Questions as text
Q1 · 2 Calculate ( 3 + 3 3 ) giving your answer correct to 1 decimal place 0580/21 Oct/Nov 2004
3 2 Calculate ( 3 + 3 3 ) giving your answer correct to 1 decimal place. Answer [2]
2 marks
Mark scheme: 2 550.6 2 M1 for 550, 551, 550.59, 550.5 seen SC1 87.7 only
This question in 0580/21 Oct/Nov 2004
Q2 · Calculate 3 2.35 2 − 1.09 2 0580/23 Oct/Nov 2010
3 Calculate 3 2.35 2 − 1.09 2 . Give your answer correct to 4 decimal places. Answer [2]
2 marks
Mark scheme: 3 1.6305 cao 2 B1 4.33(44…) seen or answer 1.63, 1.630, 1.6304….
This question in 0580/23 Oct/Nov 2010
Q3 · Calculate 810.25 ÷ 4−2 0580/21 May/June 2011
3 Calculate 810.25 ÷ 4−2 . Answer [2]
2 marks
Mark scheme: 3 48 2 B1 for 3 and 16 seen
This question in 0580/21 May/June 2011
Q4 · The first four terms of a sequence are For Examiner's T1 = 12 T2 = 12 + 22 T3 = 12 + 22 +… 0580/21 Oct/Nov 2011
18 The first four terms of a sequence are For Examiner's T1 = 12 T2 = 12 + 22 T3 = 12 + 22 + 32 T4 = 12 + 22 + 32 + 42 . Use 1 (a) The nth term is given by Tn = n(n + 1)(2n + 1). 6 Work out the value of T23. Answer(a) T23 = [2] (b) A new sequence is formed as follows. U1 = T2 – T1 U2 = T3 – T2 U3 = T4 – T3 ……. (i) Find the values of U1 and U2. Answer(b)(i) U1 = and U2 = [2] (ii) Write down a formula for the nth term, Un . Answer(b)(ii) Un = [1] (c) The first four terms of another sequence are V1 = 22 V2 = 22 + 42 V3 = 22 + 42 + 62 V4 = 22 + 42 + 62 + 82. By comparing this sequence with the one in part (a), find a formula for the nth term, Vn . Answer(c) Vn = [2]
7 marks
Mark scheme: 1 18 (a) 4324 cao 2 M1 × 23 × 24 × 47 or better 6 (b) (i) 4, 9 2 B1 either correct (ii) (n + 1)2 or n2 + 2n + 1 1 2 (c) n(n+ 1)(2n + 1) oe 2 M1 recognising Vn = 4Tn 3
This question in 0580/21 Oct/Nov 2011
Q5 · Use your calculator to find the value of (a) 30 × 2.52, Answer(a) [1] (b) 2.5 – 2 0580/22 Oct/Nov 2011
3 Use your calculator to find the value of (a) 30 × 2.52, Answer(a) [1] (b) 2.5 – 2. Answer(b) [1]
2 marks
Mark scheme: 3 (a) 6.25 cao 1 (b) 0.16 cao 1
This question in 0580/22 Oct/Nov 2011
Q6 · 18 w = LC (a) Find w when L = 8 × 10 O3 and C = 2 × 10 O9 0580/22 Oct/Nov 2011
1 18 w = LC (a) Find w when L = 8 × 10 O3 and C = 2 × 10 O9. Give your answer in standard form. Answer(a) w = [3] (b) Rearrange the formula to make C the subject. Answer(b) C = [3] Question 19 is printed on the next page.
6 marks
Mark scheme: 18 (a) 2.5 × 105 3 B2 250000 oe or M1 correct part value seen (b) C = 1/(Lw2) 3 M1 each correct move
This question in 0580/22 Oct/Nov 2011
Q7 · 210 211 212 213 214 215 216 From the list of numbers, find (a) a prime number, Answer(a)… 0580/23 Oct/Nov 2011
2 210 211 212 213 214 215 216 From the list of numbers, find (a) a prime number, Answer(a) [1] (b) a cube number. Answer(b) [1]
2 marks
Mark scheme: 2 (a) 211 cao 1 (b) 216 cao 1
This question in 0580/23 Oct/Nov 2011
Q8 · 27 Examiner's 4 Find the value of 0580/23 Oct/Nov 2011
27 Examiner's 4 Find the value of . Use 8 Give your answer as an exact fraction. Answer [2]
2 marks
Mark scheme: 16 81 k 16 4 cao 2 B1 , , or (2/3)4 seen 81 for16 81 k 5
This question in 0580/23 Oct/Nov 2011
Q9 · –2 –2 137 Show that 3 + 2 = 0580/23 Oct/Nov 2011
–2 –2 137 Show that 3 + 2 = . 36 Write down all the steps of your working. Answer [2]
2 marks
Mark scheme: 1 1 7 , M1 Both fractions seen 9 4 1 1 4 9 13 E1 Both fractions over a common denominator and + = + = 13 9 4 36 36 36 added to give 36
This question in 0580/23 Oct/Nov 2011
Q10 · Find r when (5) 3 = 125 0580/21 May/June 2012
8 Find r when (5) 3 = 125 . Examiner's Use Answer r = [2]
2 marks
Mark scheme: 8 9 2 M1 125 = 5 3
This question in 0580/21 May/June 2012
Q11 · 1.5 0.9 3 (a) Calculate 7 + 22 and write down your full calculator display 0580/23 May/June 2012
3 1.5 0.9 3 (a) Calculate 7 + 22 and write down your full calculator display. Answer(a) [1] (b) Write your answer to part (a) correct to 4 significant figures. Answer(b) [1]
2 marks
Mark scheme: 3 (a) 3.26077… 1 seen (b) 3.261 1ft their (a) to 4 significant figures
This question in 0580/23 May/June 2012
Question 12 0580/23 May/June 2012
14 Simplify the following. For Examiner's 2 Use (a) (4pq )3 Answer(a) [2] 1 − (b) (16 x 8 ) 4 Answer(b) [2]
4 marks
Mark scheme: 14 (a) 64p3q6 2 B1 64puqv or kp3q6 1 1 1 (b) 0.5x–2 or 2 oe 2 B1 u oe or 2 oe 2 x 2 x kx
This question in 0580/23 May/June 2012
Q13 · 49 2 64 10 Without using a calculator, show that = 0580/23 Oct/Nov 2012
49 2 64 10 Without using a calculator, show that = . 16 343 Write down all the steps in your working. Answer [2] 1
2 marks
Mark scheme: 10 Correct working seen 2 M1 for correct step M1 for correct step 64 64
This question in 0580/23 Oct/Nov 2012
Q14 · 11 Write 27x12 3 in its simplest form 0580/21 May/June 2013
1 11 Write 27x12 3 in its simplest form. ^ h Answer … [2] _____________________________________________________________________________________
2 marks
Mark scheme: 11 3x4 2 B1 for kx4 or 3xk IGCSE – May/June 2013 0580 21
