Chemistry • Form 4 • Periodic Table KCSE 2025 Chemistry P2 Q1 — Period 3 Trends Explain the Period 3 trends — radius, ionisation energy, melting points, oxides, oxidation number and SiCl₄ hydrolysis.
Chemistry • Form 4 • Organic Chemistry KCSE 2025 Chemistry P2 Q2 — Naming & Copper Extraction Name two organic compounds, then follow copper from its ore — gas C, the silica slag, electrolytic purification and the green patina.
Chemistry • Form 4 • Chlorine KCSE 2025 Chemistry P2 Q4 — Chlorine Prepare chlorine from NaCl and MnO₂, then work through its reactions with iron, phosphorus, hot alkali, hydrogen sulphide, iodide and litmus.
Chemistry • Form 4 • Energetics KCSE 2025 Chemistry P2 Q3 — Hess's Law Define standard enthalpy of formation, build a Hess cycle for propane to find ΔH₃, then use Q = mcΔT to find the mass of butane burned.
Chemistry • Form 4 • Electrochemistry KCSE 2025 Chemistry P2 Q5 — Down's Cell Extraction of sodium in the Down's cell — identify the electrodes, the role of the diaphragm and calcium chloride, and calculate the mass of sodium from 1000 kg of salt.
Chemistry • Form 4 • Electrochemistry KCSE 2025 Chemistry P2 Q6 — Electrolysis & Cells Electrolysis of copper(II) sulphate, a Faraday's-law relative-atomic-mass calculation, electrochemical cells and the corrosion of aluminium versus iron.
Chemistry • Form 4 • Reaction Rates KCSE 2025 Chemistry P2 Q7 — Rates of Reaction Rates of reaction — the effect of pressure and temperature, the ethanoic acid and copper(II) carbonate reaction, and reading rate off the gradient of a tangent.
Physics • Form 4 • Measurement KCSE 2025 Physics P1 Q1 — Micrometer Zero Error A micrometer with a +0.02 mm zero error reads 0.31 mm — correct the reading to find the true diameter.
Physics • Form 4 • Fluids KCSE 2025 Physics P1 Q10 — Dust Trail Why does dust rise high behind a speeding car? Fast air, low pressure, Bernoulli.
Physics • Form 4 • Kinematics KCSE 2025 Physics P1 Q11 — Deceleration An object slows uniformly from 3 m/s to rest over 10 m — find its acceleration with the equation of motion.
Physics • Form 4 • Energy KCSE 2025 Physics P1 Q13 — Non-renewable energy Name a source of non-renewable energy — and understand what makes coal, oil and natural gas non-renewable.
Physics • Form 4 • Forces KCSE 2025 Physics P1 Q12 — Inertia coin trick Flick the card from under a coin and it falls straight into the beaker — see how inertia explains the classic coin and card trick.
Physics • Form 4 • Thermal Physics KCSE 2025 Physics P1 Q15 — Heat & mixtures A full Section B heat question — specific heat capacity, latent heat of fusion, and finding the final temperature when hot and cold water are mixed.
Physics • Form 4 • Thermal Physics KCSE 2025 Physics P1 Q14 — Crawling under smoke Why are you told to crawl to the exit in a smoke-filled room? It comes down to the density of hot smoke versus cool air.
Physics • Form 4 • Forces KCSE 2025 Physics P1 Q17 — Circular Motion Define angular displacement, derive v = rω, and calculate the centripetal acceleration and force on a swinging pendulum bob.
Physics • Form 4 • Thermal Physics KCSE 2025 Physics P1 Q16 — Gas Laws Verify Boyle's law, compare the diffusion of two gases, and use Charles's law to find the new volume of a heated gas.
Physics • Form 4 • Forces KCSE 2025 Physics P1 Q19 — Momentum & Free Fall Explain free fall in a vacuum, find the change in momentum and stopping time of a braking car, and estimate a table's length using a palm.
