<?xml version="1.0" encoding="UTF-8"?><rss version="2.0"><channel><title>Tuchopini — Step-by-Step Lessons</title><description>Written, step-by-step solutions to exam questions, paired with video walkthroughs.</description><link>https://tuchopini.co.ke/</link><language>en</language><item><title>KJSEA 2025 Maths Q26 — Simultaneous Equations (Cost of Books and Pens)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q26-simultaneous-equations/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q26-simultaneous-equations/</guid><description>KJSEA 2025 Grade 9 Maths Q26 worked solution: form and solve simultaneous equations by elimination to find the cost of one book (60) and one pen (25).</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Simultaneous Equations</category></item><item><title>KJSEA 2025 Maths Q1 — Prime Numbers (Grade 9)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q1-prime-numbers/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q1-prime-numbers/</guid><description>KJSEA 2025 Grade 9 Maths Q1 solved: test cards 2, 4, 5, 9 for prime numbers using the two-factor rule and find the set with primes only — answer 2 and 5.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Prime Numbers</category></item><item><title>KJSEA 2025 Maths Q10 — Surface Area of a Cylinder (Water Contact)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q10-surface-area-of-a-cylinder/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q10-surface-area-of-a-cylinder/</guid><description>KJSEA 2025 Grade 9 Maths Q10 worked solution: find the surface area of an open cylindrical bucket in contact with water — base plus curved wall — answer 6,534.51 cm².</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Surface Area of a Cylinder</category></item><item><title>KJSEA 2025 Maths Q11 — Capacity of a Cuboid Milk Packet</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q11-capacity/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q11-capacity/</guid><description>KJSEA 2025 Grade 9 Maths Q11: find the capacity of a cuboid milk packet in litres by working out its volume and converting cm cubed to litres. Answer 0.51 L.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Capacity</category></item><item><title>KJSEA 2025 Maths Q12 — Converting Kelvin to Degrees Celsius</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q12-kelvin-to-celsius/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q12-kelvin-to-celsius/</guid><description>KJSEA 2025 Grade 9 Maths Q12: convert a Kelvin temperature to degrees Celsius by subtracting 273. See why the correct calculation is option D.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Kelvin to Celsius</category></item><item><title>KJSEA 2025 Maths Q13 — Mobile Money Charges (Grade 9)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q13-mobile-money-charges/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q13-mobile-money-charges/</guid><description>KJSEA 2025 Grade 9 Maths Q13 worked solution: subtract sent, withdrawn and transaction charges from a mobile money balance to get the amount remaining, 1,642 shillings.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Mobile Money Charges</category></item><item><title>KJSEA 2025 Maths Q14 — Percentage Error in an Estimate</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q14-percentage-error/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q14-percentage-error/</guid><description>KJSEA 2025 Grade 9 Maths Q14 solved: find the percentage error when an estimated window height of 1.5 m differs from the actual 1.2 m — answer 0.3/1.2 × 100.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Percentage Error</category></item><item><title>KJSEA 2025 Maths Q15 — Naming a Quadrilateral from its Properties (Rhombus)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q15-quadrilaterals/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q15-quadrilaterals/</guid><description>KJSEA 2025 Grade 9 Maths Q15 solved: identify the quadrilateral whose diagonals bisect at 90 degrees with equal sides. The answer is a rhombus (D).</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Quadrilaterals</category></item><item><title>KJSEA 2025 Maths Q16 — Scale Drawing (1:100)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q16-scale-drawing/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q16-scale-drawing/</guid><description>KJSEA 2025 Grade 9 Maths Q16 worked solution: a wall is 3 m long, scale 1:100. Convert to cm and divide to find the drawing length of 3 cm.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Scale Drawing</category></item><item><title>KJSEA 2025 Maths Q17 — Gradient of a Perpendicular Line</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q17-perpendicular-gradient/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q17-perpendicular-gradient/</guid><description>KJSEA 2025 Grade 9 Maths Q17 worked solution: rewrite 2y = x + 3 in y = mx + c form and use the negative reciprocal to get the perpendicular gradient of -2.