This question in 0580/21 May/June 2013
Q15 · Simplify x8 ÷ x2 0580/21 Oct/Nov 2014
11 (a) Simplify x8 ÷ x2. Answer(a) … [1] x6 13 (b) Simplify . 27 ` j Answer(b) … [2] __________________________________________________________________________________________
3 marks
Mark scheme: 11 (a) x6 1 2 x (b) 2 B1 for answer kx2 or x3k or 13 3 5
This question in 0580/21 Oct/Nov 2014
Q16 · Find the value of 1 .05 (i) c 4 m , Answer(a)(i) … [1] 2 (ii) (–8) 3 0580/22 May/June 2015
16 (a) Find the value of 1 .05 (i) c 4 m , Answer(a)(i) … [1] 2 (ii) (–8) 3 . Answer(a)(ii) … [1] 29 - 3 # 32 0.4 (b) Use a calculator to find the decimal value of . 3 Answer(b) … [1] __________________________________________________________________________________________
3 marks
Mark scheme: 16 (a) (i) 1 1 1 0.5 or – 0.5 or or − 2 2 (a)(ii) 4 1 (b) 1.37 or 1.37[4…] 1
This question in 0580/22 May/June 2015
Question 17 0580/23 May/June 2015
13 Simplify. (a) 12x12 ÷ 3x3 Answer(a) … [2] 1 (b) (256y 256 ) 8 Answer(b) … [2]
4 marks
Mark scheme: 13 (a) 4x9 final answer 2 B1 for answer kx9 or 4xk (k ≠ 0 ) (b) 2y32 final answer 2 B1 for answer ky32 or 2yk (k ≠ 0 ) 1 2
This question in 0580/23 May/June 2015
Q18 · Find the value of (a) ^ 5h8 , Answer(a) … [1] 2 1 - 3 (b) 0580/23 Oct/Nov 2015
10 Find the value of (a) ^ 5h8 , Answer(a) … [1] 2 1 - 3 (b) . c 27 m Answer(b) … [1] __________________________________________________________________________________________
2 marks
Mark scheme: 10 (a) 625 1 (b) 9 1 3x
This question in 0580/23 Oct/Nov 2015
Question 19 0580/23 Oct/Nov 2015
17 Simplify. 1 16 o e 16x y64 4 Answer … [3] __________________________________________________________________________________________
3 marks
Mark scheme: 17 3 B2 for fraction as final answer with two of x16, 2, y4 x 16 final answer 4 correct and in correct position 2y or B1 for fraction as final answer with one of x16, 2, y4 correct and in correct position
This question in 0580/23 Oct/Nov 2015
Q20 · 4112 Simplify ^16p h 0580/21 May/June 2016
16 4112 Simplify ^16p h . … [2]
2 marks
Mark scheme: 12 2p 4 final answer 2 B1 for kp 4 or 2 p k as answer
This question in 0580/21 May/June 2016
Q21 · Find the cube root of 4913 0580/23 May/June 2016
1 Find the cube root of 4913. … [1]
1 marks
Mark scheme: Question Answer Mark Part marks 1 17 1
This question in 0580/23 May/June 2016
Question 22 0580/23 May/June 2016
7 Simplify. 3 5 ^32x10h … [2]
2 marks
Mark scheme: 7 8x6 final answer 2 B1 for 8xk or cx6 29 . .
This question in 0580/23 May/June 2016
Q23 · Write 5 -3 as a fraction 0580/21 Oct/Nov 2016
5 (a) Write 5 -3 as a fraction. … [1] (b) Write 0.004 56 in standard form. … [1]
2 marks
Mark scheme: 5 (a) 1 125 (b) 1 4.56 × 10–3
This question in 0580/21 Oct/Nov 2016
Question 24 0580/21 Oct/Nov 2016
10 Simplify. 1 ^36x 16h2 … [2]
2 marks
Mark scheme: 10 6x 8 final answer 2 B1 for 6 kx , 6× x 8 or kx 8 (k ≠ 0) as final answer
This question in 0580/21 Oct/Nov 2016
Question 25 0580/23 Oct/Nov 2016
10 Calculate. (a) 2 3 - 10 + 4 2 … [1] 2 3 # tan 70° (b) 3 … [1]
2 marks
Mark scheme: 10 (a) 2.9[0] or 2.900 to 2.901 1 (b) 3.17 or 3.172 to 3.173 1 40 10
This question in 0580/23 Oct/Nov 2016
Question 26 0580/22 Feb/March 2017
15 Work out. (a) t 24 ' t 4 … [1] (b) x5 2 ^ h … [1] 8 43 (c) 81m ^ h … [2]
4 marks
Mark scheme: 15 (a) t 20 final answer 1 (b) x10 final answer 1 (c) 27m6 final answer 2 B1 for 27 m k or km 6 as final answer
This question in 0580/22 Feb/March 2017
Question 27 0580/22 May/June 2017
14 Work out. 2 3 (a) 125 … [1] J N- 2 1 (b) KK OO 3 L P … [1]
2 marks
Mark scheme: 14(a) 25 1 14(b) 9 1
This question in 0580/22 May/June 2017
Question 28 0580/23 May/June 2017
8 Simplify. 12 c a8 31 m … [2]
2 marks
Mark scheme: 8 2 2 2 k or 2a−4 final answer B1 for oe or oe (k ≠ 0) final answer a 4 a k a 4
This question in 0580/23 May/June 2017
Q29 · 2 5 -7 343 -11 0.4 2.5 3 From this list of numbers, write down (a) a cube number, … [1]… 0580/21 Oct/Nov 2017
112 5 -7 343 -11 0.4 2.5 3 From this list of numbers, write down (a) a cube number, … [1] (b) the smallest number, … [1] (c) a natural number. … [1]
3 marks
Mark scheme: 12(a) 343 1 12(b) –11 1 12(c) 343 1
This question in 0580/21 Oct/Nov 2017
Question 30 0580/22 Oct/Nov 2017
27 Simplify. 3 (a) 814 … [1] 2 4 (b) x 3 ' x - 3 … [1] 1 8 - 3 (c) 6 c y m
2 marks
Mark scheme: 27(a) 27 1 27(b) x2 final answer 1 1 2 −127(c) y 2 3 2 y 6 or 0.5y2 final answer 2 M1 for or 2 or better 8 y y 2 ky 2 or SC1 for answer or or c 2 y 2
This question in 0580/22 Oct/Nov 2017
Q31 · 1 Find the exact value of 8 2 3 # 49 - 1 0580/21 May/June 2018
211 Find the exact value of 8 2 3 # 49 - 1 . … [2]
2 marks
Mark scheme: 11 4 2 1 oe exact answer B1 for 4 or 7 7
This question in 0580/21 May/June 2018
Q32 · 4 1 -17 (a) Find the value of 0580/23 May/June 2018
3 4 1 -17 (a) Find the value of . c 81 m … [1] (b) Simplify. 3 27t 27 … [2]
3 marks
Mark scheme: 17(a) 27 1 17(b) 3t 9 final answer 2 B1 for kt 9 or for 3kt ( k ≠ 0 )
