GCSE maths past paper notes

Notes: Question 1 a) Hexagon b) 3 Question 2 a) i. 3 ii. 5 iii. 23 my answers: b) if you square root 55. There won't be a whole number. Question 3.  1/4 = 0.25 = 25% 7/100 = 0.07 = 7% 13/10 = 1.3 = 130% Question 4 a) I.  23 ii. add 5 b) the term in the sequence end with a 3 or 8 Question 5) a) L,M.N /L,N,M/  M,L,N/M,N,L/  N,L,M/N,M.L b) 4/6 Question 6 a) 12x + 8 b)  3( c -2d) Question 7) 8+9+14+11 = 42 answer: 42 Question 8) extra hours = 42 -35 = 7 £9.40 x 1.25 = £ 11.75 paid = (9.40 x 35) + (11.75 x 7) =  £411.25 answer = £411.25 Question 9) Mike drinks = 7 x 2/5 = 2.8L £4.40 + £2.60 = £7 answer : £7 Question 10) 12 - 9 = 3 12 - oldest , 3- youngest 6.4 x 5 = 32 12 + 6 + 3 = 21 32 - 21 = 11 11 = 7+4 answer = 3,4,6,7,12 question 11)  a) Rotation 90* clockwise centre (0,0) b) I. watch a video ii. watch a video Question 12)  Jack : 87% of 520kg = 452.4 kg Alex : 61% of  750kg = 457.5kg 457.5kg - 452.4kg = 5.1kg answer: Alex by 5.1kg Question 13)  Area of a circle = pi x r to the power of 2 pi x 14 to the power of 2 = 615.7 Question 14) a)  I. 360 ii.  356.1 b) I. 4 ii. 8 Question 15)  a) 90 minutes = 1.5 hour  distance = speed / time anna: D = 6km/hr x 2hr = 12km Paddy: s = 12km / 1.5 hour = 8km/hour answer: 8 b) the stopping time would have been counted as its an average for the race. Question 16) 0.85 x 620 = 520 answer: 520 question 17)  a) 10 b) watch ayt video c) y = -3x + 11 question 18) square root 12 to the power of 2 + 18 to the power of 2 answer: 21.6 Question 19 ) a)  5 / 3+4+5 x 1/3 answer: 5/36 b) 4000 Question 20 )  a) 770 / 60 = 12.8 b) the highest number may not have been 40  Question 21 ) 5s + 4j = 163 3s + 2j = 89 answer: cost of one shirt = 5 cost of one jumper = 22 Question 22) 25000 x (1.02) to the power of 5 answer: £2602.02 Question 23) a) multiples of 18 = 18,36,54,72,90,108,126,144,162,180 multiples of 20 = 20,40,60,80,100,120,140,160,180 Lcm = 180 minutes 8:37 + 180 minutes = 11:37 answer: 11:37 b) there are no delays Question 24) Question 25) x + 7 + x + 2(7 + x)= 57 x + 7 + x + 14 + 2x = 57 x + x +2x = 4x 14 + 7 = 21 4x + 21 = 57 57 - 21 = 36 4x = 36 x = 9 answer: ayesha age - 9 bennie age - 16 chloe age - 32 My answers: Question 1) a) Triangle b) 3 Question 2) a)  I. 7 ii. 5 iii. 23  b) if you square root 55 will you net get a whole number. Question 3) 13/10 Question 4)  a) I. 23 ii. add 5 iii.  the sequence usually ends with 3 or 8 Question 5) b)  4/6 Question 7) 11 + 14 + 7 + 18 = 42 Question 8) 42 - 35 = 7 9.4 x 1.25 = 11.75 (9.4 x 35) + ( 11.75 x 7 ) = 411.25 Question 9) 2/5 x 7 = 2.8l 4.40 + 2.60 = 7 Question 10 ) 10 - 9 = 3 x 12 - 9 = 3 10 - oldest   and 3 is the youngest x 12 is the oldest and 3 is the youngest 6.4 x 5 = 32 12 + 6 + 3 = 21 32 - 21 = 11 7+ 4 = 11 3,4,6,7,10 x 3,4,6,7,12 Question 11) a) Rotation clockwise 90 degrees (0,0) x Rotation 90 degrees clockwise centre (0,0) Question 12 )  87% of  520 = 524.6kg  61% of  750 =575.5kg 575. marked the rest on my book                            