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Perpendicular Gradient</category></item><item><title>KJSEA 2025 Maths Q18 — Enlargement of a Photograph (Scale Factor)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q18-enlargement/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q18-enlargement/</guid><description>KJSEA 2025 Grade 9 Maths Q18 worked solution: enlarge a 16 cm photograph by scale factor 2 to find the new length of 32 cm, explained step by step.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Enlargement</category></item><item><title>KJSEA 2025 Maths Q2 — Highest Common Factor (HCF) of 120, 180 and 24</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q2-hcf/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q2-hcf/</guid><description>KJSEA 2025 Grade 9 Maths Q2 worked solution: use the highest common factor (HCF) of 120, 180 and 24 to find the largest number of equal groups — the answer is 12.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>HCF</category></item><item><title>KJSEA 2025 Maths Q20 — Probability of Picking the Letter E</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q20-probability/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q20-probability/</guid><description>KJSEA 2025 Grade 9 Maths Q20: letters written on 11 cards, find the probability of picking the letter E. Learn the favourable-over-total method to get 3/11.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Probability</category></item><item><title>KJSEA 2025 Maths Q21 — Place Value &amp; Rounding (10,000 m Race)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q21-place-value-and-rounding/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q21-place-value-and-rounding/</guid><description>KJSEA 2025 Grade 9 Maths Q21: find how far Anita walked, write 6,784 in words, and round it to the nearest 100 — full worked solution.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Place Value &amp; Rounding</category></item><item><title>KJSEA 2025 Maths Q22 — Volume of a Cube &amp; Packing Small Cubes</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q22-volume-and-packing/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q22-volume-and-packing/</guid><description>KJSEA 2025 Grade 9 Maths Q22: find the volume of a 2.4 m cube container, then work out how many 50 cm cubes pack inside. Full worked answer: 13.824 m3 and 64 cubes.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Volume &amp; Packing</category></item><item><title>KJSEA 2025 Maths Q23 — Ratio of Men to Women to Children</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q23-ratio/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q23-ratio/</guid><description>KJSEA 2025 Grade 9 Maths Q23 solved: use the ratio 5:7:3 and 60 children to find the number of men, women, and how many more women than men.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Ratio</category></item><item><title>KJSEA 2025 Maths Q24 — Proportion (Work Rate) with Man-Hours</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q24-proportion-work-rate/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q24-proportion-work-rate/</guid><description>KJSEA 2025 Grade 9 Maths Q24 solved: use man-hours to find how many more days 3 men working 8 hours a day take to pack the same flour. Answer: 3 more days.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Proportion (Work Rate)</category></item><item><title>KJSEA 2025 Maths Q25 — Converting a Recurring Decimal to a Fraction</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q25-recurring-decimal/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q25-recurring-decimal/</guid><description>KJSEA 2025 Grade 9 Maths Q25: convert the recurring decimal 0.17 (with the 7 repeating) into a simplified fraction and get 8/45. Full worked steps.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Recurring Decimal</category></item><item><title>KJSEA 2025 Maths Q27 — Matrices: Forming and Adding Matrices</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q27-matrices/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q27-matrices/</guid><description>KJSEA 2025 Grade 9 Maths Q27 worked solution: form 2 by 3 matrices for two families&apos; fruit purchases and add them to find each family&apos;s totals.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Matrices</category></item><item><title>KJSEA 2025 Maths Q28 — Equation of a Line and x-Intercept</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q28-equation-of-a-line/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q28-equation-of-a-line/</guid><description>KJSEA 2025 Grade 9 Maths Q28: find the equation of a line through (1, 4) with gradient 1/2, then work out its x-intercept, step by step.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Equation of a Line</category></item><item><title>KJSEA 2025 Maths Q29 — Total Surface Area of a Cone</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q29-surface-area-of-a-cone/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q29-surface-area-of-a-cone/</guid><description>KJSEA 2025 Grade 9 Maths Q29: find the total surface area of a cone with slant height 20 cm and base radius 4.2 cm. Full worked steps, answer 319.44 cm².