Physics • Form 4 • Fluids KCSE 2025 Physics P1 Q18 — Archimedes' Principle State Archimedes' principle, measure the mass of water displaced, and verify that upthrust equals the weight of fluid displaced.
Physics • Form 4 • Measurement KCSE 2025 Physics P1 Q2 — Tree Height by Shadows Estimate the height of a tree from a student's height using shadows and similar triangles.
Physics • Form 4 • Forces KCSE 2025 Physics P1 Q3 — Tension in a Plank A block on a plank makes it sag — show how the tensional force acts on the plank.
Physics • Form 4 • Fluids KCSE 2025 Physics P1 Q4 — Pascal's Principle Why does toothpaste flow out when you squeeze the tube? Name and explain the principle.
Physics • Form 4 • Thermal Physics KCSE 2025 Physics P1 Q6 — Thermometer Constriction Why does a clinical thermometer keep its reading after it leaves the patient? Meet the constriction.
Physics • Form 4 • Forces KCSE 2025 Physics P1 Q8 — Unstable Equilibrium Why is an oval ball balanced on its end unstable? Follow its centre of gravity.
Physics • Form 4 • Matter KCSE 2025 Physics P1 Q5 — Shrinking Solution Volume Salt plus water gives less volume than the sum of the two — explain why using particles.
Physics • Form 4 • Forces KCSE 2025 Physics P1 Q7 — Moments & Spanners Two spanners, one nut — why does the longer one need less force? It's all in the moment.
Physics • Form 4 • Measurement KCSE 2025 Physics P1 Q9 — Calibrating a Spring You have a spring and known masses — what else do you need to calibrate a spring balance?
Mathematics • Form 4 • Statistics KCSE 2025 P2 Q10 — Upper Quartile Cumulative frequency, the Q3 position, and the grouped-data quartile formula.
Mathematics • Form 4 • Sequences & Series KCSE 2025 P2 Q1 — Arithmetic Progression Using the constant common difference of an AP to find x, then the difference itself.
Mathematics • Form 4 • Coordinate Geometry KCSE 2025 P2 Q11 — Equation of a Circle Building the circle equation from centre and radius, then finding where it crosses the x-axis.
Mathematics • Form 4 • Commercial Arithmetic KCSE 2025 P2 Q12 — Compound Interest Compound interest, finding the number of periods with logarithms, then converting to years.
Mathematics • Form 4 • Coordinate Geometry KCSE 2025 P2 Q13 — Ratio Dividing a Line Using vectors AB and AC to find the ratio in which B divides the line AC.
Mathematics • Form 4 • Matrices & Transformations KCSE 2025 P2 Q14 — Matrix & Area Scale Factor Using the determinant as area scale factor to find the possible values of a.
Mathematics • Form 4 • Calculus KCSE 2025 P2 Q15 — Kinematics (Integration) Integrating velocity to find distance, using a known point to fix the constant.
Mathematics • Form 4 • Trigonometry KCSE 2025 P2 Q16 — Trigonometric Graph Reading the amplitude and period off a sine graph to find the scalars A and omega.
Mathematics • Form 4 • Commercial Arithmetic KCSE 2025 P2 Q17 — Mixtures, Profit & Ratio Cost price of a groundnut mixture, the percentage profit on selling it, and the mixing ratio.
Mathematics • Form 4 • Commercial Arithmetic KCSE 2025 P2 Q19 — Income Tax (PAYE) Taxable income, PAYE band by band with relief, then working backwards to a new basic salary.
Mathematics • Form 4 • Algebra KCSE 2025 P2 Q18 — Rational Equation Forming a rational equation from club fees, solving the quadratic for x, and a percentage increase.
Mathematics • Form 4 • Approximations & Errors KCSE 2025 P2 Q2 — Maximum Possible Error Why errors add when you subtract two measured quantities, giving a maximum error of 1 degree.
Mathematics • Form 4 • Graphs KCSE 2025 P2 Q20 — Cubic Graph Complete the cubic table, plot the curve, read the roots, then draw a line to solve a second cubic.