Notes: Question 1) a) i. £9.43 ii 3 iii. 54 b) i.  > ii. < iii. = Question 2)  3.9kg = 4kg 87p = 90p 4 x 90 = £3.60 answer: £3.60 Question 3) a) i. 3/7 = 12/28 ii.  4  1/2 = 9/2 b)  10 / 15 - 3/15 = 7/15 answer: 7/15 Question 4) a) answer: 0.21 b) answer: 0.08 Question 5) a)  i. 5 to the power of 2 = 25 ii. 4  b) 8 x7 = 56 answer: 56 Question 6) a) i. 32 ii. 42 + 3 = 45 45 / 5 = 9 answer : 9 b) y = 5x - 3 Question 7) x = 55 because alternate y = 70 because corresponding Question 8) a) i. C ii. A iii. E b) 20 + 16 = 36 36 / 2 = 18  18 / 3 = 6 answer : 6 Question 9) a) she travels at constant speeds b) 36 c) From 10:30 to 11:00 shown on the graph by distance from home stays the same d) I. watch a yt video ii. (36 / 40 )x 60 = 54 answer: 54 Question 10) a) I.  t + 8u ii. 12a to the power of 3 b)  x =  square root y + 1 Question 11) b) positive correlation Question 12) 5 x 12 + 2 = 62 62 x 2.5 =155 Alice is correct Question 13) a)  12 b) 140 / ( 20 /5 ) =35 answer : 35 c) (210 / 60 )x 20 = 70 Rashid is incorrect Question 14) a) look at answers b) enlargement   1/3   (4,4) Question 15) a)  profit = 1.68 - 1.20 = 0.48 0.48/ 1.20 = 0.4 0.4 x 100 = 40% answer : 40% b) 100 - 20 = 80 80% = 0.8 360 / 0.8 = 450 answer : £450 Question 16) a) 1.06m = 106cm (106 - 80) / 4 = 7 answer: 7 b) the days would be smaller Question 17) a)  First Pick         Second pick red =        4/7             Red = 4/7 blue =      3/7             Blue =  3/7                                     Red =  4/7                                     Blue = 3/7 b) 16 / 49 Question 18) 100 - 15 = 85% 85% = 0.85 adult ticket = 80 x 0.85 = 68 child ticket = 40 x 0.85 = 34 (68 x 2) + 34 = 170 170 x 1.02 = 173.40 answer: £ 173.40 Question 19) 3/5 of 40 = 24 24 / 2 = 12 12 + 24 = 36 answer: 36 Question 20)   my answers:  