</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Surface Area of a Cone</category></item><item><title>KJSEA 2025 Maths Q3 — Integers (Temperature Increase)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q3-integers/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q3-integers/</guid><description>KJSEA 2025 Grade 9 Maths Q3 solved: a deep freezer at -8 degrees C rises by 15 degrees. Add integers on a number line to get the new temperature, +7 C.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Integers</category></item><item><title>KJSEA 2025 Maths Q30 — Volume &amp; Displacement (Rise in Water Level)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q30-volume-and-displacement/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q30-volume-and-displacement/</guid><description>KJSEA 2025 Grade 9 Maths Q30: a sphere is immersed in a cylindrical tin. Learn how displacement gives a 1.4 cm rise in the water level, step by step.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Volume &amp; Displacement</category></item><item><title>KJSEA 2025 Maths Q31 — Pythagoras &amp; Density</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q31-pythagoras-and-density/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q31-pythagoras-and-density/</guid><description>KJSEA 2025 Grade 9 Maths Q31 fully worked: use Pythagoras to find a leaning rod&apos;s length (6 m) and calculate density as mass over volume (4 g/cm³).</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Pythagoras &amp; Density</category></item><item><title>KJSEA 2025 Maths Q32 — Longitude and Time</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q32-longitude-and-time/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q32-longitude-and-time/</guid><description>KJSEA 2025 Grade 9 Maths Q32 worked solution: find the local time at a town using longitude difference, converting 1 degree to 4 minutes to get 10:00 a.m.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Longitude &amp; Time</category></item><item><title>KJSEA 2025 Maths Q33 — Import Duty, Excise Duty &amp; VAT</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q33-import-duty-excise-and-vat/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q33-import-duty-excise-and-vat/</guid><description>KJSEA 2025 Grade 9 Maths Q33 worked solution: find import duty, excise duty and VAT on a printing machine with a customs value of Ksh 1.2 million.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Import Duty, Excise &amp; VAT</category></item><item><title>KJSEA 2025 Maths Q34 — Geometric Construction of a Parallelogram</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q34-geometric-construction/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q34-geometric-construction/</guid><description>KJSEA 2025 Grade 9 Maths Q34: construct parallelogram ABCD with a 45 degree angle using ruler and compasses, drop a perpendicular, and find DE is about 2.8 cm.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Geometric Construction</category></item><item><title>KJSEA 2025 Maths Q35 — Linear Graphs (Milk Sales y = 50x)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q35-linear-graphs/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q35-linear-graphs/</guid><description>KJSEA 2025 Grade 9 Maths Q35 walkthrough: complete the table for y = 50x and draw the straight-line graph of a farmer&apos;s milk earnings through the origin.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Linear Graphs</category></item><item><title>KJSEA 2025 Maths Q36 — Angle of Depression (Height of a Building)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q36-angle-of-depression/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q36-angle-of-depression/</guid><description>KJSEA 2025 Grade 9 Maths Q36 solved: use the angle of depression and tangent ratio to find the height of a balcony above the ground, giving about 32.9 m.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Angle of Depression</category></item><item><title>KJSEA 2025 Maths Q37 — Bearings and Scale Drawing</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q37-bearings/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q37-bearings/</guid><description>KJSEA 2025 Grade 9 Maths Q37: use a scale drawing with bearings 120° and 210° to find the distance and bearing of C from A — answer about 86 m on 174°.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Bearings</category></item><item><title>KJSEA 2025 Maths Q38 — Net and Surface Area of a Cuboid</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q38-net-and-surface-area/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q38-net-and-surface-area/</guid><description>KJSEA 2025 Grade 9 Maths Q38: draw the net of a 5 by 3 by 2 cm cuboid and find its total surface area, which works out to 62 square centimetres.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Net &amp; Surface Area</category></item><item><title>KJSEA 2025 Maths Q39 — Statistics: Frequency Table, Mean &amp; Median</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q39-statistics/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q39-statistics/</guid><description>KJSEA 2025 Grade 9 Maths Q39: build a frequency table for 20 test marks, then find the mean (19.45) and median (18.5). Clear step-by-step statistics revision.