Updated: 19 October 2026
This mixed practice check is intended for Form 4 revision. It combines short problems that require careful selection of a method. These are original practice questions, not extracts from a completed KCSE paper and not predictions of the current examination.
On this page: original practice, explained answers and 20 short FAQs. Complete the tasks before reading the answers.
Make the method visible
Write the relationship or equation before substituting values. Keep exact fractions where useful and round only when the task requires it. The working should allow another learner to understand how the answer was obtained.
Separate a knowledge gap from a slip
If a method is sound but arithmetic fails, practise checking. If no method is available, revise the underlying concept. Do not treat all lost marks as evidence that the whole topic must be relearned.
Choose the next archived paper
Use the subject-and-year directory to select a real past paper after this check. Keep its question paper and marking scheme together. Avoid renaming this short mixed exercise as a full official paper.
Practice questions and explained answers
1. Simplify (3/4 − 1/6) ÷ 7/8.
Show suggested answer
3/4 − 1/6 = 9/12 − 2/12 = 7/12. Then 7/12 × 8/7 = 2/3.
2. Solve 2x² − 5x − 3 = 0.
Show suggested answer
Factor: (2x + 1)(x − 3) = 0. Therefore x = −1/2 or x = 3.
3. A price rises from KSh 800 to KSh 920. Find the percentage increase.
Show suggested answer
Increase = 120. Percentage increase = 120/800 × 100 = 15%.
4. Find the gradient of the line through (2, 5) and (6, 17).
Show suggested answer
Gradient = (17 − 5)/(6 − 2) = 12/4 = 3.
5. Find the equation of a line with gradient 3 passing through (2, 5).
Show suggested answer
y − 5 = 3(x − 2), giving y = 3x − 1.
6. Calculate simple interest on KSh 12,000 at 8% per annum for 9 months.
Show suggested answer
Time = 9/12 year. Interest = 12,000 × 0.08 × 9/12 = KSh 720.
7. A cylinder has radius 3.5 cm and height 10 cm. Using π = 22/7, find volume.
Show suggested answer
V = πr²h = 22/7 × 3.5² × 10 = 385 cm³.
8. Solve the simultaneous equations x + y = 11 and 2x − y = 4.
Show suggested answer
Add the equations: 3x = 15, so x = 5. Substitute to obtain y = 6.
9. A bag contains 4 green and 6 yellow counters. Two are drawn without replacement. Find the probability both are green.
Show suggested answer
First green: 4/10. Second green: 3/9. Product = 12/90 = 2/15.
10. Find the median of 4, 9, 6, 12, 7, 10 and 5.
Show suggested answer
Order: 4, 5, 6, 7, 9, 10, 12. The middle value is 7.
Frequently asked questions
Why invert the divisor fraction?
Dividing by a fraction is equivalent to multiplying by its reciprocal.
How can I verify a factorisation?
Expand the factors and compare coefficients with the original expression.
Which price is the base for percentage increase?
Use the original price.
What if a line is vertical?
Its gradient is undefined because the change in x is zero.
Can I use y = mx + c?
Yes. Substitute the given gradient and point to find c.
Why convert nine months to years?
The interest rate is quoted per annum.
Is cylinder volume measured in square centimetres?
No. Volume uses cubic units.
Can substitution replace elimination?
Yes. Either valid method can solve the simultaneous equations.
Why does the second probability change?
One counter has been removed and is not replaced.
Why order the data before finding the median?
The median depends on position in an ordered list.
Why keep fractions exact in intermediate working?
Early rounding can introduce avoidable error.
Can both roots of a quadratic be correct?
Yes. A quadratic can have two valid roots.
How do I verify the line equation?
Substitute the supplied point and check that it satisfies the equation.
Does simple interest compound each period?
No. It is calculated from the original principal for the stated time.
What does pi represent in the cylinder formula?
The ratio of a circle’s circumference to its diameter.
Why add the simultaneous equations in this example?
The opposite y terms cancel, leaving one equation in x.
Can probabilities be added for both-green draws?
These successive required events use multiplication of the appropriate conditional probabilities.
How do I check the simultaneous solution?
Substitute x = 5 and y = 6 into both original equations.
Is a median affected by original data order?
No. Sort the data before locating the middle value.
How should I use a correction?
Redo the method with different values to test understanding.
Related revision resources
- KCSE Past Papers MATHEMATICS ALT A Paper 1 2
- KCSE Past Papers by Subject and Year
- KCSE TOPIC TESTS
- KCSE Chemistry Practical: Data Interpretation Practice
- KCSE Biology Practical: Tables, Drawings and Conclusions
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For official assessment notices and examination instructions, consult KNEC. These practice answers are not official scoring guides.
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