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Power to Maths

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Submitted By thamim
Words 1102
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|Question |Working |Answer |Mark |Notes |
|1(a) | |(400 – 308)/2 + 1 |47 |2 |M1 for (400 – 308)/2 or 46 seen |
| | | | | |A1 cao |
| | | | | | |
|1(c) | | |2n – 1 |2 |B2 cao |
| | | | | |[B1 for 2n ± k where k ≠ -1] |
|2(a) | | |4 5 6 7 8 |2 |B2 for a fully correct table |
| | | |5 6 7 8 9 | |[B1 at least 5 correct entries] |
| | | |6 7 8 9 10 | | |
| | | | | | |
|2(b) | |P(7 or 8) = 7/24 |A loss of £15 |5 |M1 for P(7 or 8) {= 7/24}or P(9 or 10) {= 3/24} oe |
| | |P(9 or 10) = 3/24 | | |M1 for ‘7/24’ x 360 x 1( = 105) or’3/24’ x 360 x 2 (= 90) |
| | |7/24 x 360 x 1 = 105 | | |M1 for 360 x 0.5 (= 180) |
| | |3/24 x 360 x 2 = 90 | | |A1 for 180 and 195 seen |
| | |Takings = 360 x 0.5 = 180 | | |C1 for ‘a loss of £15’ oe |
|3(a) | |√(48/3) |±4 |2 |M1 for √(48/3) |
| | | | | |A1 for 4 or -4 or ±4 |
|3(b) | |2x + 4 = 6(x – 1) |2.5 | | |
| | |2x + 4 = 6x – 6 | |3 |M1 for 2x + 4 = 6(x – 1) |
| | |10 = 4x | | |M1 for 4 + 6 = 6x – 2x |
| | | | | |A1 cao |
|4 | |9 x 8 + ½ x 5 x 12 |102 |4 |M1 for splitting |
| | | | | |M1 for either 9 x 8 or ½ x 5 x 12 oe |
| | | | | |M1 for 9 x 8 + ½ x 5 x 12 |
| | | | | |A1 cao |
|5(a) | | |Vague response boxes |2 |B1 for a correct criticism of the question |
| | | |Question does not include a time period| |B1 for a correct criticism of the response boxes |
| | | | | | |
| | | |How many times a month do you go to a | | |
|5(b) | | |restaurant? |2 |B1 for a relevant question inc. time period |
| | | |0 1 – 3 4 – 5 6+ | |B1 for at least 3 non-overlapping response boxes |
| | | | | | |
| | | | | | |
|5(c) | | |A leading question |2 |B1 for a ‘leading/biased’ question oe |
| | | |Restricted/biased sample | |B1 for ‘small/biased’sample oe |
| | | | | | |
|6(a) | |19.5 + 19.5/5 |23.40 |3 |M1 for 19.5/5 |
| | | | | |M1 for 19.5 + 19.5/5 oe |
| | | | | |A1 cao |
| | | | | | |
|6(b) | |72 ÷ 6 = 12 |24 |3 |M1 for 72 ÷ 6 |
| | |12 x 2 | | |M1 for ‘12’ x 2 |
| | | | | |A1 cao |
| | | | | | |
|7 | |(1 – 0.3 – 0.2)/2 x 200 |50 |4 |M1 for 1 – 0.3 – 0.2 |
| | | | | |M1 for (1 – 0.3 – 0.2)/2 or 0.25 seen |
| | | | | |M1 for ‘0.25’ x 200 |
| | | | | |A1 cao |
|8 | |½ x 6 x 8 x 2 + (8+6+10) x 9 |264 cm2 |4 |M1 for ½ x 6 x 8 or 8x9 or 6x9 or 10x9 |
| | | | | |M1 for ½ x 6 x 8 x 2 + (8+6+10) x 9 oe |
| | | | | |A1 for 264 |
| | | | | |B1 ft for cm2 |
|9(a) | | |9, 3, -1, -3, -3, -1, 4 |2 |B2 for fully correct table |
| | | | | |[B1 for 1 or 2 correct entries] |
| | | | | | |
|9(b) | | |Graph |2 |B2 ft for a fully ‘correct’ graph through their points |
| | | | | |[B1 at least 6 of their correctly plotted points] |
| | | | | | |
|9(c) | | |-3.25 |1 |B1 for an answer in the range –3.1 to -3.5 |
|10(a) | |6/12 |½ |2 |M1 for 6/12 oe |
| | | | | |A1 cao |
| | |[pic] |[pic] | | |