This question in 0580/23 May/June 2018
Q33 · Calculate .0125 - 2 0580/22 Oct/Nov 2018
33 Calculate .0125 - 2 . … [1]
1 marks
Mark scheme: 3 4 1
This question in 0580/22 Oct/Nov 2018
Question 34 0580/23 Oct/Nov 2018
5 Work out. - 2 c 12527 m 3 … [1]
1 marks
Mark scheme: 5 9 1 oe 25
This question in 0580/23 Oct/Nov 2018
Q35 · 17 (a) Find the value of n when 5 n = 125 n = … [1] 1 64 - 3 (b) Simplify 3 0580/22 Feb/March 2019
1 .17 (a) Find the value of n when 5 n = 125 n = … [1] 1 64 - 3 (b) Simplify 3 . e m o … [2]
3 marks
Mark scheme: 17(a) − 3 1 17(b) m 2 1 or 0.25m final answer B1 for or 0.25 or 4–1 or m correct in final 4 4 answer
This question in 0580/22 Feb/March 2019
Q36 · Calculate 3 8.1 2 - 1.3 0 .8 0580/21 May/June 2019
3 Calculate 3 8.1 2 - 1.3 0 .8 . … [1]
1 marks
Mark scheme: 3 4.01 or 4.007 to 4.008 1
This question in 0580/21 May/June 2019
Q37 · 27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7, … [1] (b)… 0580/21 May/June 2019
12 27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7, … [1] (b) a cube number, … [1] (c) a prime number. … [1]
3 marks
Mark scheme: 12(a) 28 1 12(b) 27 1 12(c) 29 or 31 1
This question in 0580/21 May/June 2019
Q38 · 18 (a) Simplify 81y 16 4 0580/21 May/June 2019
3 18 (a) Simplify 81y 16 4 . ` j … [2] (b) 2 3 = 4 p Find the value of p. p = … [1]
3 marks
Mark scheme: 18(a) 27y 12 final answer 2 B1 for ky12 or 27 ky in final answer 18(b) 3 1 oe 2
This question in 0580/21 May/June 2019
Question 39 0580/23 May/June 2019
6 Calculate. (a) - 12 ' - 2 … [1] (b) 3 2 3 + 2 … [1]
2 marks
Mark scheme: 6(a) 6 1 6(b) 2.15 or 2.154… 1
This question in 0580/23 May/June 2019
Q40 · Calculate 256 .025 + 4 # 8 0580/23 Oct/Nov 2019
2 Calculate 256 .025 + 4 # 8 . … [1]
1 marks
Mark scheme: 2 6 1
This question in 0580/23 Oct/Nov 2019
Q41 · 3.56 5 196 8 7 12 From the list, write down a number that is (a) a multiple of 3, … [1]… 0580/22 Feb/March 2020
1 3.56 5 196 8 7 12 From the list, write down a number that is (a) a multiple of 3, … [1] (b) a cube number, … [1] (c) a prime number, … [1] (d) an irrational number. … [1]
4 marks
Mark scheme: Question Answer Marks Partial Marks 1(a) 12 1 1(b) 8 1 1(c) 5 1 1(d) 7 1
This question in 0580/22 Feb/March 2020
Question 42 0580/22 May/June 2020
21 Simplify. (a) ( 5x 4 ) 3 … [2] 3 8 (b) ( 256x 256 ) … [2]
4 marks
Mark scheme: 21(a) 125x12 2 B1 for 125xk or kx12 21(b) 8x96 2 B1 for 8xk or kx96
This question in 0580/22 May/June 2020
Q43 · 3 y 2 = 6 x and y = n x 0580/22 May/June 2020
26 3 y 2 = 6 x and y = n x . Find the value of n. n = … [2] Question 27 is printed on the next page.
2 marks
Mark scheme: 26 4 2 2 1 M1 for y 3 = x 6 or y 2 = x or y 4 = x
This question in 0580/22 May/June 2020
Q44 · 32 33 34 35 36 37 38 39 From this list of numbers, write down (a) a multiple of 8, … [1]… 0580/23 May/June 2020
1 32 33 34 35 36 37 38 39 From this list of numbers, write down (a) a multiple of 8, … [1] (b) a square number, … [1] (c) a prime number. … [1]
3 marks
Mark scheme: Question Answer Marks Partial Marks 1(a) 32 1 1(b) 36 1 1(c) 37 1
This question in 0580/23 May/June 2020
Q45 · Write down the cube number that is greater than 50 but less than 100 0580/23 Oct/Nov 2020
1 Write down the cube number that is greater than 50 but less than 100. … [1]
1 marks
Mark scheme: Question Answer Marks Partial Marks 1 64 1
This question in 0580/23 Oct/Nov 2020
Question 46 0580/23 Oct/Nov 2020
2 Calculate. 4 .00025 … [1]
1 marks
Mark scheme: 2 80 1
This question in 0580/23 Oct/Nov 2020
Q47 · N = 2 4 # 3 # 7 5 PN = K , where P is an integer and K is a square number 0580/23 Oct/Nov 2020
14 N = 2 4 # 3 # 7 5 PN = K , where P is an integer and K is a square number. Find the smallest value of P. P = … [2]
2 marks
Mark scheme: 14 21 2 B1 for 3 × 7 soi or 24 × 32 × 76 oe or answer of 21 × k2
This question in 0580/23 Oct/Nov 2020
Q48 · 18 Simplify 343x 9 3 0580/22 Feb/March 2021
2 18 Simplify 343x 9 3 . ` j … [2]
2 marks
Mark scheme: 18 49 x 6 final answer 2 B1 for 49 kx or nx 6 as final answer
This question in 0580/22 Feb/March 2021
Question 49 0580/21 May/June 2021
11 (a) Simplify fully. ( 4ab 5 ) 4 … [2] 3 = 6 (b) 2p 1 Find the value of p. p = … [1] (c) 812 ' 3 t = 9 Find the value of t. t = … [2]
5 marks
Mark scheme: 11(a) 256a 4 b 20 final answer 2 B1 for two correct elements in final answer 11(b) 27 1 11(c) 6 2 M1 for 3k ÷ 3t = 32 or 38 ÷ 3t = 3 k oe or better or 3t = 729 oe
This question in 0580/21 May/June 2021
Question 50 0580/22 May/June 2021
2 Calculate 4 .00256 . … [1]
1 marks
Mark scheme: 2 2 1 0.4 or 5
This question in 0580/22 May/June 2021
Q51 · Calculate 4 39 161 0580/22 Oct/Nov 2021
8 Calculate 4 39 161 . … [1]
1 marks
Mark scheme: 8 2.5 oe 1
This question in 0580/22 Oct/Nov 2021
Question 52 0580/23 Oct/Nov 2021
21 Simplify fully. 3 243y 10 5 ` j … [2]
2 marks
Mark scheme: 21 27y6 final answer 2 B1 for ky6 or 27yk as final answer or correct answer seen and spoilt
This question in 0580/23 Oct/Nov 2021
Q53 · Work out 5 # 62 0580/22 Feb/March 2022
