 12: Work and Time Rates
Problem Statement: Three men can dig a hectare of land for days. After working for two days, man did not turn up to work. How long did it take the remaining men to finish the work?
Methodology & Solution:
Total work required =
Work completed in first 2 days =
Remaining work =
Number of remaining workers =
Time required =
Final Answer: (or )
Problem 16: Significant Figures
Problem Statement: A balance reads . Report the mass using three significant figures.
Methodology & Solution:
Identify the first three significant digits: , , and
Examine the fourth digit: (since it is less than , round down)
Final Answer:
Problem 18: Ratios and Proportions
Problem Statement: A recipe for making fruit juice requires mixing orange juice and apple juice in the ratio . To make a total of of fruit juice, how many litres of orange juice and apple juice should be used?
Methodology & Solution:
Total ratio parts =
Volume of orange juice =
Volume of apple juice =
Final Answer: Orange juice = , Apple juice =
Problem 20: Order of Operations (BODMAS)
Problem Statement: Work out
Methodology & Solution:
Division first:
Multiplication next:
Expression becomes:
Find common denominator for which is :
Final Answer:
Problem 22: Sequential Fractions of Quantities
Problem Statement: In a recent election, of the voters cast their votes on the first day. On the second day, of the remaining voters cast their votes. If there were voters in total, how many voters cast their votes on the second day?
Methodology & Solution:
Votes cast on Day 1 =
Remaining voters =
Votes cast on Day 2 =
Final Answer:
Problem 25: Decimal Division
Problem Statement: Solve
Methodology & Solution:
Final Answer:
Strand: Algebra
Problem 9: Simplification of Algebraic Expressions
Problem Statement: Simplify
Methodology & Solution:
Expand brackets:
Collect like terms:
Final Answer:
Problem 13: System of Linear Equations (Simultaneous Equations)
Problem Statement: Jane bought apples and oranges for a total of . Her friend Alex bought apples and oranges for a total of . Form a simultaneous equation to determine the cost of one apple and one orange.
Methodology & Solution:
Let be the cost of one apple and be the cost of one orange.
Equations:
Equation (1):
Equation (2):
Multiply Equation (1) by and Equation (2) by :
Subtract the first from the second:
Substitute into Equation (2):
Final Answer:
Simultaneous System:
Cost of 1 apple , Cost of 1 orange
Problem 19: Algebraic Perimeter of a Rectangle
Problem Statement: A rectangular flower lawn has a perimeter of . Its width is and its length is . Find its length.
Methodology & Solution:
Final Answer:
Problem 21: Algebraic Substitution
Problem Statement: Given , , and . Find the value of .
Methodology & Solution:
Calculate variables:
Substitute into target expression:
Final Answer:
Strand: Measurements
Problem 4: Circular Perimeter / Circumference

Problem Statement: The figure above shows the school assembly ground with radius . Jane walked round the assembly ground thrice. How much distance did Jane cover?
Methodology & Solution:
Circumference of one round
Distance covered in 3 rounds =
Final Answer: (or )
Problem 6: Percentage Profit
Problem Statement: Mr. Onyango bought a television for and sold it for . What percentage profit did he make?
Methodology & Solution:
Final Answer:
Problem 14: Volume of a Cylinder

Problem Statement: Find the volume of the cylindrical tank shown above with height and radius .
Methodology & Solution:
Final Answer:
Problem 15: Percentage Consumption and Remaining Quantity
Problem Statement: Musa had of water in a container. He used of the water to wash his clothes. How many litres of water remained in the container?
Methodology & Solution:
Percentage remaining =
Remaining volume =
Final Answer:
Problem 23: Area of a Sector of a Circle