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Statistics</category></item><item><title>KJSEA 2025 Maths Q4 — Fractions of Time (Extra Time Calculation)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q4-fractions-of-time/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q4-fractions-of-time/</guid><description>KJSEA 2025 Grade 9 Maths Q4 worked solution: find the calculation for the extra time Kamal used planting 70 seedlings using fractions of an hour. Answer explained.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Fractions of Time</category></item><item><title>KJSEA 2025 Maths Q40 — Probability Space (Coin and Die)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q40-probability-space/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q40-probability-space/</guid><description>KJSEA 2025 Grade 9 Maths Q40: list the probability space for tossing a coin and a die, then find P(head and four). Full worked solution — answer 1/12.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Probability Space</category></item><item><title>KJSEA 2025 Maths Q5 — Indices: Solving 2^X × 2^3 = 32</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q5-indices/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q5-indices/</guid><description>KJSEA 2025 Grade 9 Maths Q5 worked solution on indices: use the laws of indices to solve 2^X times 2^3 = 32 and find X = 2 (answer C).</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Indices</category></item><item><title>KJSEA 2025 Maths Q6 — Algebraic Expressions (Number of Sheep)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q6-algebraic-expressions/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q6-algebraic-expressions/</guid><description>KJSEA 2025 Grade 9 Maths Q6 worked: form an expression for the number of sheep on a farm of 26 animals using X donkeys. Answer: 26 - 3X (option A).</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Algebraic Expressions</category></item><item><title>KJSEA 2025 Maths Q7 — Inequalities (Number of Learners to Transport)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q7-inequalities/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q7-inequalities/</guid><description>KJSEA 2025 Grade 9 Maths Q7 worked out: write the compound inequality for at least 30 but fewer than 50 learners and show it on a number line.</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Inequalities</category></item><item><title>KJSEA 2025 Maths Q8 — Order of a Matrix (Grade 9)</title><link>https://tuchopini.co.ke/lessons/kjsea-2025-maths-q8-order-of-a-matrix/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kjsea-2025-maths-q8-order-of-a-matrix/</guid><description>KJSEA 2025 Grade 9 Maths Q8: learn how to find the order of a matrix by counting rows then columns to get the answer 2 by 5 (option D).</description><pubDate>Fri, 10 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KJSEA 2025</category><category>Order of a Matrix</category></item><item><title>KCSE 2025 Maths P1 Q7 — Simplify an Algebraic Fraction</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q7-algebraic-fractions/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q7-algebraic-fractions/</guid><description>KCSE 2025 Maths Paper 1 Q7 fully worked: factorise a difference of two squares and a perfect square trinomial, cancel, and simplify to (x-2y)/(x+2y).</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Algebraic Fractions</category></item><item><title>KCSE 2025 Maths P1 Q1 — Order of Operations &amp; Surds</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q1-order-of-operations-and-surds/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q1-order-of-operations-and-surds/</guid><description>KCSE 2025 Mathematics Paper 1 Question 1: evaluate a surd expression using BODMAS and fraction division without a calculator. Full worked answer is 5/6.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Order of Operations &amp; Surds</category></item><item><title>Alliance Form 3 P1 Q10 — Density, Mass &amp; Volume of a Square Brass Plate</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q10-density-mass-and-volume/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q10-density-mass-and-volume/</guid><description>Alliance Form 3 KCSE Maths P1 Q10: find the length of a square brass plate from its mass, thickness and density. Full unit conversions and worked solution giving 25 cm.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Density, Mass &amp; Volume</category></item><item><title>Alliance Form 3 P1 Q1 — Order of Operations (BODMAS)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q1-order-of-operations-bodmas/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q1-order-of-operations-bodmas/</guid><description>Evaluate a fraction of signed numbers without a calculator using BODMAS in Alliance Form 3 Maths Paper 1 Q1. Simplify top and bottom, then divide to get -2.