KJSEA 2025 Maths Q26 — Simultaneous Equations
Solve two simultaneous equations by elimination to find the cost of a book and a pen.
KJSEA 2025 Maths Q1: Prime Numbers
Which set has prime numbers only? Test 2, 4, 5 and 9 with the two-factor rule.
KJSEA 2025 Maths Q10 — Cylinder Surface Area
Find the bucket surface touching the water: circular base plus curved wall, top left out.
KJSEA 2025 Q11 — Capacity
Find the capacity of a cuboid milk packet in litres.
KJSEA 2025 Q12 — Kelvin to Celsius
Choose the calculation that converts a Kelvin reading to degrees Celsius.
Q13 — Mobile Money Charges
Work out the balance left after sending and withdrawing money plus charges.
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?
KJSEA 2025 Maths Q15 — Quadrilaterals
Which quadrilateral has diagonals that bisect each other at 90 degrees? It's the rhombus.
Q16 Scale Drawing
Use a 1:100 scale to find how long a 3 m wall is on the drawing.
KJSEA 2025 Maths Q17 — Perpendicular Gradient
Find the gradient of a line perpendicular to 2y = x + 3 using the negative reciprocal rule.
KJSEA 2025 Q18 — Enlargement
Enlarge a 16 cm photograph by a scale factor of 2 to find its new length.
KJSEA 2025 Maths Q2 — HCF
Find the largest number of equal groups by taking the HCF of 120, 180 and 24.
KJSEA 2025 Maths Q20 — Probability
Find the probability of drawing a card marked E from 11 lettered cards.
KJSEA 2025 Maths Q21 — Place Value & Rounding
Subtraction, number words and rounding 6,784 to the nearest 100.
KJSEA 2025 Maths Q22 — Volume & Packing
Find a cube's volume, then count how many small cubes fit inside.
KJSEA 2025 Maths Q23 — Ratio
Sharing a Thanksgiving crowd in the ratio 5:7:3 to find men, women, and the difference.
KJSEA 2025 Maths Q24 — Work Rate
Solve a work-rate problem using man-hours to find how many extra days are needed.
Q25 — Recurring Decimal to Fraction
Turn 0.17 recurring into a fraction using the multiply-and-subtract trick.
KJSEA 2025 Maths Q27 — Matrices
Form two 2 by 3 matrices for weekly fruit buys, then add them to get each family's totals.
Q28 — Equation of a Line
Point-gradient form to find a line through (1, 4), then solve for the x-intercept.
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.
KJSEA 2025 Maths Q3 — Integers
Add a positive integer to a negative one to find a new temperature.
KJSEA 2025 Maths Q30 — Volume & Displacement
A ball sinks in a tin — find how much the water rises using displacement.
KJSEA 2025 Maths Q31: Pythagoras & Density
Find a leaning rod's length with Pythagoras, then work out density from mass and volume.
KJSEA 2025 Q32 — Longitude & Time
Use the longitude difference between two towns to work out the local time at town P.
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.
KJSEA 2025 Maths Q34 — Parallelogram Construction
Construct parallelogram ABCD, drop a perpendicular from D to AB, and measure DE.
Q35 — Linear Graphs
Complete the table for y = 50x and draw the milk-earnings line.
KJSEA 2025 Maths Q36 — Angle of Depression
Find the height of Dowdy's balcony using a 35° angle of depression and the tangent ratio.
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°.
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.
KJSEA 2025 Maths Q39 — Mean & Median
Tally 20 test marks into a frequency table, then calculate the mean and median.
KJSEA 2025 Maths Q4 — Fractions of Time
Which calculation gives the extra time used planting 70 seedlings? A clear fractions-of-time walkthrough.
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.
KJSEA 2025 Maths Q5 — Indices
Use the laws of indices to solve 2^X × 2^3 = 32 and find X.
KJSEA 2025 Q6 — Algebraic Expressions
Write an algebraic expression for the number of sheep on a 26-animal farm.
KJSEA 2025 Maths Q7 — Inequalities
Turn 'at least 30 but fewer than 50 learners' into a compound inequality and graph it.
KJSEA 2025 Maths Q8 — Order of a Matrix
Count the rows and columns to state a matrix's order — worked step by step.
KCSE 2025 P1 Q7 — Algebraic Fractions
Factorise the top and bottom, cancel the common factor, and simplify the algebraic fraction.
KCSE 2025 Maths P1 Q1 — Order of Operations
Use BODMAS and fraction skills to evaluate a square-root expression by hand.