Mathematics • Form 4 • Probability KCSE 2025 P2 Q22 — Probability Probability space, both numbers greater than 3, sum not exceeding 6, then same-colour and mixed-colour draws.
Mathematics • Form 4 • Geometry KCSE 2025 P2 Q21 — 3D Geometry (Cuboid) Length RM in a cuboid, then the angle to the base, between two lines, and the obtuse angle between two planes.
Mathematics • Form 4 • Matrices & Transformations KCSE 2025 P2 Q23 — Matrix Transformations Image under T1, describing the stretch, the single combined matrix, then area by determinant scale factor.
Mathematics • Form 4 • Surds KCSE 2025 P2 Q3 — Rationalising Surds Rationalising a surd denominator with its conjugate to read off a and b.
Mathematics • Form 4 • Calculus KCSE 2025 P2 Q24 — Area Under a Curve Definite integral, area above the axis by rectangle minus curve, area below, then the whole shaded region.
Mathematics • Form 4 • Variation KCSE 2025 P2 Q6 — Direct Variation y varies directly as the square of (x+1): find k and the connecting equation.
Mathematics • Form 4 • Geometry KCSE 2025 P2 Q7 — Loci & Construction Constructing the 50-degree angle locus as a circular arc, then locating Q at half the triangle's area.
Mathematics • Form 4 • Binomial Expansion KCSE 2025 P2 Q4 — Binomial Expansion Expand (2 + 1/2x) to the power 5, then estimate 2.05^5 from the first four terms.
Mathematics • Form 4 • Geometry KCSE 2025 P2 Q5 — Circle: Tangent & Angles Alternate segment theorem plus angle at centre to find the acute angle BOC.
Mathematics • Form 4 • Latitude & Longitude KCSE 2025 P2 Q8 — Longitude & Nautical Miles Converting 9000 nautical miles along the equator into degrees of longitude to find point U.
Mathematics • Form 4 • Calculus KCSE 2025 P2 Q9 — Rate of Change from a Graph Drawing a tangent to a displacement-time curve at t = 0.5 s and reading its gradient as the velocity.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q1: Prime Numbers Which set has prime numbers only? Test 2, 4, 5 and 9 with the two-factor rule.
Mathematics • Grade 9 • Measurement KJSEA 2025 Maths Q10 — Cylinder Surface Area Find the bucket surface touching the water: circular base plus curved wall, top left out.
Mathematics • Grade 9 • Measurement KJSEA 2025 Q11 — Capacity Find the capacity of a cuboid milk packet in litres.
Mathematics • Grade 9 • Measurement KJSEA 2025 Q12 — Kelvin to Celsius Choose the calculation that converts a Kelvin reading to degrees Celsius.
Mathematics • Grade 9 • Measurement KJSEA 2025 Maths Q14 — Percentage Error Which calculation gives the percentage error when an estimate of 1.5 m misses the actual 1.2 m?
Mathematics • Grade 9 • Numbers Q13 — Mobile Money Charges Work out the balance left after sending and withdrawing money plus charges.
Mathematics • Grade 9 • Measurement Q16 Scale Drawing Use a 1:100 scale to find how long a 3 m wall is on the drawing.
Mathematics • Grade 9 • Geometry KJSEA 2025 Maths Q15 — Quadrilaterals Which quadrilateral has diagonals that bisect each other at 90 degrees? It's the rhombus.
Mathematics • Grade 9 • Geometry KJSEA 2025 Q18 — Enlargement Enlarge a 16 cm photograph by a scale factor of 2 to find its new length.
Mathematics • Grade 9 • Geometry KJSEA 2025 Maths Q17 — Perpendicular Gradient Find the gradient of a line perpendicular to 2y = x + 3 using the negative reciprocal rule.
Mathematics • Grade 9 • Statistics KJSEA 2025 Maths Q20 — Probability Find the probability of drawing a card marked E from 11 lettered cards.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q2 — HCF Find the largest number of equal groups by taking the HCF of 120, 180 and 24.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q21 — Place Value & Rounding Subtraction, number words and rounding 6,784 to the nearest 100.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q23 — Ratio Sharing a Thanksgiving crowd in the ratio 5:7:3 to find men, women, and the difference.