Notes: Question 1) a) obtuse b) 45 Question 2) a) 3 : 7 b) 50 / 20 = 2.5 answer: 2.5 Question 3) 5 x ( 3 -1) = 10 (3 + 6 - 2) / 2= 3.5 Question 4) 40 x 0.2 = 8 answer: 8 Question 5) a)  10 b) 1 Question 6) a) 30, 60, 90, 120, 150 b) 30 Question 7) a)  (2.3) b) watch a yt video Question 8) 3(4) - 5 = 7 answer = 7 Question 9) a) you know how to answer this question b) 64 dots because 8 x 8 = 64 c) 14 Question 10) a)  Gaming b) if you simplify 150/ 360  c) 150 + 90 + 30 = 270  360 - 270 = 90 360 degrees = 300 minutes ( divide by 4) 90 degrees = 75 minutes 75 minutes = 1 hour and 15 min answer = 1 hour and 15 minutes Question 11) a) 12 b)                                   vanilla       /      lemon       /    chocholate wafer = 24                  4                        10                      10 no wafer = 41           12                        15                    14 c)  V = 4 + 12 + 9 + 1 = 26 L = 10 + 15 + 10 = 35 C = 10 + 14 + 11 + 4 = 39 answer : chocolate is the most popular Question12) 35 - 5 = 30 4x = 30 30 / 4 = 7.5  x = 7.5 answer: 7.5 Question 13) (240 / 40) x 1.3 x 4.5  = 35.1 answer: 35.1 Question14) 14 000 - 10 000 / 1700 = 2.35 answer : 3 Question 15) a)  200 / 50 = 4 7 x 4 = 28 answer : 28g b)  (9/ 8) x 10 = 11.25 answer : 11 .25 Question 16) Question 17) a)  6 . 48 x 10 to the power minus 5 as an ordinary number = 0.0000648 b)  Question 18)   Question 19) a) Question 20) Question 21)  23/ 50 x 300 = 138 (300 - 138) / 3 x 2 = 108 answer: 108 Question 22 ) Question 23 ) Question 24 ) Question 25 ) no because 6/10 = 0/6 and 11/ 15 = 0.7 Question 26 ) a) 4.045 and 4.055 b) 4 Question 27 ) ( x + 5) ( x -2)  answer: x = -5 and x = 2 Question28 ) a)  I. h to the power of 0 ii. f to the power of 6 my answers:

Question 1 ) a) you know how to answer this question b) i. Germany ii. 25 iii. 6 Question 2 ) a) cylinder b) put a 90-degree angle on the right Question 3 ) 320 x 1.14 = 364.80 answer: 364.80 Question 4 ) a) I. 20 ii. 5 iii. 11 iv. 27 b) 7 Question 5 ) a)  1 : 19 b) 8 x 1.5 = 12 answer: 12 Question 6 ) a)  x = 10  b) x = 4 Question 7 ) a)  81.5 b) 0.00569 Question 8 ) y = x / 3 + 9 Question 9 ) 140 / 7 = 20 4 x 20 = 80.   3 x 20 = 60 80 / 5 = 16    60 / 4 = 15 answer: 15 Question 10 ) Question 11 ) a)  (2,4) b) you can answer this question Question 12 )  8 + ( 3 x 5 ) = 23 answer: 23 Question 13 ) circumference of a circle =  pi x diameter pi x 10 = 31.41 answer: 31.42 Question 14 ) a) i.   x = 7 ii.  x = 12 b) 9x ( 2x + 1 ) Question 15 )  a)   Question 16) 5x + 3 +  7x + 4  + 9x - 10 + 2x + 3 +  5x + 8 = 28x + 8 (28x + 8) / 4 = 7x + 2 answer : 7x + 2 Question 17 ) 2pm - 8:30pm = 6.5 hours 12 x 6.5 = 78 78 x 2 = 156 ( thursday and friday) 12 x 1.5 = 18 18 x 5 = 90 ( Saturday) 156 + 90 = 246 answer: £246 Question 18 ) 20, 40, 80 , 100 , 120 , 140 35 , 70 , 105 , 140 LCM = 140 minutes 140 minutes = 2 hours and 20 minutes 8:30 + 2 hours and 20 minutes = 10:50  answer : 10:50 Question 19 ) Question 20 ) square root  30 to the power of  2  minus   8.4 to the power of 2 answer : x = 28.8 Question 21 ) 60 x 2.25 = 135 135 - 125 = 10 10 / 125 = 0.08 0.08 x 100 = 8 answer: 8  Question 22 ) Question 23 )  6400 x 1.025 to the power of 8 = 7,797.78 6400 + 6400 x 0.027 x 8 = 7782.4 7,797.78 - 7,782.4 = 15 .38 answer: 15.38     Question 24 ) a)        you know how to answer this question b) 0.4 x 0.3 = 0.12 answer: 0.12             Question 25 ) 7r + 15c = 7.00 7 ( c + 0.12 ) + 15 = 7.00 7c + 0.84 + 15c 15c + 7c = 7.00 - 0.84 22c = 6.16 c = 0.28 answer : 0.28 Question 26 ) 33 - 5n Question 27 ) a)       Laptop      both        Ipad      neither                 19            12         36               5 b) 19 + 12 + 36 + 5 = 72 answer: 36 /72