Problem Statement: Find the area of the shaded sector shown above with angle and radius . Leave your answer in terms of .
Methodology & Solution:
Final Answer:
Problem 24: Compound Interest
Problem Statement: Anna invested in a savings account offering an annual compound interest rate of . How much will her investment be worth after ?
Methodology & Solution:
Compound interest formula:
Final Answer:
Problem 26: Compound Appreciation
Problem Statement: James bought land for . Over the years, the land's value appreciated at a rate of per year. What is the value of the land after ?
Methodology & Solution:
Final Answer:
Problem 27: Total Surface Area of a Cuboid
Problem Statement: Find the total surface area of a cuboid wooden desk top with length , width , and height .
Methodology & Solution:
Final Answer:
Problem 28: Radius of a Cylinder from Volume
Problem Statement: A cylinder has a volume of and a height of . What is the radius of the cylinder?
Methodology & Solution:
Final Answer: (or )
Problem 29: Commission Calculation
Problem Statement: Lisa earns a commission on her sales. In a given month, she made total sales of . How much commission did Lisa earn?
Methodology & Solution:
Final Answer:
Strand: Geometry
Problem 10: Total Surface Area of a Triangular Prism (Wedge)

Problem Statement: What is the total surface area of the wedge shown above?
Methodology & Solution:
The wedge is a triangular prism with triangular faces of base and height , hypotenuse , and prism length .
Area of 2 triangular end faces:
Area of bottom rectangular face:
Area of vertical back face:
Area of slanted top face:
Total Surface Area:
Final Answer:
Problem 17: Perimeter of an Isosceles Triangular Garden
Problem Statement: Find the perimeter of the triangular flower garden with base and vertical height .
Methodology & Solution:
The vertical height bisects the base into two right-angled triangles with base and height .
Slanted side length =
Final Answer:
Strand: Data Handling and Probability
Problem 30: Interpretation of Pie Charts

Problem Statement: The pie chart represents David's performance in an exam out of marks. The angle for English is . How many marks did he score in English?
Methodology & Solution:
Final Answer:
Integrated Science Study Notes
Scientific Inquiry & Matter
Importance of Studying Integrated Science
Enables learners to acquire foundational knowledge to understand natural processes and the physical environment.
Develops critical thinking, inquiry skills, scientific attitudes, and problem-solving abilities necessary for STEM careers.
Definitions of Pure Substances
Element: A pure substance consisting of only one type of atom that cannot be broken down into simpler substances by chemical methods.
Compound: A pure substance composed of two or more different elements chemically combined in fixed proportions by mass.
States and Properties of Matter
Three States of Matter: Solid, Liquid, Gas.
Properties of Gases:
Have no fixed shape or volume and expand to fill any container.
Highly compressible due to large intermolecular spaces.
Exert pressure equally in all directions and diffuse rapidly.
Chemical Symbols
: Magnesium
: Hydrogen
: Copper
Classification of Substances
Substance | Group Classification |
|---|---|
Oxygen gas () | Molecule / Element |
Aluminum () | Element |
Sodium chloride () | Compound |
Chemical & Physical Changes

Dehydration and Hydration of Copper(II) Sulphate
Type of Change: Reversible chemical change / Dehydration.
Explanation: Heating blue hydrated copper(II) sulphate drives off water of crystallization, leaving behind white anhydrous copper(II) sulphate powder and water droplets on cooler test tube walls.
Other Examples: Heating hydrated cobalt(II) chloride or hydrated sodium carbonate.
General Categories of Changes in Matter
Physical changes (e.g., state changes like melting, freezing, boiling).
Chemical changes (e.g., rusting, combustion, neutralization).
Changes of state (sublimation, deposition, condensation).
Effect of Impurities on Boiling Point
Observation: Adding salt to pure water increases its boiling point from to .
Explanation: Dissolving a non-volatile solute (salt) lowers the vapor pressure of the liquid, requiring higher heat energy to equal atmospheric pressure, thus causing boiling point elevation.
Acids, Bases, and Indicators
Indicator Colour Changes
Indicator | Acidic Solution | Neutral Solution | Basic Solution |
|---|---|---|---|
Methyl Orange | Red | Orange | Yellow |
Phenolphthalein | Colourless | Colourless | Pink |
Cell Biology & Physiological Processes
Total Magnification Calculation
Formula:
Given: Eyepiece = , Objective =
Calculation:
Animal Cell Structure & Function
Cytoplasm (Part 3): Fluid medium containing cell organelles; serves as the primary site for metabolic and chemical reactions.
Organism Source: Can be obtained from animal tissues, human cheek cells, or unicellular organisms like Amoeba.
Osmosis vs. Diffusion Experiment