Density: Length of a Brass Plate
Use density, mass and thickness to find the side length of a thin square brass plate.
Form 3 P1 Q1 — BODMAS Evaluation
Use BODMAS to evaluate a signed-number fraction and get -2.
Alliance F3 P1 Q11 — Algebraic Fractions
Add two algebraic fractions and simplify by finding the common denominator.
Q12 Time — A Slow Clock
A clock loses 15 seconds every hour — find what it shows after 60 hours.
Diagonal of a Cube Face
Use the volume to find the edge, then Pythagoras for the face diagonal.
Form 3 P1 Q14 — Linear Inequalities
Split a compound inequality into two parts, solve each, and graph the solution on a number line.
Vectors: Magnitude of AB
Find AB from OA and OB, then use Pythagoras to get its length to one decimal place.
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.
Alliance F3 P1 Q18 — Tiles & Profit
Count the tiles for a floor, cost 15 rooms, then price each carton for a 12.5% profit.
Form 3 P1 Q19 — Bearings & Scale Drawing
Bearings, right-angle trig and Pythagoras to find PS, a bearing and the ranch area.
Form 3 P1 Q2 — Bells & LCM
Three bells and their LCM tell you exactly when they last chimed together.
Coordinate Geometry: Lines L, P & Q
Find the equations of three related lines and the point where the perpendicular meets the parallel line.
Form 3 P1 Q21 — Combined Transformations
Enlarge, reflect and rotate a square, then name the single transformation that links the two images.
Cone with a Conical Hole
Use similar cones to find the hole radius, volume removed and total remaining surface area.
Speed–Time Graph (Cheetah)
Read a cheetah's speed–time graph to find its top speed, accelerations and average speed.
Q24 — Commission & Percentages
Find monthly earnings from commission plus salary, then reverse the process to get total sales and units sold.
Form 3 P1 Q3 — Simultaneous Equations
Turn a hiring word problem into two equations and solve by elimination.
Currency Exchange: Buying vs Selling Rates
Convert $100,000 to shillings then to pounds using the correct bank rates.
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.
Alliance F3 P1 Q6 — Laws of Indices
Simplify a fractional-power expression using the laws of indices — step by step to 75.
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.
Cylinder Surface Area: Find the Diameter
Radius equals height and total surface area is 154 cm² — find the diameter to 2 d.p.
Triangle Construction (Q10)
Construct triangle ABC and measure angle ABC, confirmed by the sine rule.
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.
Histogram Frequencies (KCSE 2025 P1 Q12)
Find the two missing frequencies from histogram bar heights using frequency density.
Reflection: Finding the Mirror Line
Use the perpendicular bisector to construct the mirror line and finish the reflected triangle.
Net of a Prism
Unfold a trapezoidal prism into four rectangles and two trapezium ends to draw its labelled net.
KCSE 2025 Maths P1 Q15 — Trigonometry
Use a triangle's area to unlock a hidden angle, then find BC with tan.
Tangent to a Curve at a Point
Differentiate the curve, find the gradient at P, then form the tangent line.
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.
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.
KCSE 2025 P1 Q19 — Coordinate Geometry
Gradients, parallel and perpendicular line equations, and the intersection point P.
KCSE 2025 Maths P1 Q2 — Ratio
Change an hourly rate in the ratio 8:7 and find the pay for 10½ hours.
KCSE 2025 P1 Q20 — Matrices
Solve a sand transport problem using the matrix method and calculate the transporter's profit.
KCSE 2025 P1 Q21 — Vectors
Column vector PQ, solving for scalars k and h, then the magnitude of ka.
KCSE 2025 P1 Q22 — Trapezium Construction
Construct trapezium ABCD, then work out the area lying outside the arc of centre A.
KCSE 2025 P1 Q23 — Mean & Median
Build a frequency table and estimate the mean and median money spent on petrol.
KCSE 2025 P1 Q3: Indices
Solve for x by rewriting every term as a power of 2, then comparing indices.
KCSE 2025 P1 Q24 — Maximum Area
Maximise the area of a plot of land using differentiation.
KCSE 2025 P1 Q6 — Highest Common Factor
Find the least number of families by using the HCF of 240 kg and 150 kg.
Area by Counting Squares
Estimate the un-flooded area of a rectangular farm by counting grid squares.
KCSE 2025 P1 Q4: Double Inequality
Split a double inequality into two parts, solve each, then combine to get 1 < x ≤ 4.