notes: Question 1 ) a) you know how to answer this question b) 2 Question 2 ) a)  6 12 / 2 = 6 answer: 6 b) 1/5 = 0.2 8 x 0.2 = 1.6  1.6 = 1 3/5 answer : 1 and 3/5 c)  1 - 1/6 =  5/6 3/5 - 5/6 = 7/30 Question 3 ) a) equiliteral b)  i. rhombus ii. rectangle c)  5 faces and 8 edges Question 4 ) a)   i.    1.22 answer:  1.22 ii.   1.3 - 1.13 = 0.17 answer: 0.17 iii.  8.47 / 7 = 1.21 answer: 1.21 b) 1.22 Question 5 ) a) i. 28 ii.  95 iii. 10kg = £4 4 x 180/10 = 72 answer: 72 b) the verticle scale is not linear Question 6 ) 36% =   36/100 =18/50 = 9/25 answer: 36% is bigger because when you convert to a fraction and simplify it is bigger than 7/20 Question 7 ) a) 3 b) 7 x7 = 49 answer: 49 c) 1/6 Question 8 ) £45 - £20 = £25 answer: £25 Question 9 ) a) x = y + 2 b)  d = C/ pi Question 10 ) a) i.  x = 3 ii.  y = x Question 11 ) 770 / ( 5 + 4 + 2 ) = 70 5 x 70 = 350 4 x 70 = 280 2 x 70 = 140 answer : flour = 350g                 butter = 280g                sugar = 140g Question 12 ) a) 80 / 4 = 20 answer: 20 b) 20 x 40/2 = 400 Question 13 ) a) 3.16 x 10 to the power of - 3 b) 2 x 4 = 8 10 to the power 2   x   10 to the power of 5 = 10 to the power of 7 answer: 8 x 10 to the power of 7 Question 14 ) a) 19 and 31 b) 2,10.12 Question 15 ) a) 3x to the power of 2   +   xy    -   2y to the power of 2 b) 6x + 3d + cx + 5c = 10x + 17 6 + c = 10  c =4 3d + 5c = 17    d= -1 answer: c = 4 and d = -1 c) (x-2)(x-5) answer: x = 2 and x =5 Question 16 ) a) 36 and 45 b) Even and Prime are not mutually exclusive. The correct answer is 8/12 Question 17 ) a)  57.8 - 54.2 = 3.6 3.6 / 0.3 = 12 answer: 12 b) the answer would be bigger Question 18 ) a) 100 + 20 / 100 2400 x 1.2 = 2000 answer: 200 Question 19 ) Question 20 ) Question 21 ) pi x 6 to the power of 2 - pi x to the power of 2 answer: 36 pi  - pi x to the power of 2 my answers:

Notes: Question 1) a. represents 4 people b. 14 people c. 4 key Question 2) 30 Question 3) a. 0.375 b.42/100 = 21/50 Question 4) 25 Question 5) a. Unlikely b. 2/5 or 3/5 Question 6) 0.403, 0.41, 0.4374, 0.438 Question 7) a. circle the number 3 b. 11a-2c c. x =6  Question 8)   a. £18 x 2 =£36. £36 +£14 = £50 b. Adult =  100% =£18 ( divide by 5) 20% = £3.60 (add 100% and 20%) 120% = £21.60 Child =  100% = £4 (divide by 10) 10% = £1.40 (divide by 2)  5% = £0.70 ( add 10% and 5%) 15% = £2.10 ( add 15% and 100%) 115% = £16.10 new cost = (£21.60 x 2) + 16.10 = £59.30 £59.30 - 50 = £9.30 answer = £9.30 Question 9) a. LE, TL / LE, BM/ BP, TL/BP, BM,TL/ TL,BM b. 2/5 Question 10)  a. to do the sketch watch a yt video  Quadrilateral 1 name: rectangle Quadrilateral 2 name: parrellogram b. learn how to the drawing on yt  triangle 1 : 30, 30, 120 traingle 2 : 60,60,60   my answers:

