Muchemi

1 21 1(mod 23) 22  or 21 21(mod 23) 23  or 21 2(mod 23) 23  − B1 1.2 80 3 21 (mod 23) =   +  80 3 8 21 (mod 23) =   +  −  M1 1.1b For example  −  −    − −   −    (( 2) ( 2) 16 4 ( 7) 7 4 49 28 3 18 54 4 2 3 2 )3  −  ( 2 mod 23 16384 mod 23 )14 ( ) ( )  −  ( 2 4 mod 23 )14 7 ( ) ( )  −  −    (( 2) ( 2) 3 )3   21 441 4 mod 2 =   = = ( ) ( )7 ( )7   (3 7...

1(a) Form an expression for total KE M1 3.1a 1 1 2 2 2 2 3 (3 ( 1) ) 2 (( 6) 2 ) 2 2   + − +   − + A1 1.1b = 55 (J) A1 1.1b (3) 1(b) Use of change in momentum M1 3.1a 2 3 ( 2 ) (3 ) 3     − + − −   i j i j A1 1.1b = ( 15 5 ) − + i j (N s) A1 1.1b (3) 1(c) Either: Use impulse on B to form equation M1 3.1a (15 5 ) 2 ( 6 2 ) i j v i j − = − − + ( B ) A1 1.1b vB = (1.5 0.5 ) i j − (m s-1) A1 1.1b Or: Use CLM to form equation M1 3.1...

1 (a) Awrt 2.485 B1 1.1b (1) (b) h = 0.5 B1 1.1b 1 "0.5" 1.946 3.332 2 2.485 2.944 4 2.225 2.725 3.1 ( ) ( 46) 3  + + + + + +     1 48.52 6 =  M1 1.1b 8.09 cao A1 1.1b (3) (c) 0.5 "8.09" 4.045 or 4.04  = or 4.05 (awrt either) B1ft 2.2a (1) (5 mar

1(a) z = − 2 5i B1 1.2 (z z − + − − = (2 5i 2 5i ... ))( ( )) or Sum of roots = 4, Product of roots = 29 → z2 +... M1 3.1a = − + z z 2 4 29 A1 1.1b z z az bz z z z cz 4 3 2 2 2 − + + + = − + + + ( )( ) M1 3.1a z z 2 − + = 2 5 0 A1 2.2a z z z 2 − + =  = 2 5 0 ... M1 1.1b z =  1 2i A1 1.1b (7) (b) B1ft 1.1b B1 1.1b (2) (9 marks) Notes (a) Note: if there are multiple attempts or attempts which start in main scheme before switching to an Alt, then mark t...

1(a) Knowledge 2, Application 2, Analysis 1 Knowledge/implicit understanding and analysis: up to 3 marks e.g. ● The percentage change in quantity demanded is less responsive to a change in price (1) ● Is relatively low e.g. between 0 and -1 (or 0 and 1) / PED<1 (1) ● Diagram showing price inelastic demand (1) ● An increase in price will result in an increase in total revenue (1) ● Reference to a characteristic e.g necessity, small proportion of income, few substitutes (1)...

1(a) Knowledge 2 Application 1 Analysis 1 Knowledge/Analysis: Up to 3 marks for one reason e.g. • Price elasticity of demand measures the responsiveness of demand to a proportionate change in price/formula (1) • Closeness of substitutes (1) young people have greater availability of substitutes – bus, walk, cycle/closer substitutes/adults bus dependent (1) • Proportion of income spent (1) greater proportion for younger people spent on bus travel (1) • Degree of necessity (1) ...

1(a) Knowledge/understanding 2, Application 2, Analysis 2, Evaluation 2 • September’s figure of 83,135 EVs is near the capacity of the factory which is 88,000 • Tesla’s capacity utilisation is therefore • 83,135 x 100 88,000 = 94.5% (94.47%) • For Tesla the nearer it gets to 100% capacity utilisation the more efficient the factory becomes as all resources are being used and average costs should reduce • Under-utilisation of 5.5% means that some resources such as machine...

1(a) Knowledge/understanding 1, Application 3 Knowledge/understanding: 1 mark for correct formula for calculating index: (Average price of bread in 2023/Average price of bread in 2018) x 100 OR (price in current year/price in base year) x 100 (1) Application: up to 3 marks for calculating the index for 2023: £1.36/£1.05 (1) = 1.295 1.295 x 100 OR 1.30 X 100 (1) and 1 mark for the correct answer: 130 (1) NB if no working is shown award marks as below: • If the answer given is 1...

1(a) Knowledge/Understanding 1, Application 2 Analysis 1 Knowledge/Understanding: up to 1 mark for explaining a reason e.g. • It can gain economies of scale (1) Application: up to 2 marks are available for contextualised answers, e.g. • TUI can spread its fixed costs over more passengers (1) • TUI has lost market share to Jet2holidays and wants to be market leader (1) Analysis: Up to 1 mark available for developing the reason. • Reducing average costs could allow TUI to lowe...

1(a) An answer that makes reference to the following points: • (the relative isotopic mass is) the mass of an atom (of an isotope) • relative to 1/12 of the mass of a carbon-12 atom or relative to a carbon-12 atom which has a mass of (exactly) 12 (1) (1) Allow weight for mass Do not award reference to average/mean mass Accept divided by 1/12 of the mass of a carbon-12 atom Allow reference to moles such as The mass of one mole of atoms of an isotope relative to 1/12 of the mass...