2 Work out 5 # 62 . Give your answer correct to 2 decimal places. … [2]
2 marks
Mark scheme: 2 80.50 cao 2 B1 for 80.498… or 80.5 or correctly rounding their more accurate decimal to 2 dp
This question in 0580/22 Feb/March 2022
Q54 · Calculate 4 5 - 5 4 0580/21 May/June 2022
2 Calculate 4 5 - 5 4 . … [1]
1 marks
Mark scheme: 2 399 1
This question in 0580/21 May/June 2022
Q55 · 2 Simplify fully ( 216y 216 ) 2 0580/21 May/June 2022
322 Simplify fully ( 216y 216 ) 2 . … [2]
2 marks
Mark scheme: 22 36y144 final answer 2 B1 for ky144 or 36 ky final answer k ≠ 0 or correct answer seen and spoilt
This question in 0580/21 May/June 2022
Q56 · Find the highest common factor (HCF) of 12a 3 b and 20a 2 b 2 0580/22 May/June 2022
15 Find the highest common factor (HCF) of 12a 3 b and 20a 2 b 2 . … [2]
2 marks
Mark scheme: 15 4a 2 b final answer 2 M1 for two correct parts out of three from 4, a2 and b in final answer
This question in 0580/22 May/June 2022
Q57 · M k 32 Work out the value of when m = 4 and k = 7 0580/23 May/June 2022
m k 32 Work out the value of when m = 4 and k = 7 . 3 … [2]
2 marks
Mark scheme: 2 792 or 792.1… 2 4 7 3 M1 for oe 3 or B1 for 1372
This question in 0580/23 May/June 2022
Q58 · 17 Simplify 3125 x 3125 5 0580/21 Oct/Nov 2022
1 17 Simplify 3125 x 3125 5 . ` j … [2]
2 marks
Mark scheme: 17 5x 625 final answer 2 B1 for final answer kx 625 or 5 kx or correct answer spoiled
This question in 0580/21 Oct/Nov 2022
Q59 · Find the sum of 32 and - 32 0580/22 Oct/Nov 2022
3 Find the sum of 32 and - 32 . … [1]
1 marks
Mark scheme: 3 0 1
This question in 0580/22 Oct/Nov 2022
Q60 · X = 3 2 # 5 2 # 7 # 199 57 when written as a product of its prime factors 0580/22 Oct/Nov 2022
12 x = 3 2 # 5 2 # 7 # 199 57 when written as a product of its prime factors. Write x ' 315 as a product of its prime factors. … [2]
2 marks
Mark scheme: 12 5 19957 2 M1 for [315 =] 32 5 7 oe or 32 52 7 ÷ 315 = 5
This question in 0580/22 Oct/Nov 2022
Question 61 0580/22 Oct/Nov 2022
20 Simplify fully. 3 (a) ( 81x 16 ) 4 … [2] 1 1 - 2 (b) 2 e y o … [1]
3 marks
Mark scheme: 20(a) 27x12 final answer 2 B1 for kx12 or 27xc final answer or for 27x12 then spoilt 20(b) [±] y 1
This question in 0580/22 Oct/Nov 2022
Q62 · Find the highest common factor (HCF) of 12x 12 and 16x 16 0580/22 Feb/March 2023
11 Find the highest common factor (HCF) of 12x 12 and 16x 16. … [2]
2 marks
Mark scheme: 11 4x12 final answer 2 B1 for 4xk or kx12 or for 4x12 seen then spoiled
This question in 0580/22 Feb/March 2023
Q63 · 15 Simplify 3125 w 3125 5 0580/22 Feb/March 2023
1 15 Simplify 3125 w 3125 5 . ` j … [2]
2 marks
Mark scheme: 15 5w625 final answer 2 B1 for kw625 or 5wk final answer or for 5w625 then spoiled
This question in 0580/22 Feb/March 2023
Q64 · 17 Simplify 81 x 12 4 0580/21 May/June 2023
3 17 Simplify 81 x 12 4 . ` j … [2]
2 marks
Mark scheme: 17 27 x 9 final answer 2 B1 for answer 27 x n or nx 9 , or for correct answer seen and spoilt
This question in 0580/21 May/June 2023
Q65 · Calculate 42 + 3 .04 0580/23 May/June 2023
13 Calculate 42 + 3 .04 . … [1]
1 marks
Mark scheme: 13 8.03 or 8.032 to 8.033 1
This question in 0580/23 May/June 2023
Q66 · 3 3 p # 3 2p = 729 Find the value of p 0580/22 Oct/Nov 2023
13 (a) 3 3 p # 3 2p = 729 Find the value of p. p = … [2] (b) Simplify. 1 ( 32x 10 ) 5 … [2]
4 marks
Mark scheme: 13(a) 1.2 oe 2 B1 for 32 p + 3 p or 3 6 soi 13(b) 2x 2 final answer 2 B1 for kx 2 or 2 kx as final answer or correct answer spoiled
This question in 0580/22 Oct/Nov 2023
Q67 · Find the lowest common multiple (LCM) of 12x 8 and 8x 12 0580/22 Oct/Nov 2023
16 Find the lowest common multiple (LCM) of 12x 8 and 8x 12. … [2]
2 marks
Mark scheme: 16 24x12 final answer 2 B1 for 24 kx or kx12 in final answer
This question in 0580/22 Oct/Nov 2023
Question 68 0580/23 Oct/Nov 2023
17 (a) Simplify. 2 64y 27 3 ` j … [2] (b) Simplify. x - 5 x 2 - 25 … [2]
4 marks
Mark scheme: 17(a) 16y18 final answer 2 B1 for 16yk or ky18 as final answer or correct answer spoiled 17(b) 1 2 B1 for (x + 5)(x – 5) final answer x + 5
This question in 0580/23 Oct/Nov 2023
Q69 · Calculate 5.76 + 2.83 0580/22 Feb/March 2024
2 Calculate 5.76 + 2.83 . … [1]
1 marks
Mark scheme: 2 24.352 1
This question in 0580/22 Feb/March 2024
Question 70 0580/21 May/June 2024
5 Calculate. (a) 3 343 - 40.96 … [1] (b) (192 + 4 # 16 ) .125 … [1]
2 marks
Mark scheme: 5(a) 3 1 0.6 or 5 5(b) 1024 1
This question in 0580/21 May/June 2024
Question 71 0580/23 May/June 2024
12 Simplify. 32g 16 (a) 16g 8 … [2] 3 (b) `625k 8j4 … [2]
4 marks
Mark scheme: 12(a) 2g 8 final answer 2 B1 for final answer kg 8 or 2 g k or correct answer seen then spoilt 12(b) 125k 6 final answer 2 B1 for final answer ck 6 or 125k c or correct answer seen then spoilt
This question in 0580/23 May/June 2024
Q72 · 0 Calculate 1 + 10 .9 # 0 .42 0580/22 Oct/Nov 2024
310 Calculate 1 + 10 .9 # 0 .42 . … [1]
1 marks
Mark scheme: 10 1.4 oe 1
This question in 0580/22 Oct/Nov 2024
Question 73 0580/22 Feb/March 2025