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Order of Operations (BODMAS)</category></item><item><title>Alliance Form 3 P1 Q11 — Simplifying Algebraic Fractions</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q11-algebraic-fractions/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q11-algebraic-fractions/</guid><description>Alliance Form 3 KCSE Maths Paper 1 Q11: add and simplify two algebraic fractions using a common denominator to get (A squared + B squared) over 2(A squared - B squared).</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Algebraic Fractions</category></item><item><title>Alliance Form 3 P1 Q12 — Time: A Slow Clock (KCSE Maths)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q12-time-a-slow-clock/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q12-time-a-slow-clock/</guid><description>Alliance Form 3 P1 Q12: a clock loses 15 seconds an hour. Learn to find elapsed hours, total time lost, and the clock reading — final answer 18:45.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Time — A Slow Clock</category></item><item><title>Alliance Form 3 P1 Q13 — Diagonal of a Cube Face</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q13-diagonal-of-a-cube/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q13-diagonal-of-a-cube/</guid><description>Alliance Form 3 P1 Q13 (KCSE Maths): find the face diagonal of a cube whose volume is 1,728 cubic centimetres using cube roots and Pythagoras — answer 16.97 cm.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Diagonal of a Cube</category></item><item><title>Alliance Form 3 P1 Q14 — Solving Compound Linear Inequalities</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q14-linear-inequalities/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q14-linear-inequalities/</guid><description>Alliance Form 3 Paper 1 Q14: solve the compound inequality x-5 ≤ 3x-8 &lt; 2x-3, flip the sign when dividing by a negative, and show the answer on a number line.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Linear Inequalities</category></item><item><title>Alliance Form 3 P1 Q15 — Vectors: Magnitude of AB</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q15-vectors-magnitude/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q15-vectors-magnitude/</guid><description>Alliance Form 3 KCSE Maths P1 Q15: find vector AB from position vectors OA and OB, then use Pythagoras to get its magnitude, the square root of 26 (5.1).</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Vectors (Magnitude)</category></item><item><title>Alliance Form 3 P1 Q17 — Ratio, Trips &amp; Profit (Farmer&apos;s Maize)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q17-ratio-and-profit/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q17-ratio-and-profit/</guid><description>Alliance Form 3 KCSE Maths P1 Q17 worked solution: use the drying ratio 15:16 to find mass lost, count lorry trips, and set a selling price for 26% profit.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Ratio &amp; Profit</category></item><item><title>Alliance Form 3 P1 Q18 — Area, Tiles &amp; Profit</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q18-area-tiles-and-profit/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q18-area-tiles-and-profit/</guid><description>Alliance Form 3 KCSE Maths P1 Q18: work out how many 30 cm tiles cover a floor, the cost for 15 rooms, and the carton selling price for a 12.5% profit.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Area, Tiles &amp; Profit</category></item><item><title>Alliance Form 3 P1 Q19 — Bearings &amp; Scale Drawing</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q19-bearings-and-scale-drawing/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q19-bearings-and-scale-drawing/</guid><description>Alliance Form 3 KCSE Maths P1 Q19 worked out: use bearings, right-angle trig and Pythagoras to find distance PS, the bearing of P from S, and the ranch area.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Bearings &amp; Scale Drawing</category></item><item><title>Alliance Form 3 P1 Q2 — LCM &amp; Time (Ringing Bells)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q2-lcm-and-time-bells/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q2-lcm-and-time-bells/</guid><description>Alliance Form 3 Maths Paper 1 Q2: three bells ring every 9, 15 and 21 minutes. Use the LCM to find when they last rang together — answer 5:45 p.m.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>LCM &amp; Time (Bells)</category></item><item><title>Alliance Form 3 P1 Q20 — Coordinate Geometry: Equations of Lines</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q20-coordinate-geometry/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q20-coordinate-geometry/</guid><description>Alliance Form 3 KCSE Maths Paper 1 Q20 worked out: find equations of a line, its perpendicular and parallel lines, and where they intersect at (2, 5).</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Coordinate Geometry</category></item><item><title>Alliance Form 3 P1 Q21 — Transformations on a Grid (Enlargement, Reflection, Rotation)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q21-transformations/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q21-transformations/</guid><description>Alliance Form 3 KCSE Maths P1 Q21: enlarge scale factor 3, reflect in the y-axis, rotate 90 degrees, then find the single mapping is a reflection in y = -x.