|10(b) | | | |3 |M1 for [pic] |
| | | | | |M1 for [pic] |
| | | | | |A1 cao |
| | | | | | |
|11(a) | |44800 ÷ 5 |8960 |2 |M1 for 44800 ÷ 5 |
| | | | | |A1 cao |
| | | | | | |
|11(b) | |7130 x 5 |35650 |2 |M1 for 7130 x 5 |
| | | | | |A1 cao |
|12(a) | |3x > 2 – 12 |x > -10/3 oe |2 |M1 for 3x > 2 – 12 |
| | | | | |A1 for x > -10/3 or better |
| | | | | | |
|12(b) | |x2 – 7x + 3x – 21 |x2 – 4x – 21 |2 |M1 for 3 correct out of 4 terms or 4 correct terms ignoring signs |
| | | | | |A1 for x2 – 4x – 21 oe |
|13 | |165 ÷ 82 > 2 |Since 165 ÷ 82 > 2 |3 |M1 for considering 165 ÷ 82 or 133 ÷ 82 oe |
| | |133 ÷ 82 < 2 |and 133 ÷ 82 < 2, the scale factors are| |A1 for correct estimated answers |
| | | |different; so not similar | |C1 for a correct conclusion based upon their answers |
| | | | | | |
|14 | | |Triangle with coordinates (-3,-1.5), |3 |B3 for a correct triangle |
| | | |(-4.5,-1.5) and (-3,-4.5) | |[B2 for an enlargement of 1.5 about (0,0) or for an enlargement of -1 about |
| | | | | |(0,0) |
| | | | | |B1 for an enlargement of 1.5 about any point] |
|15(a) | |[pic] − 5 = 3x – 6 |3/8 |4 |M1 for 3x – 6 |
| | | | | |M1 for x − 15 = 9x – 18 |
| | | | | |M1 for rearranging so that numbers and x-terms or on opposite sides of the |
| | | | | |equation |
| | | | | |A1 for 3/8 oe |
| | |(x – 6)(x + 3) | | | |
|15(b) | | |x= 6 and x = -3 |3 |M1 for (x ± 6)(x ± 3) |
| | | | | |A1 for x = 6 and |
| | | | | |A1 for x = -3 |
|16(a) | |26 |64 |1 |B1 cao |
| | | | | | |
|16(b) | | |3 |1 |B1 cao |
| | | | | | |
|16(c) | |√(24x32) = 22 x 3 |12 |2 |M1 for 22 x 3 oe |
| | | | | |A1 cao |
| | | | | | |
|16(d) | |1/42 |1/16 |1 |B1 cao |
| | | | | | |
|17(a) | |4 = k/32 |9 |4 |M1 for F = k/x2 |
| | |F = 36/x2 | | |M1 for 4 = k/32 |
| | |36/22 | | |M1 for ‘36’/22 |
| | | | | |A1 cao |
| | | | | | |
|17(b) | |64 = 36/x2 |3/4 |2 |M1 for 64 = 36/x2 |
| | |√(36/64) | | |A1 cao |
|18 | |[pic] |10/21 | |M1 for [pic] |
| | |[pic] | | |M1 for [pic] |
| | | | | |M1 for [pic] |
| | | | | |A1 for 10/21 oe |
|19 | |√8(√5 + √20) - √5 × √2 |83.33… |4 |M1 for √8(√5 + √20) - √5 × √2 oe |
| | |=2√2(√5 + 2√5) - √5 × √2 | | |M1 for 2√2(√5 + 2√5) - √10 |
| | |=2√2×3√5 - √5 × √2 | | |M1 for 5√10 / 6√10 x 100 |
| | |=6√10 - √10 = 5√10 | | |A1 for 83.33… |
| | |5√10 / 6√10 x 100 | | | |
| | |500/6 | | | |
|20(i) | |q + ½ (p – q) |½ (p+q) |5 |M1 for QP = q – p |
| | | | | |M1 for OS = q + ½ QP |
|(ii) | |RS = ½ (p+q) – ½ p = ½ q |Proof | |A1 for ½ (p+q) |
| | |RS = ½ OQ parallel | | |M1 for RS = ½ (p+q) – ½ p |
| | | | | |C1 for conclusion of proof; ie RS = ½ q and relating this to OQ = q |
|21(a) | | |πx2/3 |2 |B1 for πx2/3 oe |
| | | |2πx/3 | |B1 for 2πx/3 oe |
| | | | | | |
|21(b) | |A = 2πx/3 = 2πr |27 |3 |M1 for 2πx/3 = 2πr |
| | |r = x/3 | | |M1 for 1/3 x π x (x/3)2 x h = 3 x πx2/3 |
| | |V = 1/3 x π x (x/3)2 x h = 3 x πx2/3 | | |A1 cao |
| | |1/3 (1/3)2 x h =1 | | | |

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