Notes: Question 3) a) 24 c)  0.6 x 350 = 390 answer: 390 Question 4) 144 Question 5) b) 2.5 c)  115/5  x  (2+5) = 161 Question 6) 3 + (2 x 4) = 11 answer: 11 Question 7) b) ( x + -6) ( x + 5) x = -6 x = -5 My answers:  

notes: Question 1) b)  3,5 Question 3) b) 1 + 2 x (3 + 5 )= 17 Question 5) a) Rhombus b) 2 c) 12 Question 6)  a) Entertainment b)  4 x 20 = 80 answer: 80 c)  240/1200 x 100 = 20 answer: 20 Question 8) 0.38 + 1.31 / 2 = 1.07 answer: 1.07     my answers:

Notes: Question 1) b) 8 Question 2) b) -6 Question 3) c) 42.9 Question 4) b) y = 3 Question 5) incorrect Question 6) b) y = 4/5 Question 7)  a) ii.  2/6 2 x 3 = 6 answer: 4/6 Question 8) a)   Divivng  = 5 = 20 swimming = 10 = 120 Paddleboarding = 6 = 72 Kayaking =  my answers:

Question 1) a) i. 44 ii. Acute angle b) parallel  Question 2) a) i .> ii.  = b) 184 300 c) 0.625 Question 3) a) 42 b) 81 c) 11, 23 and 41 Question 4) a) 1/5 of 40 = 8 10% of 40 = 4 8+4 = 12 40 - 12 = 28 28/40 = 7/10 answer : 7/10 Question 5) a) i. ( 4.3) ii.  ( -2, -1) b) you know how to do this / watch a yt video c) you know how to do this / watch a yt video Question 6) 17% = 0.17 0.17 x 54 =9.18 answer : 9.2 Question 7) a) 12t - 10u b) 5 ( v + 4w)  c)  ( x + 3)    (x + 7 ) x + 3 = 0     x + 7 = 0 x = -3          x = -7 answer : x = -3 or x = -7 Question 8) a) 240 b) 10 c) 1.3kg = 1300g 15 / 6 = 2.5 550 x 2.5 = 1,375g answer : No,  Question 9) a)  30 b) i.  Name of scorer /  Number of goals /      Angle of sector          Wayne            /      48                        /      144                          /          Harry           /        5                         /                 15                  /          Obi             /       24                      /        72                            /          Anthony    /          13                 /              39                      / ii. watch a YT video Question 10) 52/ 61 = 0.852 0.852 x 100 = 82.5% answer: No because, he has scored 85.2% Question 11) 53 x 6 = 318 answer: Garry is incorrect, 7 coaches are needed. Question 12) S = D / T ----> D = S x T D = 2 x 16 = 32m  S = 32 /4 = 8mph answer : 8 mph Question 13) a) 3 b) 25,000cm = 250m 1cm : 250m = 6cm : 1500m answer : 1.5km c) 6/13 Question 14) a) 5.43 x 10 to the power of 5 b) 0.063 c) Pierre is incorrect because 24.4 is not in standard form. It should be 2.44 x 10 to the power of 8 Question 15) 86 - 14 = 72 72 / 6 = 12 answer : £12 Question 16) watch a yt video Question 17) 2017 - 2014 = 3 years 5% = 0.05 240 000 x 1.05 to the power of 3 = 277 830 answer : £277 830 Question 18) a) you know how to the working out answer : 2 x 5 x 7 to the power of 2 b) 25, 50, 75, 100 . 125, 150, 175 , 200 40, 80. 120 . 160, 200 LCM = 200 200m = 3 hrs and 20 minutes 9am + 3 hrs and 20 minutes = 12:20 answer : 12 : 20 pm  Question 19) To the shops           From the shops bus =    0.3              bus = 0.8 walks =   0.7           walks = 0.2                                 bus = 0.8                                walks = 0.2 Question 20) 1 - 0.24 = 0.76 Question 21) 112% = 38.64 ( / 112) 1% = 0.345 ( x 100) 100% = 34.5  answer : 34.5 Question 22) Question 23) Question 24)  