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Transformations</category></item><item><title>Alliance Form 3 P1 Q22 — Cone with a Conical Hole</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q22-cone-with-a-conical-hole/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q22-cone-with-a-conical-hole/</guid><description>Alliance Form 3 KCSE Maths P1 Q22: find the hole radius, volume removed, slant height and remaining surface area of a cone with a similar conical hole.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Cone with a Conical Hole</category></item><item><title>Alliance Form 3 P1 Q23 — Speed–Time Graph of a Cheetah</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q23-speed-time-graph/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q23-speed-time-graph/</guid><description>Alliance Form 3 KCSE Maths P1 Q23: use area under a speed–time graph to find maximum speed, accelerations and average speed for a cheetah covering 825 m.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Speed–Time Graph</category></item><item><title>Alliance Form 3 P1 Q24 — Commission &amp; Percentages (KCSE Maths)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q24-commission-and-percentages/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q24-commission-and-percentages/</guid><description>Alliance Form 3 Paper 1 Q24 worked solution: compute a saleswoman&apos;s commission and salary, then work backwards to find total sales and number of handbags sold.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Commission &amp; Percentages</category></item><item><title>Alliance Form 3 P1 Q3 — Simultaneous Equations (Technicians &amp; Artisans)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q3-simultaneous-equations/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q3-simultaneous-equations/</guid><description>Alliance Form 3 KCSE Maths Paper 1 Q3: form and solve simultaneous equations from a word problem to find hiring costs. Answer: 11,500 shillings.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Simultaneous Equations</category></item><item><title>Alliance Form 3 P1 Q4 — Currency Exchange (Buying vs Selling Rates)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q4-currency-exchange/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q4-currency-exchange/</guid><description>Alliance Form 3 KCSE Maths P1 Q4 worked solution: convert dollars to shillings then to pounds using the bank&apos;s buying and selling rates. Answer: £63,172.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Currency Exchange</category></item><item><title>Alliance Form 3 P1 Q5 — Angles of a Regular Polygon</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q5-angles-of-a-regular-polygon/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q5-angles-of-a-regular-polygon/</guid><description>Alliance Form 3 KCSE Maths P1 Q5: a regular polygon has interior angle 3x and exterior angle x-20. Learn to find the number of sides — the answer is 12.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Angles of a Regular Polygon</category></item><item><title>Alliance Form 3 P1 Q6 — Laws of Indices (Simplify with Fractional Powers)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q6-laws-of-indices/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q6-laws-of-indices/</guid><description>Alliance Form 3 KCSE Maths P1 Q6: simplify an index expression with fractional powers using the power-of-a-power and division rules to get 75.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Laws of Indices</category></item><item><title>Alliance Form 3 P1 Q8 — Trigonometry: Complementary Angles</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q8-trigonometry-complementary-angles/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q8-trigonometry-complementary-angles/</guid><description>Alliance Form 3 Paper 1 Q8 worked solution: use the complementary angle rule sin A = cos(90 - A) to solve sin(x+60)=cos 2x and find tan(x+60).</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Trigonometry (Complementary Angles)</category></item><item><title>Alliance Form 3 P1 Q9 — Surface Area of a Cylinder (Find the Diameter)</title><link>https://tuchopini.co.ke/lessons/alliance-form3-p1-q9-surface-area-of-a-cylinder/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/alliance-form3-p1-q9-surface-area-of-a-cylinder/</guid><description>Alliance Form 3 KCSE Maths P1 Q9: a closed cylinder with radius equal to height has total surface area 154 cm². Learn to find the diameter, 7.00 cm.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE (Form 3)</category><category>Surface Area of a Cylinder</category></item><item><title>KCSE 2025 Maths P1 Q10 — Construct Triangle ABC and Measure Angle ABC</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q10-triangle-construction/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q10-triangle-construction/</guid><description>KCSE 2025 Maths Paper 1 Q10: construct triangle ABC with AB 5 cm, angle A 120 degrees, BC 10 cm, then measure angle ABC as about 34 degrees.