Mathematics • Grade 9 • Measurement KJSEA 2025 Maths Q22 — Volume & Packing Find a cube's volume, then count how many small cubes fit inside.
Mathematics • Grade 9 • Algebra KJSEA 2025 Maths Q27 — Matrices Form two 2 by 3 matrices for weekly fruit buys, then add them to get each family's totals.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q24 — Work Rate Solve a work-rate problem using man-hours to find how many extra days are needed.
Mathematics • Grade 9 • Numbers Q25 — Recurring Decimal to Fraction Turn 0.17 recurring into a fraction using the multiply-and-subtract trick.
Mathematics • Grade 9 • Algebra KJSEA 2025 Maths Q26 — Simultaneous Equations Solve two simultaneous equations by elimination to find the cost of a book and a pen.
Mathematics • Grade 9 • Measurement KJSEA 2025 Maths Q29 — Surface Area of a Cone Find the total surface area of a solid cone with slant height 20 cm and radius 4.2 cm.
Mathematics • Grade 9 • Geometry Q28 — Equation of a Line Point-gradient form to find a line through (1, 4), then solve for the x-intercept.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q3 — Integers Add a positive integer to a negative one to find a new temperature.
Mathematics • Grade 9 • Measurement KJSEA 2025 Maths Q30 — Volume & Displacement A ball sinks in a tin — find how much the water rises using displacement.
Mathematics • Grade 9 • Measurement KJSEA 2025 Maths Q31: Pythagoras & Density Find a leaning rod's length with Pythagoras, then work out density from mass and volume.
Mathematics • Grade 9 • Measurement KJSEA 2025 Q32 — Longitude & Time Use the longitude difference between two towns to work out the local time at town P.
Mathematics • Grade 9 • Geometry KJSEA 2025 Maths Q34 — Parallelogram Construction Construct parallelogram ABCD, drop a perpendicular from D to AB, and measure DE.
Mathematics • Grade 9 • Numbers KJSEA 2025 Q33 — Import Duty, Excise & VAT Work out import duty, excise duty and VAT as percentages of a Ksh 1.2 million customs value.
Mathematics • Grade 9 • Algebra Q35 — Linear Graphs Complete the table for y = 50x and draw the milk-earnings line.
Mathematics • Grade 9 • Trigonometry KJSEA 2025 Maths Q36 — Angle of Depression Find the height of Dowdy's balcony using a 35° angle of depression and the tangent ratio.
Mathematics • Grade 9 • Geometry KJSEA 2025 Maths Q37 — Bearings Draw the two legs to scale, join A to C, then measure to get 86 m on a bearing of 174°.
Mathematics • Grade 9 • Measurement KJSEA 2025 Q38 — Cuboid Net & Surface Area Draw the net of a 5 by 3 by 2 cm cuboid and add all six faces to get 62 cm squared.
Mathematics • Grade 9 • Statistics KJSEA 2025 Maths Q39 — Mean & Median Tally 20 test marks into a frequency table, then calculate the mean and median.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q4 — Fractions of Time Which calculation gives the extra time used planting 70 seedlings? A clear fractions-of-time walkthrough.
Mathematics • Grade 9 • Numbers KJSEA 2025 Maths Q5 — Indices Use the laws of indices to solve 2^X × 2^3 = 32 and find X.
Mathematics • Grade 9 • Algebra KJSEA 2025 Maths Q7 — Inequalities Turn 'at least 30 but fewer than 50 learners' into a compound inequality and graph it.
Mathematics • Grade 9 • Statistics KJSEA 2025 Maths Q40 — Probability Space List all 12 outcomes of tossing a coin and a die, then find the probability of a head and a four.
Mathematics • Grade 9 • Algebra KJSEA 2025 Q6 — Algebraic Expressions Write an algebraic expression for the number of sheep on a 26-animal farm.
