PLC Papers Created For:

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1 PLC Papers Created For: Year 10 Topic Practice Papers: Surds

2 Surds 1 Grade 8 Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Simplify i) 45 ii) 00 Question Expand and simplify i) 5(4+ 5) ii) (6 )(4+ )

3 Question 3 Rationalise the denominators i) 1 10 ii) 3 15 iii) Total /10

4 Surds 3 Grade 8 Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Grace has made several mistakes in her simplifying surds homework. In each case explain her error and give the correct answer. i) 3+ 3 = 6 ii) ( 3 + 4) = = 19 Question Write 3 50 ( ) in the form a b, where a and b are integers..

5 Question 3 Calculate the length of the side labelled as x 5 7 x 5+ 7 Total /10

6 Surds 4 Grade 8 Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Sebastian has made several mistakes in his simplifying surds homework. In each case explain his error and give the correct answer. i) = 0 36 ii) ( 6 ) = 6 4= Question Work out the nth term for the geometric sequence below.,8,16,64....

7 Question 3 Andy s kitchen has designed his new kitchen to have carpeted and tiled sections. The darkened area represents where he will be laying the tiles. Calculate, in m, how much carpet Andy will need for this room. (All measurements are in metres) Not drawn to scale m Total /10

8 Surds Grade 8 Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Simplify 19 (1) Question Expand and simplify i) (3 7) ii) (7 + )(7 )

9 Question 3 Rationalise the denominators i) 1 + ii) (5) Total /10

10 PLC Papers Created For: Year 10 Topic Practice Papers: Surds

11 Surds 1 Grade 8 Solutions Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Simplify i) (A1) ii) (A1) Question Expand and simplify i) 5(4+ 5) (M1) (A1) ii) (6 )(4+ ) (M1 for any three correct terms) + (A1)

12 Question 3 Rationalise the denominators i) (A1) ii) (A1) iii) (5-7) (M1) 7 7 (5 7-7) (A1) 7 Total /10

13 Surds 3 Grade 8 Solutions Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Grace has made several mistakes in her simplifying surds homework. In each case explain her error and give the correct answer. i) 3+ 3 = 6 C1 for a valid explanation A1 for 3 ii) ( 3 + 4) = = 19 C1 for a valid explanation A1 for Question Write 3 50 ( ) in the form a b, where a and b are integers. 50 = 10 or ( ) 3 = (M1 for either surd simplified) 8 (A1).

14 Question 3 Calculate the length of the side labelled as x 5 7 x 5+ 7 Use of Pythagoras theorem (M1) or (M1 for either expansion) x = 64 (M1) x = 8 (A1) Total /10

15 Surds 4 Grade 8 Solutions Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Sebastian has made several mistakes in his simplifying surds homework. In each case explain his error and give the correct answer. i) = 0 36 C1 for a valid explanation A1 for 10 ii) ( 6 ) = 6 4= C1 for a valid explanation A1 for Question Work out the nth term for the geometric sequence below.,8,16,64... M1 for recognition of as common ratio A1 for ( ) n.

16 Question 3 Andy s kitchen has designed his new kitchen to have carpeted and tiled sections. The darkened area represents where he will be laying the tiles. Calculate, in m, how much carpet Andy will need for this room. (All measurements are in metres) Not drawn to scale M1 for any correct multiplication which will give an area M1 for (7 + 3)(9-3) = or 5( + 3) = M1 for A1 for 47 m Total /10

17 Surds Grade 8 Solutions Objective: Simplify expressions involving surds, including rationalising the denominator and calculate exactly with surds Question 1 Simplify (A1) (1) Question Expand and simplify i) (3 7) (M1 for any three correct terms) (A1) ii) (7 + )(7 ) (M1 for any three correct terms) 41 (A1)

18 Question 3 Rationalise the denominators and simplify as far as possible. i) (M1) ( + )( - ) - (A1) ii) (1-5)( + 5) (M1) ( - 5)( + 5) (M1) (A1) (5) Total /10