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Triangle Construction</category></item><item><title>KCSE 2025 Maths P1 Q11 — Profit and Loss</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q11-profit-and-loss/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q11-profit-and-loss/</guid><description>KCSE 2025 Mathematics Paper 1 Q11 solved: use profit and loss equations to find the cost price of an item. Clear step-by-step working, answer Ksh 2,500.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Profit &amp; Loss</category></item><item><title>KCSE 2025 Maths P1 Q12 — Histogram Frequencies from Bar Heights</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q12-histogram-frequencies/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q12-histogram-frequencies/</guid><description>KCSE 2025 Maths Paper 1 Q12: use frequency density and class width to find missing histogram frequencies. Learn why class boundaries give widths of 5 and 10.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Histogram Frequencies</category></item><item><title>KCSE 2025 Maths P1 Q13 — Reflection and the Mirror Line</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q13-reflection/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q13-reflection/</guid><description>KCSE 2025 Maths Paper 1 Q13: find the mirror line of a reflection as the perpendicular bisector of a point and its image, then complete the image triangle.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Reflection</category></item><item><title>KCSE 2025 Maths P1 Q14 — Net of a Trapezoidal Prism</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q14-net-of-a-prism/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q14-net-of-a-prism/</guid><description>KCSE 2025 Maths Paper 1 Q14: draw the labelled net of a trapezium-cross-section prism. Learn to unfold four rectangles and two trapezium ends step by step.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Net of a Prism</category></item><item><title>KCSE 2025 Maths P1 Q15 — Trigonometry: Finding a Side Using Area and Tangent</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q15-trigonometry/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q15-trigonometry/</guid><description>KCSE 2025 Mathematics Paper 1 Question 15 solved: use the area of triangle ABD to find angle A, then apply the tangent ratio to get BC = 4.62 cm.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Trigonometry</category></item><item><title>KCSE 2025 Maths P1 Q16 — Tangent to a Curve</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q16-tangent-to-a-curve/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q16-tangent-to-a-curve/</guid><description>KCSE 2025 Maths Paper 1 Q16: find the tangent to y = 3x^2 - 4x at P(1, -1) using differentiation, ending with the line 2x - y = 3.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Tangent to a Curve</category></item><item><title>KCSE 2025 Maths P1 Q17 — Speed, Distance &amp; Time (Meeting Point &amp; Average Speed)</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q17-speed-distance-and-time/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q17-speed-distance-and-time/</guid><description>KCSE 2025 Maths Paper 1 Q17 fully solved: closing speed, meeting time, distance to C, and the car&apos;s average speed from C to A of 108 km/h.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Speed, Distance &amp; Time</category></item><item><title>KCSE 2025 Maths P1 Q18 — Volume &amp; Surface Area of a Pyramid on a Block</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q18-volume-and-surface-area/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q18-volume-and-surface-area/</guid><description>KCSE 2025 Mathematics Paper 1 Q18: find the volume of a pyramid mounted on a square block and the surface area of one half after cutting along the plane of symmetry.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Volume &amp; Surface Area</category></item><item><title>KCSE 2025 Maths P1 Q19 — Coordinate Geometry (Parallel &amp; Perpendicular Lines)</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q19-coordinate-geometry/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q19-coordinate-geometry/</guid><description>KCSE 2025 Maths Paper 1 Q19 worked out: find gradients, equations of parallel line L2 and perpendicular line L3, then the intersection point P(-1, 2).</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Coordinate Geometry</category></item><item><title>KCSE 2025 Maths P1 Q2 — Ratio: Changing an Hourly Rate</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q2-ratio/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q2-ratio/</guid><description>KCSE 2025 Maths Paper 1 Q2 solved: use the ratio 8:7 to change Baraka&apos;s hourly pay, then find his earnings for 10 and a half hours — final answer Ksh 2,520.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Ratio</category></item><item><title>KCSE 2025 Maths P1 Q20 — Matrices: Transport, Cost and Profit</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q20-matrices/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q20-matrices/</guid><description>KCSE 2025 Maths Paper 1 Q20: form two equations, solve them with the matrix method to get x = 9 and y = 5, then find a profit of Ksh 19,500.