Mathematics • Grade 9 • Algebra KJSEA 2025 Maths Q8 — Order of a Matrix Count the rows and columns to state a matrix's order — worked step by step.
Mathematics • Form 3 • Algebra Alliance F3 P1 Q11 — Algebraic Fractions Add two algebraic fractions and simplify by finding the common denominator.
Mathematics • Form 3 • Measurement Density: Length of a Brass Plate Use density, mass and thickness to find the side length of a thin square brass plate.
Mathematics • Form 3 • Measurement Q12 Time — A Slow Clock A clock loses 15 seconds every hour — find what it shows after 60 hours.
Mathematics • Form 3 • Measurement Diagonal of a Cube Face Use the volume to find the edge, then Pythagoras for the face diagonal.
Mathematics • Form 3 • Numbers Form 3 P1 Q1 — BODMAS Evaluation Use BODMAS to evaluate a signed-number fraction and get -2.
Mathematics • Form 3 • Geometry Vectors: Magnitude of AB Find AB from OA and OB, then use Pythagoras to get its length to one decimal place.
Mathematics • Form 3 • Algebra Form 3 P1 Q14 — Linear Inequalities Split a compound inequality into two parts, solve each, and graph the solution on a number line.
Mathematics • Form 3 • Numbers Ratio, Trips & Profit — Q17 A three-part ratio and profit problem: mass lost after drying, number of lorry trips, and the selling price for a 26% profit.
Mathematics • Form 3 • Measurement Alliance F3 P1 Q18 — Tiles & Profit Count the tiles for a floor, cost 15 rooms, then price each carton for a 12.5% profit.
Mathematics • Form 3 • Numbers Form 3 P1 Q2 — Bells & LCM Three bells and their LCM tell you exactly when they last chimed together.
Mathematics • Form 3 • Geometry Form 3 P1 Q21 — Combined Transformations Enlarge, reflect and rotate a square, then name the single transformation that links the two images.
Mathematics • Form 3 • Geometry Form 3 P1 Q19 — Bearings & Scale Drawing Bearings, right-angle trig and Pythagoras to find PS, a bearing and the ranch area.
Mathematics • Form 3 • Geometry Coordinate Geometry: Lines L, P & Q Find the equations of three related lines and the point where the perpendicular meets the parallel line.
Mathematics • Form 3 • Measurement Cone with a Conical Hole Use similar cones to find the hole radius, volume removed and total remaining surface area.
Mathematics • Form 3 • Measurement Speed–Time Graph (Cheetah) Read a cheetah's speed–time graph to find its top speed, accelerations and average speed.
Mathematics • Form 3 • Numbers Q24 — Commission & Percentages Find monthly earnings from commission plus salary, then reverse the process to get total sales and units sold.
Mathematics • Form 3 • Numbers Currency Exchange: Buying vs Selling Rates Convert $100,000 to shillings then to pounds using the correct bank rates.
Mathematics • Form 3 • Algebra Form 3 P1 Q3 — Simultaneous Equations Turn a hiring word problem into two equations and solve by elimination.
Mathematics • Form 3 • Geometry Alliance F3 P1 Q5 — Angles of a Regular Polygon Use angles on a straight line and the exterior-angle sum to find how many sides the polygon has.
Mathematics • Form 3 • Algebra Alliance F3 P1 Q6 — Laws of Indices Simplify a fractional-power expression using the laws of indices — step by step to 75.
Mathematics • Form 3 • Trigonometry Complementary Angles: Solving for tan(x+60) Use the sine-cosine complementary rule to solve sin(x+60)=cos 2x, then find tan 70 degrees.
Mathematics • Form 3 • Measurement Cylinder Surface Area: Find the Diameter Radius equals height and total surface area is 154 cm² — find the diameter to 2 d.p.
Mathematics • Form 4 • Geometry Triangle Construction (Q10) Construct triangle ABC and measure angle ABC, confirmed by the sine rule.