20 (a) Simplify. 300 + 48 … [2] (b) Rationalise the denominator and simplify. 9 2 + 7 … [3]
5 marks
Mark scheme: 20(a) 14 3 2 B1 for 10 3 or 4 3 If 0 scored SC1 for answer 7 12 20(b) 3( 7 − 2 ) oe simplified 3 9 2 − 7 ( ) B2 for or better 4 − 7 9 2 − 7 or M1 for oe 2 + 7 2 − 7
This question in 0580/22 Feb/March 2025
Q74 · - 2319 Find the value of 27 0580/21 May/June 2025
- 2319 Find the value of 27 . … [2]
2 marks
Mark scheme: 19 1 2 1 1 M1 for 9–1 or for or 9 3 2 3 729
This question in 0580/21 May/June 2025
Q75 · Find the value of 2 (a) 125 3 … [2] - 25 (b) 4 0580/22 May/June 2025
17 Find the value of 2 (a) 125 3 … [2] - 25 (b) 4 . … [2]
4 marks
Mark scheme: 17(a) 25 2 2 2 3 3 125 5 3 M1 for or 3 1252 or ( ) ( ) or B1 for 3 125 = 5 17(b) 1 2 1 1 [] M1 for or 32–1 or 32 2 5 1024
This question in 0580/22 May/June 2025
Q76 · 18 (a) 3 Rationalise the denominator 0580/22 May/June 2025
9 18 (a) 3 Rationalise the denominator. Give your answer in its simplest form. … [2] (b) ( 5 - 2 )( 1 + 3 2 ) = c + k 2 Find the value of c and the value of k. c = … k = … [2]
4 marks
Mark scheme: 18(a) 3 3 cao 2 9 3 M1 for × oe 3 3 18(b) [c =] –1 2 B1 for each [k =] 14 or for 3 correct terms from 5 + 15 2 − 2 − 3 2 2 oe
This question in 0580/22 May/June 2025
Q77 · Find the lowest common multiple (LCM) of 15xy 3 and 18x 4 y 0580/23 May/June 2025
14 Find the lowest common multiple (LCM) of 15xy 3 and 18x 4 y . … [2]
2 marks
Mark scheme: 14 90x4y3 final answer 2 B1 for two correct parts from: 90, x4 and y3 or for 3×5×x×y×y×y and 2×3×3×x×x×x×x×y or for correct answer seen then spoilt
This question in 0580/23 May/June 2025
Question 78 0580/23 May/June 2025
15 (a) Simplify. 27 + 12 … [2] 40 8 (b) = k , where k is an integer. 5 2 Find the value of k. k = … [2] (c) Rationalise the denominator. 1 3 - 5 … [2]
6 marks
Mark scheme: 15(a) 5 3 2 B1 for 3 3 or 2 3 15(b) 16 2 8 4 2 M1 for 40 2 2 , 8 2 2 , or 2 40 8 2 or better 5 2 2 or B1 for 8 4 or 256 15(c) 3 + 5 2 1 3 + 5 M1 for oe 4 3 − 5 3 + 5
This question in 0580/23 May/June 2025
Q79 · Find the value of (a) 5 -5 # 5 5 … [1] 3 (b) 125 2 0580/21 Oct/Nov 2025
6 Find the value of (a) 5 -5 # 5 5 … [1] 3 (b) 125 2. … [2]
3 marks
Mark scheme: 6(a) 1 cao 1 6(b) 25 cao 2 2 2 3 3 125 5 3 M1 for or 3 1252 or ( ) ( ) or B1 for 3 125 = 5
This question in 0580/21 Oct/Nov 2025
Q80 · Find the value of (a) 3 2 ' 3 -2 … [2] - 23 (b) 16 0580/22 Oct/Nov 2025
14 Find the value of (a) 3 2 ' 3 -2 … [2] - 23 (b) 16 . … [2]
4 marks
Mark scheme: 14(a) 81 2 B1 for 34 or 32 × 9 or 9 × 9 14(b) 1 2 1 1 [ ]64 M1 for 4 3 or 64–1 or 4096
This question in 0580/22 Oct/Nov 2025
Q81 · Write down the value of 730 0580/23 Oct/Nov 2025
12 (a) Write down the value of 730. … [1] 7 (b) Find the value of -2 . 3 … [2] (c) Write 27 # 812 in the form 3n. … [2]
5 marks
Mark scheme: 12(a) 1 1 12(b) 63 2 1 M1 for 3–2 = soi 9 12(c) 311 2 M1 for 33 or (34)2 or better
This question in 0580/23 Oct/Nov 2025
Question 82 0580/23 Oct/Nov 2025
24 (a) Simplify. 125 - 20 … [2] (b) NOT TO 2 2 cm SCALE 3 8 cm The area of this rectangle is k cm 2. Work out the value of k. k = … [2] (c) Rationalise the denominator. 1 7 + 2 … [2]
6 marks
Mark scheme: 24(a) 2 3 5 B1 for 5 5 or 2 5 24(b) 24 2 M1 for 6 16 oe or 6 2 2 2 or 3 8 8 24(c) 2 7 − 2 1 2 1 7 − 2 or 7 ‒ M1 for oe 3 3 3 7 + 2 7 − 2
This question in 0580/23 Oct/Nov 2025
![Question 1: 2 Calculate ( 3 + 3 3 ) giving your answer correct to 1 decimal place. Answer [2]](https://img.pastlit.com/crops/841d65e1-fd33-4b75-9694-94ace21a938f/q2.webp)
![Question 2: Calculate 3 2.35 2 − 1.09 2 . Give your answer correct to 4 decimal places. Answer [2]](https://img.pastlit.com/crops/e2834dac-0216-4836-829f-5ce9e730fc3f/q3.webp)
![Question 3: Calculate 810.25 ÷ 4−2 . Answer [2]](https://img.pastlit.com/crops/1797517c-fbf1-46d8-857b-7a19d829d29a/q3.webp)
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2 / 28![Question 5: Use your calculator to find the value of (a) 30 × 2.52, Answer(a) [1] (b) 2.5 – 2. Answer(b) [1]](https://img.pastlit.com/crops/798ef607-6d89-4be5-9995-3dd1d508fb59/q3.webp)
![Question 6: 18 w = LC (a) Find w when L = 8 × 10 O3 and C = 2 × 10 O9. Give your answer in standard form. Answer(a) w = [3] (b) Rearrange the formula t…](https://img.pastlit.com/crops/798ef607-6d89-4be5-9995-3dd1d508fb59/q18.webp)
3 / 28![Question 7: 210 211 212 213 214 215 216 From the list of numbers, find (a) a prime number, Answer(a) [1] (b) a cube number. Answer(b) [1]](https://img.pastlit.com/crops/ff5911e7-b59e-4249-a6b6-f6cad2c1fdbe/q2.webp)
![Question 8: 27 Examiner's 4 Find the value of . Use 8 Give your answer as an exact fraction. Answer [2]](https://img.pastlit.com/crops/ff5911e7-b59e-4249-a6b6-f6cad2c1fdbe/q4.webp)
![Question 9: –2 –2 137 Show that 3 + 2 = . 36 Write down all the steps of your working. Answer [2]](https://img.pastlit.com/crops/ff5911e7-b59e-4249-a6b6-f6cad2c1fdbe/q7.webp)
4 / 28![Question 10: Find r when (5) 3 = 125 . Examiner's Use Answer r = [2]](https://img.pastlit.com/crops/2346ec6b-d055-4a6f-b6c8-4c76b616bea6/q8.webp)