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Matrices</category></item><item><title>KCSE 2025 Maths P1 Q21 — Vectors, Column Vectors &amp; Magnitude</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q21-vectors/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q21-vectors/</guid><description>KCSE 2025 Maths Paper 1 Q21 solved: find column vector PQ, solve for scalars k and h, and get the magnitude of ka as 2 root 10, about 6.32.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Vectors</category></item><item><title>KCSE 2025 Maths P1 Q22 — Trapezium Construction and Area Outside an Arc</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q22-trapezium-construction/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q22-trapezium-construction/</guid><description>KCSE 2025 Maths Paper 1 Q22: construct trapezium ABCD with ruler and compasses, measure DC and DE, draw an arc, then find the area outside it — 22.1 cm².</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Trapezium Construction</category></item><item><title>KCSE 2025 Maths P1 Q23 — Statistics: Mean &amp; Median from Grouped Data</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q23-statistics-mean-and-median/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q23-statistics-mean-and-median/</guid><description>KCSE 2025 Maths Paper 1 Q23: group 40 riders&apos; petrol data into classes, then estimate the mean (Ksh 436) and median (Ksh 428) amount spent on fuel.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Statistics (Mean &amp; Median)</category></item><item><title>KCSE 2025 Maths P1 Q3 — Solving an Indices Equation</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q3-indices/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q3-indices/</guid><description>KCSE 2025 Mathematics Paper 1 Question 3 worked out: solve an indices equation by writing 4, 8 and 32 as powers of 2 to get x = 3/4.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Indices</category></item><item><title>KCSE 2025 Maths P1 Q24 — Differentiation (Maximum Area)</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q24-differentiation-max-area/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q24-differentiation-max-area/</guid><description>KCSE 2025 Maths Paper 1 Q24: use differentiation to find the plot dimensions that maximise area, giving a 10 m by 20 m rectangle and 3600 square metres.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Differentiation (Max Area)</category></item><item><title>KCSE 2025 Maths P1 Q6 — Highest Common Factor (Least Number of Families)</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q6-highest-common-factor/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q6-highest-common-factor/</guid><description>KCSE 2025 Maths Paper 1 Q6 fully solved: use the HCF of 240 and 150 to find the largest equal share and the least possible number of needy families — the answer is 13.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Highest Common Factor</category></item><item><title>KCSE 2025 Maths P1 Q5 — Area by Counting Squares</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q5-area-by-counting-squares/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q5-area-by-counting-squares/</guid><description>KCSE 2025 Maths Paper 1 Q5: estimate the un-flooded area of a 210 m by 120 m farm on a 1 cm grid by counting squares. Answer about 15,300 square metres.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Area by Counting Squares</category></item><item><title>KCSE 2025 Maths P1 Q4 — Solving a Double Inequality</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q4-inequalities/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q4-inequalities/</guid><description>KCSE 2025 Mathematics Paper 1 Question 4 worked solution: split and solve the double inequality on (5-2x)/3 to get the combined answer 1 &lt; x ≤ 4.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Inequalities</category></item><item><title>KCSE 2025 Maths P1 Q9 — Clock That Loses Time</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q9-clock-time-lost/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q9-clock-time-lost/</guid><description>KCSE 2025 Maths Paper 1 Q9: a clock loses 18 seconds every hour. Learn to find the total time lost and the wrong time it reads on Saturday — answer 10:43 am.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Clock (Time Lost)</category></item><item><title>KCSE 2025 Maths P1 Q8 — Cone from a Sector</title><link>https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q8-cone-from-a-sector/</link><guid isPermaLink="true">https://tuchopini.co.ke/lessons/kcse-2025-maths-p1-q8-cone-from-a-sector/</guid><description>KCSE 2025 Maths Paper 1 Q8 fully worked: a 550 cm² sector is rolled into an open cone of radius 7 cm. Find the slant height, then use Pythagoras to get height 24 cm.</description><pubDate>Thu, 09 Jul 2026 00:00:00 GMT</pubDate><category>Mathematics</category><category>KCSE 2025</category><category>Cone from a Sector</category></item></channel></rss>