Mathematics • Form 4 • Numbers KCSE 2025 Maths P1 Q1 — Order of Operations Use BODMAS and fraction skills to evaluate a square-root expression by hand.
Mathematics • Form 4 • Numbers KCSE 2025 P1 Q11 — Profit & Loss Set up profit and loss equations, add them to eliminate the cost price, and find what the shopkeeper paid.
Mathematics • Form 4 • Statistics Histogram Frequencies (KCSE 2025 P1 Q12) Find the two missing frequencies from histogram bar heights using frequency density.
Mathematics • Form 4 • Geometry Reflection: Finding the Mirror Line Use the perpendicular bisector to construct the mirror line and finish the reflected triangle.
Mathematics • Form 4 • Trigonometry KCSE 2025 Maths P1 Q15 — Trigonometry Use a triangle's area to unlock a hidden angle, then find BC with tan.
Mathematics • Form 4 • Geometry Net of a Prism Unfold a trapezoidal prism into four rectangles and two trapezium ends to draw its labelled net.
Mathematics • Form 4 • Calculus Tangent to a Curve at a Point Differentiate the curve, find the gradient at P, then form the tangent line.
Mathematics • Form 4 • Measurement KCSE 2025 P1 Q17 — Speed, Distance & Time Two vehicles meet on a 160 km road — find the meeting time, distance and the car's return speed.
Mathematics • Form 4 • Measurement KCSE 2025 P1 Q18 — Volume & Surface Area A right pyramid sits on a 6 by 6 by 10 block — find its volume, then the surface area of one cut half.
Mathematics • Form 4 • Numbers KCSE 2025 Maths P1 Q2 — Ratio Change an hourly rate in the ratio 8:7 and find the pay for 10½ hours.
Mathematics • Form 4 • Geometry KCSE 2025 P1 Q19 — Coordinate Geometry Gradients, parallel and perpendicular line equations, and the intersection point P.
Mathematics • Form 4 • Algebra KCSE 2025 P1 Q20 — Matrices Solve a sand transport problem using the matrix method and calculate the transporter's profit.
Mathematics • Form 4 • Geometry KCSE 2025 P1 Q21 — Vectors Column vector PQ, solving for scalars k and h, then the magnitude of ka.
Mathematics • Form 4 • Geometry KCSE 2025 P1 Q22 — Trapezium Construction Construct trapezium ABCD, then work out the area lying outside the arc of centre A.
Mathematics • Form 4 • Statistics KCSE 2025 P1 Q23 — Mean & Median Build a frequency table and estimate the mean and median money spent on petrol.
Mathematics • Form 4 • Calculus KCSE 2025 P1 Q24 — Maximum Area Maximise the area of a plot of land using differentiation.
Mathematics • Form 4 • Algebra KCSE 2025 P1 Q4: Double Inequality Split a double inequality into two parts, solve each, then combine to get 1 < x ≤ 4.
Mathematics • Form 4 • Algebra KCSE 2025 P1 Q3: Indices Solve for x by rewriting every term as a power of 2, then comparing indices.
Mathematics • Form 4 • Measurement Area by Counting Squares Estimate the un-flooded area of a rectangular farm by counting grid squares.
Mathematics • Form 4 • Numbers KCSE 2025 P1 Q6 — Highest Common Factor Find the least number of families by using the HCF of 240 kg and 150 kg.
Mathematics • Form 4 • Measurement Cone from a Sector Roll a 550 cm² sector into a cone of radius 7 cm and find its height.
Mathematics • Form 4 • Algebra KCSE 2025 P1 Q7 — Algebraic Fractions Factorise the top and bottom, cancel the common factor, and simplify the algebraic fraction.
Mathematics • Form 4 • Measurement KCSE 2025 P1 Q9 — Slow Clock A clock loses 18 seconds an hour — what does it read on Saturday at 11:20 am?
Crisp, step-by-step Mathematics solutions for the next generation of scholars —
paired with short video walkthroughs.
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