KJSEA Mathematics: Mixed Diagnostic Questions and Worked Answers

Updated: 19 October 2026

Use this short mixed check to identify the next topic to revise. Attempt all ten original questions before opening the worked answers. This is Grade 9 revision practice, not a complete KJSEA paper or an official scoring instrument.

On this page: original practice, explained answers and 20 short FAQs. Complete the tasks before reading the answers.

Set up the diagnostic

Use paper for working and record the time taken. Try the questions without notes, using only the equipment your teacher permits. Leave a small space beside each answer to explain any correction later.

Read your results by skill

Group errors into number, algebra, geometry, measurement and data. A wrong answer can come from an arithmetic slip, a misunderstood word or a missing concept. Write the reason beside the correction instead of copying the answer alone.

Return to the archive with a purpose

After correcting this check, choose a learning-area paper from the existing Mathematics directory. Set one goal, such as writing units consistently or showing each algebra step. Use a different question to check whether the correction has transferred.

Practice questions and explained answers

1. Calculate 3/4 + 2/3.

Show suggested answer

Use denominator 12: 9/12 + 8/12 = 17/12 = 1 5/12.

2. A bag costing KSh 2,400 is reduced by 15%. Find the new price.

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Discount = 0.15 × 2,400 = 360. New price = 2,400 − 360 = KSh 2,040.

3. Solve 3x − 5 = 16.

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Add 5: 3x = 21. Divide by 3: x = 7.

4. Share KSh 1,800 in the ratio 2:3.

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There are 5 parts. One part = 1,800/5 = 360. Shares are KSh 720 and KSh 1,080.

5. A triangle has angles 48° and 67°. Find the third angle.

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Angles total 180°. Third angle = 180 − 48 − 67 = 65°.

6. Find the area of a rectangle 7.5 m long and 4 m wide.

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Area = length × width = 7.5 × 4 = 30 m².

7. A cyclist covers 18 km in 45 minutes. Find average speed in km/h.

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45 minutes = 0.75 hours. Speed = 18/0.75 = 24 km/h.

8. Find the mean of 6, 8, 8, 10 and 13.

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Sum = 45 and count = 5. Mean = 45/5 = 9.

9. A bag holds 3 red and 5 blue counters. Find the probability of drawing red.

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There are 8 equally likely counters. Probability = 3/8.

10. Simplify 2a + 3b + 4a − b.

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Combine like terms: (2a + 4a) + (3b − b) = 6a + 2b.

Frequently asked questions

Why use a common denominator?

It expresses the fractions in equal-sized parts before addition.

Is the discount the final price?

No. Subtract the discount from the original price.

How can I check x = 7?

Substitute it: 3 × 7 − 5 = 16.

Why add the ratio parts?

Their total gives the number of equal units in the whole amount.

Does the angle rule apply to any triangle?

The interior angles of a plane triangle total 180 degrees.

Why write square metres for area?

Area measures the number of unit squares covering a surface.

Why convert minutes to hours?

The requested speed is in kilometres per hour.

Can the mean be a value not listed?

Yes. The mean need not be one of the observations.

Why is probability less than one here?

Only some of the counters are red.

Can a terms and b terms be combined?

Only like terms combine; 6a and 2b remain separate.

Must an improper fraction become a mixed number?

Use the form requested; 17/12 and 1 5/12 are equivalent.

How do I spot a percentage error?

Estimate the discount: 15 percent should be less than one fifth of the original price.

Can a ratio share be larger than the total?

Not in this positive whole-sharing example; the shares must add to KSh 1,800.

How do I check the third angle?

Add all three and confirm a total of 180 degrees.

Does changing metres to centimetres change the physical area?

No. It changes the numerical value and unit representation, not the surface.

Is average speed the same as the fastest speed?

No. It is total distance divided by total time for the journey.

How do I check a mean?

Multiply it by the number of observations and compare with the total.

What does a probability denominator represent here?

It is the total number of equally likely counters.

Why preserve algebra signs?

A minus sign affects the term that follows it and can change the result.

How should I choose follow-up questions?

Select unfamiliar questions testing the specific skill that caused difficulty.

Related revision resources

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For official assessment notices and examination instructions, consult KNEC. These practice answers are not official scoring guides.