OCR GCSE MATHS EXAM :3.5 USING ALGEBRA TO SOLVE PROBLEMS(Algebraic expressions)A+GRADED QUESTIONS AND ANSWERS

Exercise 1 1 Which of the following simplify to p? a b c d 2 These triangles are similar but not congruent. Are the following true or false? a b c d TIP An equation is two expressions linked by an ‘=’ sign, for example, 2 + 2x = 4x. An identity is an equation where the expressions on either side of the = sign are exactly the same when simplified. For example: 2x + 3x = 4x + x 3 Which one of these is an identity? Explain your answer. a b 4 Which of these are identities? a b c d e 3.5 USING ALGEBRA TO SOLVE PROBLEMS ©Cambridge University Press and OCR 2021 2 5 Are the following statements true or false? a b If you multiply out you get the expression . c when expanded is . d always has the same value as . 6 Work out the value of a if . 7 a − b and 2a + 3b are the first two terms of a linear sequence. What is the third term of the sequence? TIP Factorise means to write the expression as a product of its factors using brackets. 8 a Expand and simplify . b Factorise your answer to a in the form , where p and q are values to be found. 9 a Write an algebraic expression for each length marked ‘?’ in this rectangle. b Write and simplify an expression for the perimeter of the rectangle. c Given that and calculate the area of the rectangle. 10 A rectangle has width and length . A square has sides of length . Show that the perimeter of the rectangle is twice the perimeter of the square. PS 11 A rectangular lawn has a length y metres and width 2x metres.