Topics / GCSE / Mathematics / Algebra Translating problems into equations Learn it by playing
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Lesson notes Turning words into algebra Choose a letter for the unknown and say what it stands for: "let x be the number of sweets." Translate key phrases: "3 more than" is +3; "twice a number" is 2x; "5 less than" is x - 5; "the product of" means multiply; "the sum of" means add. "Is" or "gives" or "equals" usually marks the equals sign. Forming and solving equations Write the information as an equation, solve it, then answer the original question in words with units. A number is doubled and 7 is added, giving 25: 2x + 7 = 25, so x = 9. Consecutive integers are n, n + 1, n + 2. Consecutive even integers are 2n, 2n + 2, 2n + 4 for integer n. Geometry and perimeter problems Use the perimeter or angle facts: a rectangle with sides x and x + 4 and perimeter 28 gives 2x + 2(x + 4) = 28, so x = 5. Angles in a triangle sum to 180°; angles on a straight line sum to 180°; angles round a point sum to 360°. Problems with two unknowns and quadratics With two unknowns, form two equations and solve simultaneously. Area problems often lead to quadratics: a rectangle of width x, length x + 3 and area 40 gives x2 + 3x - 40 = 0; reject a negative length. Checking Substitute back into the words of the problem to check it makes sense. Slides Sign up free to view the lesson slides
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Practice questions Free preview — 8 of 35 questions. Sign up to see them all. 1. What is \"five more than x\" in algebra?
Easy 2. What is "twice a number, plus 3"?
Easy A 2(x + 3)B 2x + 3C x2 + 3D 3x + 23. A number is trebled and 4 is subtracted to give 20. Which equation is formed?
Easy A 3x - 4 = 20B 3(x - 4) = 20C 3x + 4 = 20D x - 4 = 604. A number is trebled and 4 is subtracted to give 20. What is the number?
Easy 5. Pens cost £p each. Five pens and a £2 notebook cost £12. What is p?
Easy 6. Two numbers add to 30. One is 6 more than the other. What is the smaller?
Easy 7. The sum of three consecutive integers is 48. What is the smallest?
Easy 8. Sam is 4 years older than Jo. Their ages sum to 30. How old is Jo?
Easy More questions 9. A rectangle has sides x and x + 4 and perimeter 28 cm. What is x?
Easy 10. The angles of a triangle are x, 2x and 3x. What is the smallest angle?
Medium 11. The angles of a triangle are x, x + 10 and x + 20. What is x?
Medium 12. A taxi charges £3 plus £2 per km. A journey costs £17. How far is it?
Medium 13. Tickets cost £8 each and a £5 booking fee is added. The total is £53. How many tickets?
Medium 14. A number squared is 5 more than 4 times the number. Which equation is formed?
Medium A x2 = 4x + 5B x2 = 5x + 4C 2x = 4x + 5D x2 + 5 = 415. Three consecutive even numbers add to 54. What is the largest?
Medium 16. I think of a number, double it, and subtract 5. The result is the same as adding 3 to the number. What is it?
Medium 17. A rectangle is x wide and x + 3 long with area 40. Which equation is formed?
Medium A x2 + 3x - 40 = 0B x2 + 3 = 40C 2x + 3 = 40D x2 - 3x = 4018. A rectangle is x cm wide and (x + 3) cm long, with area 40 cm². What is its width?
Medium 19. Adult tickets cost £7 and child tickets £4. 10 tickets cost £52. How many adult tickets were bought?
Medium 20. The sum of the squares of two consecutive positive integers is 61. What are they?
Medium A 5 and 6B 4 and 5C 6 and 7D 3 and 421. Angles on a straight line add up to:
Easy 22. Angles around a point add up to:
Easy 23. Two angles on a straight line are 2x and x + 30. What is x?
Medium 24. A pen costs 20p more than a pencil. Together they cost £1.10. What does the pencil cost?
Medium 25. Why should you state what the unknown represents?
Easy A to make the answer clearer and check the contextB to make the answer longerC it is not necessaryD to avoid using algebra26. In a word problem, x represents a physical length. An equation gives x = −3. What does this tell you about that candidate answer?
Medium A the answer is correctB the solution must be rejectedC length is 3D add 627. Which equation matches "a number divided by 4, plus 2, equals 9"?
Easy A \frac{x}{4} + 2 = 9B \frac{x + 2}{4} = 9C 4x + 2 = 9D \frac{4}{x} + 2 = 928. "Twice a number" can be written 2x.
Easy True or false?
29. Angles on a straight line add to 360°.
Easy True or false?
30. You should check a solution back in the words of the problem.
Easy True or false?
31. Consecutive integers can be written n, n + 2, n + 4.
Easy True or false?
32. A negative length can be accepted as the final physical answer to an area problem.
Medium True or false?
33. Which expressions mean "3 more than twice x"?
Medium A 2x + 3B 3 + 2xC 2(x + 3)D 3x + 2E 2x - 334. Which statement is modelled by 2x + 4 = 18?
Easy A double a number and add 4 to get 18B add 4 to a number and double it to get 18C multiply a number by 4 to get 18D subtract 4 and halve to get 1835. The sides of a triangle are x, x + 2 and 2x - 1 cm. The perimeter is 21 cm. Find the longest side.
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