Independent School Entrance (ISEB Pre-Test and 11+ CEM style) · Mathematics

Algebra, ratio and problem solving

40 practice questions, each with the answer and an explanation.

Practise Algebra, ratio and problem solving now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 40 questions

  1. Solve 4(2x - 3) = 3x + 13.
  2. Three consecutive odd numbers add up to 99. What is the largest of them?
  3. If a = 3 and b = -2, what is the value of a² - 2ab + b²?
  4. The first terms of a sequence are 7, 11, 15, 19. What is the 50th term?
  5. The ratio of boys to girls in a club is 3 : 5. When 6 more boys join, the numbers of boys and girls are equal. How many members were in the club before the boys joined?
  6. Pasta is sold in three packs: 750 g for £1.80, 500 g for £1.15 and 1.2 kg for £2.64. Which pack is the cheapest per 100 g?
  7. A clock gains 3 minutes every hour. It is set correctly at 6:00 am on Monday. What time does it show at 6:00 pm on Tuesday of the same week?
  8. A ticket rose in price from £25 to £28.50. What is the percentage increase?
  9. A taxi charges a fixed £3.20 plus £1.75 for each mile. A journey costs £20.70. How many miles was it?
  10. Three pens and two rulers cost £4.10. One pen and two rulers cost £2.30. What is the cost of one pen?
  11. Two trains are 480 km apart and travel towards each other on the same track at 70 km/h and 50 km/h. How long until they meet?
  12. Solve x/3 + x/4 = 14.
  13. Which expression is equal to 3(x + 4) - 2(x - 5)?
  14. Sam saves £6 in week 1. Each week after that he saves £2.50 more than in the week before. How much has he saved altogether after 5 weeks?
  15. If y = 3x² - 5, what is y when x = -4?
  16. A number machine multiplies the input by 4, subtracts 7, then divides by 3. The output is 15. What was the input?
  17. A café offers 4 starters, 5 main courses and 3 desserts. A customer chooses one starter, one main course and either one dessert or no dessert. How many different meals are possible?
  18. Eight people at a meeting each shake hands once with every other person. How many handshakes take place?
  19. Anya is three times as old as Ben. In 8 years' time she will be twice as old as he is. How old is Anya now?
  20. Tap A fills a pool in 6 hours and tap B fills it in 3 hours. How long do they take together?
  21. A number is increased by 40% to give 91. What was the original number?
  22. Between which two consecutive whole numbers does √200 lie?
  23. An arithmetic sequence has 23 as its 5th term and 38 as its 8th term. What is the 1st term?
  24. Ella works 7.5 hours a day from Monday to Thursday at £11.40 an hour. On Friday she works 6 hours paid at time and a half. How much does she earn in the week?
  25. The midnight temperatures on five nights were -4°C, -1°C, 2°C, -6°C and 3°C. What was the mean temperature?
  26. On a map with a scale of 1 : 25,000, two villages are 7.2 cm apart. What is the real distance between them?
  27. Lena reads 3/8 of a book on Monday and 1/4 of it on Tuesday. She still has 45 pages to read. How many pages are in the book?
  28. How many different 3-digit numbers can be made from the digits 1, 2, 3 and 4 if each digit may be used at most once in a number?
  29. Tom changes £250 into euros at £1 = €1.16. He spends €135 and changes the rest back to pounds at £1 = €1.25. How many pounds does he get back?
  30. In a class of 30 pupils, 18 play football, 14 play hockey and 5 play neither. How many play both sports?
  31. Factorise fully 6x² + 9x.
  32. Which of these is the greatest speed?
  33. What percentage of 80 is the same as 24% of 150?
  34. What is the smallest positive whole number that leaves remainder 3 when divided by 7 and remainder 2 when divided by 5?
  35. A return rail ticket costs £24.60 for an adult and half price for a child. What is the cost for 2 adults and 3 children?
  36. A printer prints 24 pages in 40 seconds. How long will it take to print 540 pages at the same rate?
  37. The triangular numbers begin 1, 3, 6, 10, 15, ... What is the sum of the 9th and 10th triangular numbers?
  38. Shirts cost £18 each and a shop has a '3 for 2' offer, where the cheapest of every three shirts is free. Zara buys 7 shirts. How much does she pay?
  39. Two children share 126 marbles. Aziz has 18 more than three times as many marbles as Beth. How many marbles does Aziz have?
  40. Two positive whole numbers have a sum of 25 and a product of 144. What is the larger number?

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