Petri Dish A (Raw Potato): Water moves by osmosis from the petri dish through the living semi-permeable cell membranes of raw potato into the cavity, dissolving the salt to form a liquid salt solution.
Petri Dish B (Boiled Potato): Boiling destroys/denatures cell membranes, rendering them fully permeable. Osmosis cannot occur; hence salt in the cavity remains dry.
Key Differences Between Osmosis and Diffusion
Feature | Osmosis | Diffusion |
|---|---|---|
Molecules Moved | Solvent/Water molecules only | Solute or gas/liquid particles |
Membrane Requirement | Requires a semi-permeable membrane | Does not require a membrane |
Medium | Occurs strictly in liquid solutions | Occurs in gases, liquids, and solids |
Factors Affecting Photosynthesis Rate
Light intensity
Carbon dioxide concentration
Temperature
Water availability
Physics, Electricity & Magnetism
Properties of Magnets
Directive Property: Freely suspended magnet points in the geographic North-South direction.
Poles Property: Like poles repel; unlike poles attract. Magnetic poles always exist in pairs.
Non-magnetic materials: Erasers (made of rubber/synthetic materials) are non-magnetic and cannot be attracted by magnets.
Safety Measures During Thunderstorms
Avoid standing under tall isolated trees or touching metallic objects in open fields.
Stay indoors, stay away from window frames, and disconnect electrical appliances.
Electrical Circuit Measuring Instruments

Digital Multimeter: Used to measure current, voltage, and electrical resistance.
Ammeter / Galvanometer: Used to measure or detect electric current flow.
Environmental & Safety Practices
Classes of Fire and Extinguishers
Fire Class | Combustible Source | Recommended Extinguisher |
|---|---|---|
Class A | Solid combustibles (wood, paper, textiles) | Water or Foam Extinguisher |
Class B & E | Flammable liquids (Class B) & Electrical fires (Class E) | Carbon Dioxide () or Dry Powder |
Class F | Cooking fats and oils | Wet Chemical Extinguisher |
Agriculture Study Notes
Fish Preparation & Meat Handling

Procedures in Fish Preparation
Procedure (a) Descaling: Removing fish scales using a scaler or knife scraper.
Procedure (b) Gutting / Eviscerating: Slitting the belly and removing internal organs and viscera.
Meat Preservation Methods
Salting / Curing
Sun drying / Dehydration
Smoking
Refrigeration / Freezing
Last Steps of Dressing a Poultry Carcass
Evisceration (removal of internal entrails/organs).
Final washing, chilling, and packaging/weighing.
Importance of Hygiene in Meat Handling
Prevents bacterial contamination and foodborne infections.
Extends shelf life and prevents spoilage.
Soil and Water Conservation
Reasons for Soil Conservation
Preserves topsoil fertility and essential plant nutrients.
Prevents water and wind erosion.
Maintains soil organic matter and moisture retention capacity.
Prevents land degradation and desertification.
Methods of Farm Water Harvesting
Roof catchment systems with plastic/corrugated gutters and storage tanks.
Farm ponds and water pans.
Earth dams and shallow wells.
Soil Conservation Structures

Structure Name: Stone lines / Stone bunds.
Conservation Mechanism: Reduces velocity of surface runoff, traps eroded sediment, and increases water infiltration into soil.
Gardening Systems & Value Addition

Framed Structures for Suspended Gardens
Veranda / Corridor posts of school buildings.
School boundary fences and vertical timber frames.
Dedicated wooden or metal hanging racks.