![Question 11: 1.5 0.9 3 (a) Calculate 7 + 22 and write down your full calculator display. Answer(a) [1] (b) Write your answer to part (a) correct to 4 si…](https://img.pastlit.com/crops/7d2ecca1-d244-4252-a128-f49d8668c0e9/q3.webp)
![Question 12: Simplify the following. For Examiner's 2 Use (a) (4pq )3 Answer(a) [2] 1 − (b) (16 x 8 ) 4 Answer(b) [2]](https://img.pastlit.com/crops/7d2ecca1-d244-4252-a128-f49d8668c0e9/q14.webp)
5 / 28![Question 13: 49 2 64 10 Without using a calculator, show that = . 16 343 Write down all the steps in your working. Answer [2] 1](https://img.pastlit.com/crops/73c2e362-eb78-4535-a178-14563a324ae3/q10.webp)
![Question 14: 11 Write 27x12 3 in its simplest form. ^ h Answer ............................................... [2] _____________________________________…](https://img.pastlit.com/crops/567ded07-0b3f-4c8c-875b-2d005c37e2c5/q11.webp)
![Question 15: (a) Simplify x8 ÷ x2. Answer(a) ................................................ [1] x6 13 (b) Simplify . 27 ` j Answer(b) ................…](https://img.pastlit.com/crops/a724e0db-d396-4e7c-8e05-d846dab51964/q11.webp)
6 / 28![Question 16: (a) Find the value of 1 .05 (i) c 4 m , Answer(a)(i) ................................................ [1] 2 (ii) (–8) 3 . Answer(a)(ii) ...…](https://img.pastlit.com/crops/0166788e-45f2-4de0-bd76-935f9dda492d/q16.webp)
![Question 17: Simplify. (a) 12x12 ÷ 3x3 Answer(a) ................................................ [2] 1 (b) (256y 256 ) 8 Answer(b) ....................…](https://img.pastlit.com/crops/992655a4-fa94-476e-8c14-90dd542b6353/q13.webp)
7 / 28![Question 18: Find the value of (a) ^ 5h8 , Answer(a) ................................................ [1] 2 1 - 3 (b) . c 27 m Answer(b) ...............…](https://img.pastlit.com/crops/af3628a1-64d3-4836-835a-05060fa7df47/q10.webp)
![Question 19: Simplify. 1 16 o e 16x y64 4 Answer ................................................ [3] __________________________________________________…](https://img.pastlit.com/crops/af3628a1-64d3-4836-835a-05060fa7df47/q17.webp)
![Question 20: 4112 Simplify ^16p h . ................................................... [2]](https://img.pastlit.com/crops/8d4c0e0a-fb51-4215-96bb-a7eff9382b2e/q12.webp)
![Question 21: Find the cube root of 4913. .................................................. [1]](https://img.pastlit.com/crops/9ebe8dee-fff4-4d3e-8385-64f2e2620945/q1.webp)
8 / 28![Question 22: Simplify. 3 5 ^32x10h .................................................. [2]](https://img.pastlit.com/crops/9ebe8dee-fff4-4d3e-8385-64f2e2620945/q7.webp)
![Question 23: (a) Write 5 -3 as a fraction. ................................................. [1] (b) Write 0.004 56 in standard form. ..................…](https://img.pastlit.com/crops/4bdcb565-fe08-4ff2-9869-66252b3e9fbe/q5.webp)
![Question 24: Simplify. 1 ^36x 16h2 ................................................. [2]](https://img.pastlit.com/crops/4bdcb565-fe08-4ff2-9869-66252b3e9fbe/q10.webp)
![Question 25: Calculate. (a) 2 3 - 10 + 4 2 ................................................. [1] 2 3 # tan 70° (b) 3 ...................................…](https://img.pastlit.com/crops/c5831d50-0b22-426b-b25c-e55fa5a0d567/q10.webp)
9 / 28![Question 26: Work out. (a) t 24 ' t 4 ................................................... [1] (b) x5 2 ^ h .............................................…](https://img.pastlit.com/crops/ad8e95d4-1fac-4050-9d0a-89c408ad2db4/q15.webp)
![Question 27: Work out. 2 3 (a) 125 ................................................. [1] J N- 2 1 (b) KK OO 3 L P ......................................…](https://img.pastlit.com/crops/cae494a3-a333-4a4a-8193-3f050cf63cf3/q14.webp)
![Question 28: Simplify. 12 c a8 31 m ................................................... [2]](https://img.pastlit.com/crops/1d2bd0d3-9e62-4a4b-ba54-a2ef55b231ec/q8.webp)
10 / 28![Question 29: 2 5 -7 343 -11 0.4 2.5 3 From this list of numbers, write down (a) a cube number, ................................................... [1] (…](https://img.pastlit.com/crops/52a69d3f-dfec-4502-861f-c2976e8007f6/q12.webp)
![Question 30: Simplify. 3 (a) 814 .............................................. [1] 2 4 (b) x 3 ' x - 3 .............................................. […](https://img.pastlit.com/crops/f58fe106-fb06-4f53-b748-06e94598dfe7/q27.webp)
![Question 31: 1 Find the exact value of 8 2 3 # 49 - 1 . .............................................. [2]](https://img.pastlit.com/crops/8d976e5a-5038-41a1-a843-b62c57272b14/q11.webp)
11 / 28![Question 32: 4 1 -17 (a) Find the value of . c 81 m ................................................. [1] (b) Simplify. 3 27t 27 .......................…](https://img.pastlit.com/crops/6e0dc1f2-2cde-44da-a2ab-92b6d0285837/q17.webp)
![Question 33: Calculate .0125 - 2 . ................................................ [1]](https://img.pastlit.com/crops/89eda026-7406-41bc-bd06-ed159e01f609/q3.webp)
