Topic 2c (foundation) – Homework on Pictograms
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The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence Name: H/w 1 – Grade A / A* Simplifying Surds and Expanding Brackets 1. (a) Teacher Assessment Find the value of 169 (i) ........................................................................................................................... Answer ……………………………………… (1) 2 2 34 (ii) ........................................................................................................................... ........................................................................................................................... Answer ……………………………………… (2)(Total 3 marks) 2. (a) 8 50 Simplify ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer ......................................................................... (2) (b) Hence simplify ( 8 50 )( 24 54 ) giving your answer in its simplest surd form. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer ......................................................................... (3) (Total 5 marks) 3. Show that 2 50 2 is an integer. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... (Total 2 marks) The Robert Smyth School 1 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence 4. Show that 12 75 48 6 ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ (Total 3 marks) 5. Find values of a and b such that (2 + 3)(4 – 3) = a + b3 ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer a = ............................ b = ............................ 6. Work out 2 3 3 8 (Total 2 marks) Give your answer in the form a b 6 where a and b are integers. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer .............................................................. (Total 3 marks) The Robert Smyth School 2 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence 7. (a) Simplify (i) 3 3 Answer ................................................................ (1) (ii) 3 3 Answer ................................................................ (1) (b) Show that 75 12 75 12 simplifies to 3 7 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 5 marks) 8. (a) Expand and simplify (2 + 3 3 )(4 2 – 3 ) Give your answer in the form a+b 2 +c 3+d 6 where a, b, c and d are integers. .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… Answer ............................................ (3) (Total 3 marks) The Robert Smyth School 3 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence 9. Show that ( 48 + 24 )2 can be expressed in the form p + q where p and q are integers to be found. 2 ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ............................................................................ (Total 3 marks) 10. (a) You are given that 12 + 27 = a3 where a is an integer. Find the value of a. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer .......................................................... (2) (b) Find the value of (m + p)2 when m = 2 and p = 8 ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer ........................................................ (2) (Total 4 marks) The Robert Smyth School 4 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence 11. (a) (i) Show that 20 = 2 5 ……………...........……………..…….........…………………………………. ……………...........……………..…….........…………………………………. (1) (ii) Expand and simplify ( 2 + 10 )2 ……………...........……………..…….........…………………………………. ……………...........……………..…….........…………………………………. Answer ………………………………….. (2) (b) Is this triangle right-angled? Not to scale 2 + 10 You will need to use the fact that: Longest side2 = shorter side2 + other shorter side2 3 Do you know what theory this is? 2 + 5 You must show your working. ……………...........……………..……...................…………………………………. ……………...........……………..……...................…………………………………. ……………...........……………..……...................…………………………………. ……………...........……………..……...................…………………………………. ……………...........……………..……...................…………………………………. ……………...........……………..……...................…………………………………. ……………...........……………..……...................…………………………………. ……………...........……………..……...................…………………………………. (3) (Total 6 marks) Success: The Robert Smyth School Target: 5 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence H/w 2 – Grade A / A* Rationalising the Denominator 1. (a) Simplify Teacher Assessment 18 + 32 .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… Answer ................................................ (2) (b) Rationalise 1 6 .....................………………………………………………………………………… .....................………………………………………………………………………… Answer ................................................ (1) (Total 3 marks) 2. Rationalise the denominator and simplify fully 18 2 ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ Answer ............................................................... (Total 2 marks) 3. (a) Rationalise the denominator and simplify fully 1 12 ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer ......................................................................... (2) The Robert Smyth School 6 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence (b) By simplifying 32 – 18 , write 3 ( 32 – 18 ) in its simplest form. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer ......................................................................... (3) (Total 8 marks) 4. Rationalise the denominator of 2 3 3 Simplify your answer fully. .........................................................................................................................................…. .........................................................................................................................................…. .........................................................................................................................................…. .........................................................................................................................................…. .........................................................................................................................................…. .........................................................................................................................................…. .........................................................................................................................................…. Answer .................................................................. (Total 3 marks) 5. (a) Rationalise the denominator of 18 and simplify your answer fully. 3 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .......................................................................... (2) (Total 2 marks) The Robert Smyth School 7 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence 6. 150 6 12 Simplify fully .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. Answer …………………………………......... (Total 4 marks) 7. (a) By rationalising the denominator, simplify 15 5 ..................................................................................................................................... ..................................................................................................................................... Answer .................................................................. (b) Show that 3 12 2 (2) 27 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 4 marks) 8. (a) Write 600 54 in the form p 6 where p is an integer. ..................................................................................................................................... ..................................................................................................................................... Answer ................................................................... (2) (b) Hence write 600 54 338 in the form q. You may use 338 = 2 × 132 ..................................................................................................................................... ..................................................................................................................................... Answer .................................................................... (2) (Total 4 marks) The Robert Smyth School 8 Success: The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence 9. (a) Rationalise and simplify 1 8 .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… Answer ............................................ (2) (b) By simplifying 12 + 108 , write 12 108 8 Target: in the form a b where a and b are integers. .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… .....................………………………………………………………………………… Answer ............................................ (3)(Total 5 marks) 10. (a) Simplify fully the following expression, leaving your answer in surd form. 75 12 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .................................................................. (2) (b) Given that 135 = 3 5, simplify the expression giving your answer in surd form. 3 135 75 12 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .................................................................. The Robert Smyth School 9 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence (3) (Total 5 marks) H/w 3 – Grade A / A* Problem solving using surds 1. (a) Express 5 + Teacher Assessment 20 in the form p 5 ..................................................................................................................................... ..................................................................................................................................... Answer .......................................................................... (2) (b) Hence, or otherwise, simplify fully 5 20 45 – 20 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .......................................................................... (3) (Total 5 marks) 2. (a) Simplify 10 by rationalising the denominator. 5 Give your answer in its simplest form. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer ……………………………………… (2) (b) Show that 125 – 45 125 45 1 4 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) The Robert Smyth School 10 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence (Total 7 marks) 3. (a) Find the value of m when 75 – 9 m 3 3 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer m = ................................................... (3) (b) Given that r 6 , s 8 and t 12 (i) Simplify fully, t rs ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... Answer .................................................... (2) (ii) Show that r t 6 2s 2 ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (Total 7 marks) The Robert Smyth School 11 The Robert Smyth School Mathematics Faculty Topic 12 Surds Innovation & excellence 4. Two rectangles, A and B, are equal in area. ( 10 – 2) cm B A 3 cm Not to scale ( 10 + 2) cm Calculate the length of rectangle B. Give your Answer in the form p 3 . ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ................................................................... cm (Total 4 marks) 5. The area of this rectangle is 30 cm2. x cm Find the value of x, writing your answer in the form a b where a and b are integers. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer ...................................................................cm (Total 3 marks) Success: The Robert Smyth School Target: 12