Benefits of Innovative Container Gardens
Maximizes production in small or marginal land space.
Easy weed, pest, and disease control.
Conserves soil moisture and water efficiency.
Definition of Kitchen Garden
A small plot or containerized cropping area near a home or school where vegetables, herbs, and fruits are grown for daily consumption.
Value-Added Products
From Groundnuts: Peanut butter, groundnut cooking oil, salted/roasted groundnut snacks.
Processing Raw Honey: Removes wax, pollen, and impurities; delays crystallization; improves shelf life and commercial value.
Crop & Livestock Management
Identification of Crop Damage
Damage (a): Pest infestation (caterpillars feeding on leaf blade).
Damage (b): Disease infection (wilting/fungal blight).
Mango Tree Management
Regular pruning of dead/diseased branches.
Regular weeding, mulching, and pest/disease control.
Safe Rearing in Poultry Folds
Move fold cages regularly to fresh pasture to prevent disease accumulation.
Ensure predator-proof mesh wire enclosure.
Provide adequate ventilation, shade, clean water, and feed.
Importance of Farm Layout
Optimizes land use and operational efficiency.
Minimizes cross-contamination between crop and livestock enterprises.
Pre-Technical Studies Study Notes
Safety Practices & Tools

Firefighter Personal Protective Equipment (PPE)
A: Fire Helmet / Hard hat
B: Visor / Face shield / Fire coat
C: Protective Gloves / Trousers
D: Safety Boots / Firefighting Boots
Common Workplace Hazards
Physical Hazards: Slippery floors, loose scaffolding, exposed moving machine parts.
Chemical Hazards: Toxic cleaning fumes, hazardous chemical solvents.
Electrical/Ergonomic Hazards: Exposed wiring, poor posture/seating.
Construction Tools

Plumb Bob (Left): Used to check and establish vertical alignment (plumb line) in construction.
Hand Plane / Wooden Plane (Right): Used for smoothing, flattening, and shaping timber surfaces.
Computer Systems & Waste Management
Categories of Computer Hardware
Projector: Output Device.
Mouse: Input Device.
Keying Input Device for TV: Remote Control / Keypad.
Storage Devices

i: Optical Disc Drive (CD/DVD Drive)
ii: Hard Disk Drive (HDD)
E-Waste Management Methods
Safe recycling of electronic components.
Donating, refurbishing, or repurposing computer cases and functional hardware.
Data Security Reasons in Environmental Management
Prevents unauthorized tampering or loss of environmental research data.
Guarantees regulatory compliance.
Protects confidential natural resource mapping data.
Business Studies, Resources & Communication
Agricultural Features on KSh 100 Kenyan Currency
Depiction of tea picking / harvesting.
Livestock and crop farming imagery.
Factors of Production and Their Rewards
Factor of Production | Reward |
|---|---|
Labour | Salaries or wages |
Land | Rent or rates |
Capital | Interest |
Entrepreneurship | Profit |
Classification of Economic Resources
Economic Resource | Category |
|---|---|
Teacher | Human Resource |
Land | Natural Resource |
Cup | Capital / Man-made Resource |
Pilot | Human Resource |
Desk | Capital / Man-made Resource |
Water | Natural Resource |
Goods vs. Services
Goods: Tangible physical items that can be touched, stored, and transferred (e.g., books, furniture).
Services: Intangible activities, work, or performances provided to satisfy needs (e.g., teaching, medical treatment).
Entrepreneurship & Investor Protection
Entrepreneurship: The process of identifying business opportunities, organizing resources, taking financial risks, and establishing an enterprise for profit.
Importance of Investor Protection:
Encourages local and foreign capital investment.
Stimulates economic expansion and job creation.
Protects assets from unlawful expropriation or fraud.
Communication Channels & Ethics
Written Communication Channels: Letters/Memos, SMS/Text messages, Emails.
Principles of Ethical Communication: Honesty/Truthfulness, Transparency, Respect/Fairness, Confidentiality.
ICT Communication Tools: Mobile smartphones, Computers/Laptops, Email/Internet systems.