![Question 34: Work out. - 2 c 12527 m 3 .................................................[1]](https://img.pastlit.com/crops/ac2305d0-804d-4de0-86f1-31373ef0e978/q5.webp)
![Question 35: .17 (a) Find the value of n when 5 n = 125 n = .................................................... [1] 1 64 - 3 (b) Simplify 3 . e m o ...…](https://img.pastlit.com/crops/50a671f6-75fb-475e-84dc-fd079da353e9/q17.webp)
12 / 28![Question 36: Calculate 3 8.1 2 - 1.3 0 .8 . ............................................ [1]](https://img.pastlit.com/crops/21bc4f5e-b7a2-4c15-a558-62dfcb74f98c/q3.webp)
![Question 37: 27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7, ............................................ [1] (b) a cube …](https://img.pastlit.com/crops/21bc4f5e-b7a2-4c15-a558-62dfcb74f98c/q12.webp)
![Question 38: 18 (a) Simplify 81y 16 4 . ` j ............................................ [2] (b) 2 3 = 4 p Find the value of p. p = ....................…](https://img.pastlit.com/crops/21bc4f5e-b7a2-4c15-a558-62dfcb74f98c/q18.webp)
13 / 28![Question 39: Calculate. (a) - 12 ' - 2 .................................................... [1] (b) 3 2 3 + 2 ..........................................…](https://img.pastlit.com/crops/a1f9a6f4-437f-4a21-8c6d-43b0eda49e93/q6.webp)
![Question 40: Calculate 256 .025 + 4 # 8 . .................................................... [1]](https://img.pastlit.com/crops/1c6ecf99-2ede-42f2-a23a-702f08671501/q2.webp)
![Question 41: 3.56 5 196 8 7 12 From the list, write down a number that is (a) a multiple of 3, ................................................. [1] (b)…](https://img.pastlit.com/crops/5a548fc7-c62f-44c4-b364-f15aeaa79b9b/q1.webp)
14 / 28![Question 42: Simplify. (a) ( 5x 4 ) 3 ................................................. [2] 3 8 (b) ( 256x 256 ) .......................................…](https://img.pastlit.com/crops/18c5a2ed-8336-40c6-aadd-0949ffec9f43/q21.webp)
![Question 43: 3 y 2 = 6 x and y = n x . Find the value of n. n = ................................................. [2] Question 27 is printed on the next…](https://img.pastlit.com/crops/18c5a2ed-8336-40c6-aadd-0949ffec9f43/q26.webp)
15 / 28![Question 44: 32 33 34 35 36 37 38 39 From this list of numbers, write down (a) a multiple of 8, ................................................. [1] (b…](https://img.pastlit.com/crops/c5b4f966-7e3f-4fb2-bbcf-0067ecea3add/q1.webp)
![Question 45: Write down the cube number that is greater than 50 but less than 100. ................................................. [1]](https://img.pastlit.com/crops/631fcbc5-68c7-4811-adcb-016218dea11a/q1.webp)
![Question 46: Calculate. 4 .00025 ................................................. [1]](https://img.pastlit.com/crops/631fcbc5-68c7-4811-adcb-016218dea11a/q2.webp)
16 / 28![Question 48: 18 Simplify 343x 9 3 . ` j ................................................. [2]](https://img.pastlit.com/crops/c699d6f6-82c9-4324-840c-6952ab4b0ec9/q18.webp)
![Question 49: (a) Simplify fully. ( 4ab 5 ) 4 ................................................. [2] 3 = 6 (b) 2p 1 Find the value of p. p = .............…](https://img.pastlit.com/crops/ca39f2af-6ef1-47b7-8fd3-0216d79713e7/q11.webp)
![Question 50: Calculate 4 .00256 . ................................................. [1]](https://img.pastlit.com/crops/ca7734d9-f387-4aea-a042-8235723053d8/q2.webp)
17 / 28![Question 51: Calculate 4 39 161 . ................................................. [1]](https://img.pastlit.com/crops/2b9003b9-13b2-4dd6-9ae2-511b67ed403d/q8.webp)
![Question 52: Simplify fully. 3 243y 10 5 ` j ................................................. [2]](https://img.pastlit.com/crops/577d5a03-d9fe-40c0-b51e-54dd76d5701a/q21.webp)
![Question 53: Work out 5 # 62 . Give your answer correct to 2 decimal places. ................................................. [2]](https://img.pastlit.com/crops/5b6344f7-8440-4f61-84d7-5041ff1ffd9c/q2.webp)
![Question 54: Calculate 4 5 - 5 4 . ................................................. [1]](https://img.pastlit.com/crops/f094acd9-71e4-4ca4-b953-2f6d6b71a702/q2.webp)
![Question 55: 2 Simplify fully ( 216y 216 ) 2 . ................................................. [2]](https://img.pastlit.com/crops/f094acd9-71e4-4ca4-b953-2f6d6b71a702/q22.webp)
18 / 28![Question 56: Find the highest common factor (HCF) of 12a 3 b and 20a 2 b 2 . ................................................. [2]](https://img.pastlit.com/crops/fe915e34-bd24-42bd-83c4-d0836846ccd0/q15.webp)
![Question 57: m k 32 Work out the value of when m = 4 and k = 7 . 3 ................................................. [2]](https://img.pastlit.com/crops/e0be5ca8-d9fb-4976-addd-9c0e1d225995/q2.webp)
![Question 58: 17 Simplify 3125 x 3125 5 . ` j ................................................. [2]](https://img.pastlit.com/crops/2dbcd88f-4b7c-4625-aa04-cfa31aafd09e/q17.webp)