Notes: Question 1 ) a) you know how to answer this question b) you know this question c) 18 / 60 = 0.3 0.3 x 100 = 30 answer: 30 Question 2 ) a) I.  7  1/4 ii.  63 / 7 = 9  9 x 4 = 36 answer: 36 b) 4/5 = 0.8 7/9 = 0.77 answer: 4/5 is bigger because if you convert it into a decimal, the number is bigger. c) 1/5 = 8/40   1/4 = 10/40 answer: 9/40 Question 3 ) a) 12.4 x 10 = 124 not 12.4 b) 6.45 x 4 / 3 = 8.6 answer: £8.60 Question 4 ) a)  I. 3.2 ii. 115 b) Question 5 ) a) you know how to solve this b) you know how to solve this Question  6 ) a)  corresponding b) Question 7 ) 1p coin -  3/10 = 6 / 20 6 x 1 = 6 2p coin - 2/5 = 8 /20 2 x 8 = 16 16 + 6 = 22 57 - 22 = 35 35 / 5 = 7 7 - 2 = 5 5/20 ( 5p coins ) 1/20 ( 10p coins) answer:  1p ( 6) , 2p (8), 5p (5), 10p ( 1) Question 8 ) a) I.  11 ii.  1/16 b)  (3) to the power of 2 answer: 9 c) 5 Question 9 ) a) 7 x 5 = 35 hours 420 / 35 = 12 answer : 12 b) I. 20% is reasonable because she is only missing out one day. ii.  420 x 0.8 = 336 answer = £336 Question 10 ) a)   I.  4 - n ii. 2n b)  4 x 4 / 3  answer: 16 /6 Question 11 ) a) 18,29 b) 7 c)  y-x,  x+y,  2y + x Question 12 ) a) to make it easier to work out the area b) 6400 x 3 = 19,200 answer: 19,200 Question 13 ) a) just look at the answers b) 9 x 6 = 54 answer: 54 Question 14 ) 30/330 = 1/11 answer : 1/11 Question 15 ) 160 / 2.5 = 64 answer: 64 Question 16 ) 8 + 3 = 11 (6400 + 16200) / 11  answer: yes Question 17 ) a) x = y+3/7 b) I. you know how to solve this ii. ( x+6)( x + 2) Question 18 ) 75 x 4 = 300  300 - (76 x 2 ) = 148 answer: 69.76,76,79 Question 19 ) a) 11/3: 5/2 answer:  22:15 b) 90 + 132 + 36 = 258 answer: 258 Question 20 ) Question 21 ) a) b) all the sides are the same length   my answers:

Notes: Question 1) c) 1/5 Question 2) 8400 x 0.12 = 1,008 (1,008 x 3) + 8400 = 11,424 answer: 11,424 Question 3) b) z = 14 or z = -14 Question 4) Question 5) Question 6) a)  i.  Certain ii. evens b) i. 6 ii. 21/55 iii. 28/55 Question 7) 11 x £15.65 = £172.15 £403.51 - 172.15 = 231.36 231.36 / 24 = 9.64 answer: 9.64 Question 8) a) 50 / 40 = 1.25 720 / 1.25 = 576 answer: 576 b) 50 x 2 = 100 20 x 4 = 80 10 x 9 = 90 5 x 12 = 60 100 + 80 + 90 + 60 = 330 330 / 1.17 = 282 answer: 282 Question 9) Question 10) a) i. 15,11 ii. 38 and 193 b) 4n + 1 Question 11) a) 380/1000 x £2 = 0.76 answer: 0.76 b) 280/ 20 = 14 answer: 14 Question 12) 2 x ( 12 + 15 + 7.4 ) = 68.8 answer: 68.8 Question 13) a)  12.65 < m < 12.75 b) Question 14) b) Rotation centre (0,0) 90 clockwise Question 15) Question 16) a) ii. No, because the markings in relevant region are above 2mm Question 17) a) Question 18) Question 19) Question 20) Question 21) Question 22) my answers: