Common Entrance Mathematics: Ratio, measurement and word problems
Share in a ratio, use speed, distance and time, and find perimeter, area and averages. 20 original, exam-style questions with worked answers.
Read every question with its answer and working.
Question 1 of 20
Boys and girls in a class are in the ratio 3 : 2. There are 30 children. How many are girls?
Answer: C. 12. 3 + 2 = 5 parts. Each part is 30 ÷ 5 = 6. Girls = 2 × 6 = 12.
Question 2 of 20
Write the ratio 24 : 36 in its simplest form.
Answer: B. 2 : 3. Divide both numbers by 12 to get 2 : 3.
Question 3 of 20
Share ₦1,200 between Ada and Bola in the ratio 1 : 3. How much does Bola get?
Answer: A. ₦900. 1 + 3 = 4 parts, so each part is ₦300. Bola gets 3 × 300 = ₦900.
Question 4 of 20
A car travels 150 km in 3 hours. What is its speed?
Answer: D. 50 km/h. Speed = distance ÷ time = 150 ÷ 3 = 50 km/h.
Question 5 of 20
A bus travels at 60 km/h for 2½ hours. How far does it go?
Answer: C. 150 km. Distance = speed × time = 60 × 2.5 = 150 km.
Question 6 of 20
A train covers 240 km at 80 km/h. How long does the journey take?
Answer: B. 3 hours. Time = distance ÷ speed = 240 ÷ 80 = 3 hours.
Question 7 of 20
A rectangle is 12 cm long and 5 cm wide. What is its perimeter?
Answer: A. 34 cm. Perimeter = 2 × (12 + 5) = 2 × 17 = 34 cm.
Question 8 of 20
What is the area of a rectangular field 15 m long and 8 m wide?
Answer: D. 120 m². Area = length × width = 15 × 8 = 120 m².
Question 9 of 20
What is the area of a triangle with base 10 cm and height 6 cm?
Answer: C. 30 cm². Area = ½ × base × height = ½ × 10 × 6 = 30 cm².
Question 10 of 20
Two angles of a triangle are 65° and 45°. What is the third angle?
Answer: B. 70°. Angles in a triangle add up to 180°. 65 + 45 = 110, and 180 − 110 = 70°.
Question 11 of 20
Angles on a straight line add up to 180°. One angle is 125°. What is the other?
Answer: A. 55°. 180 − 125 = 55°.
Question 12 of 20
How many minutes are there in 2½ hours?
Answer: D. 150. 2 × 60 = 120, plus 30 = 150 minutes.
Question 13 of 20
A film starts at 4:45 pm and lasts 1 hour 50 minutes. When does it end?
Answer: C. 6:35 pm. 4:45 + 1 hour = 5:45. Add 50 minutes: 6:35 pm.
Question 14 of 20
Four pens cost ₦200. How much do seven pens cost?
Answer: B. ₦350. One pen costs 200 ÷ 4 = ₦50. Seven pens cost 7 × 50 = ₦350.
Question 15 of 20
Change 3.5 kg to grams.
Answer: A. 3,500 g. 1 kg = 1,000 g, so 3.5 × 1,000 = 3,500 g.
Question 16 of 20
Change 2,400 cm to metres.
Answer: D. 24 m. 100 cm = 1 m, so 2,400 ÷ 100 = 24 m.
Question 17 of 20
Ade buys 3 books at ₦450 each and pays with ₦2,000. How much change does he get?
Answer: C. ₦650. 3 × 450 = 1,350. Then 2,000 − 1,350 = ₦650.
Question 18 of 20
What is the mean (average) of 4, 7, 9 and 12?
Answer: B. 8. Add them: 4 + 7 + 9 + 12 = 32. Divide by 4: 32 ÷ 4 = 8.
Question 19 of 20
What is the median of 2, 9, 4, 6 and 14?
Answer: A. 6. Put them in order: 2, 4, 6, 9, 14. The middle number is 6.
Question 20 of 20
A bus carries 45 passengers. How many buses are needed for 380 pupils?
Answer: D. 9. 380 ÷ 45 is a little more than 8, and you cannot use part of a bus, so 9 buses are needed.
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Common Entrance questions parents ask
What is the Common Entrance examination?
It is the entrance exam Primary 6 pupils take to move on to secondary school in Nigeria. The National Common Entrance Examination (NCEE) is used for the Federal Unity Colleges, and many states and schools set their own. Papers, subjects and dates differ between exam bodies and from year to year, so always check your child’s exam for the current format.
Which areas do these worksheets cover?
Mathematics, English, quantitative reasoning, verbal reasoning and general knowledge (basic science, social studies and civic education). Each area has worksheets of 20 questions with worked answers.
Are these the real past questions?
No. They are original, exam-style practice questions with worked answers, written to build the same skills. They are not copies of past papers.
How do Answers, Practice and Test yourself differ?
Answers shows every question with its answer and working. Practice shows if you are right straight after each question. Test yourself hides the answers until you have answered all 20, then shows your score and every answer.
What does “ready” mean?
Scoring 16 out of 20 (80%) or more in a test. Your best score is saved in this browser. It is a practice guide and not a prediction of an exam result.
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No. Hour of Math is independent and is not affiliated with any examination body.