![Question 59: Find the sum of 32 and - 32 . ................................................. [1]](https://img.pastlit.com/crops/94b8d77b-65b3-4c82-9e84-6d9cf1da9564/q3.webp)
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![Question 61: Simplify fully. 3 (a) ( 81x 16 ) 4 ................................................. [2] 1 1 - 2 (b) 2 e y o ..............................…](https://img.pastlit.com/crops/94b8d77b-65b3-4c82-9e84-6d9cf1da9564/q20.webp)
![Question 62: Find the highest common factor (HCF) of 12x 12 and 16x 16. ................................................. [2]](https://img.pastlit.com/crops/f751e8e7-c910-4f37-b0cd-fb04d456ce9a/q11.webp)
![Question 63: 15 Simplify 3125 w 3125 5 . ` j ................................................. [2]](https://img.pastlit.com/crops/f751e8e7-c910-4f37-b0cd-fb04d456ce9a/q15.webp)
20 / 28![Question 64: 17 Simplify 81 x 12 4 . ` j ................................................. [2]](https://img.pastlit.com/crops/2237c940-2c50-4edb-99ef-1b2d578231a2/q17.webp)
![Question 65: Calculate 42 + 3 .04 . ................................................. [1]](https://img.pastlit.com/crops/7dcd0d34-3973-477a-b4a3-7459b2e5cc99/q13.webp)
![Question 66: (a) 3 3 p # 3 2p = 729 Find the value of p. p = ................................................. [2] (b) Simplify. 1 ( 32x 10 ) 5 ........…](https://img.pastlit.com/crops/bb970e6a-400e-4f9d-ab94-159ed77af5a2/q13.webp)
![Question 67: Find the lowest common multiple (LCM) of 12x 8 and 8x 12. ................................................. [2]](https://img.pastlit.com/crops/bb970e6a-400e-4f9d-ab94-159ed77af5a2/q16.webp)
21 / 28![Question 68: (a) Simplify. 2 64y 27 3 ` j ................................................. [2] (b) Simplify. x - 5 x 2 - 25 ...........................…](https://img.pastlit.com/crops/941c807d-4ebd-4d96-837b-4412062da67b/q17.webp)
![Question 69: Calculate 5.76 + 2.83 . ................................................. [1]](https://img.pastlit.com/crops/ffce0d1f-92f4-44a4-84e1-42f039d0ff4c/q2.webp)
![Question 70: Calculate. (a) 3 343 - 40.96 ................................................. [1] (b) (192 + 4 # 16 ) .125 ...............................…](https://img.pastlit.com/crops/d8901c84-c0af-46f6-83ab-884502794630/q5.webp)
22 / 28![Question 71: Simplify. 32g 16 (a) 16g 8 ................................................. [2] 3 (b) `625k 8j4 ..........................................…](https://img.pastlit.com/crops/833822da-405a-40cc-abc5-2fdb402e89a4/q12.webp)
![Question 72: 0 Calculate 1 + 10 .9 # 0 .42 . ................................................. [1]](https://img.pastlit.com/crops/42d3ee11-e06e-451d-869c-ca109e4a2f36/q10.webp)
23 / 28![Question 73: (a) Simplify. 300 + 48 ................................................. [2] (b) Rationalise the denominator and simplify. 9 2 + 7 ........…](https://img.pastlit.com/crops/4caa3010-5506-4e5a-91ba-d201f22207da/q20.webp)
![Question 74: - 2319 Find the value of 27 . ................................................. [2]](https://img.pastlit.com/crops/21f02c8a-018b-433e-a2e0-6af89b0ab12e/q19.webp)
24 / 28![Question 75: Find the value of 2 (a) 125 3 ................................................. [2] - 25 (b) 4 . ..........................................…](https://img.pastlit.com/crops/3be19518-e2a4-44ca-94a1-2292db96c948/q17.webp)
![Question 76: 18 (a) 3 Rationalise the denominator. Give your answer in its simplest form. ................................................. [2] (b) ( 5 …](https://img.pastlit.com/crops/3be19518-e2a4-44ca-94a1-2292db96c948/q18.webp)
![Question 77: Find the lowest common multiple (LCM) of 15xy 3 and 18x 4 y . ................................................. [2]](https://img.pastlit.com/crops/8579dd7c-ee4c-4db2-b8c1-950af11fb0bf/q14.webp)
25 / 28![Question 78: (a) Simplify. 27 + 12 ................................................. [2] 40 8 (b) = k , where k is an integer. 5 2 Find the value of k. …](https://img.pastlit.com/crops/8579dd7c-ee4c-4db2-b8c1-950af11fb0bf/q15.webp)
![Question 79: Find the value of (a) 5 -5 # 5 5 ................................................. [1] 3 (b) 125 2. .......................................…](https://img.pastlit.com/crops/590a197d-28bb-4633-ba44-69c1212b3bc7/q6.webp)
26 / 28![Question 80: Find the value of (a) 3 2 ' 3 -2 ................................................. [2] - 23 (b) 16 . ......................................…](https://img.pastlit.com/crops/8decf0e5-c38c-4c4f-bfa1-f4337efc28d6/q14.webp)
![Question 81: (a) Write down the value of 730. ................................................. [1] 7 (b) Find the value of -2 . 3 .....................…](https://img.pastlit.com/crops/5611f938-bc84-400e-a1e1-5390deabb338/q12.webp)
27 / 28![Question 82: (a) Simplify. 125 - 20 ................................................. [2] (b) NOT TO 2 2 cm SCALE 3 8 cm The area of this rectangle is k…](https://img.pastlit.com/crops/5611f938-bc84-400e-a1e1-5390deabb338/q24.webp)
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