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1 1. Number a. Using a calculator or otherwise i ii b. Bus tour tickets
2 . Algebra a. Write as a single fraction b. 1 5 c. Factorize completely i ii d. V r r h V r h V h e. a a b 3 a a b 4 1 a 4, b 1 3. Sets and construction a. Sets Part b is deliberately omitted
3 4. Functions, relations a. Calculate i. 3 1 f ( ) 4 7; g( ) g(0) g(5) 8 ii. 3 1 f ( ) 4 7; g( ) fg(5) f (8) 5 iii. f ( ) 4 7 f 1 (1) b. Coordinate Geometry y y1 i. Gradient of PQ 1 7 ( 1) 6 1 y1 y ii.,, 4,3 The midpoint of PQ iii. The equation of the perpendicular bisector y y m y y 1
4 5. Plain geometry and transformations a. Consider the triangles RST and RPQ are corresponding to each other Also RTS and RQP are corresponding to each other meaning RST = RPQ and RTS = RQP RS ST RP PQ 15 4 PQ 19.cm 1 PQ Coordinates of E (4,) The transformation that maps triangle DEF to D E F is a 90 degree anticlockwise rotation with center (0, 0)
5 6. Measurement a. Measurement on the map i. 1 cm : 5000cm 1 cm : 0.5km 31.8 km ii. 1 cm : 5000cm 1 cm : 0.5km units b. Circle measurements i. Calculating the diameter; Using Pythagoras theorem, any two sides of the square and AC as the diameter AC 11 AC AC 11 AC or AC 4 AC AC AC 11
6 ii. The area of the circle 1 radius cm A r 7.78 A cm iii. The area of the square is 11cm iv. The area of the shaded region cm cm 7. Statistics a. Draw the bar chart b. Range is Highest lowest = 35
7 c... i. The greatest production occurred in 011 ii. This information is shown with the height of the bar, it s the highest bar d... i. The greatest change occurred between 011 and 01 ii. The difference between the bars is larger here than with the other consecutive years e. The bar chart is used for comparisons, there s no trend line to show what might happen in future years. 8. Problem solving/investigation a. Draw the net figure
8 b. Copy and complete the table
9 9.. a. Variation i. k y k y k ii. k so; y iii. Calculating a and b 6 1. ; 6 5 a 1. 6 y 6 y 0.3 b 0 b. Quadratic Function i. The solutions of ii. The minimum point is 3, iii. iv. Draw the graph
10 v. Solving 6 8 5
11 10. Measurement, geometry and trigonometry a..circle theorem i. HKL 0 HJL 0, angles in the same segment are equal ii. 0 JOK 80, Triangle JOK is isosceles, OKJ=OJK iii. 0 JHK 40, Triangle HJK is a right angled triangle, JHK and HKJ are complimentary b. Bearings i. Complete the diagram
12 ii. Calculate BC, using the cosine rule BC cos 60 BC 76km iii. Calculate angle ABC using the sine rule sin ABC sin sin 60 ABC 76 ABC sin iv. The bearing of C measured from B Vectors and Matrices a. Matrices i. c 0 0 b3 3 c 1 b ii. 5, 4 iii. The transformation T is a reflection in the -ais iv. The transformation that maps Q back unto P is the same transformation T
13 b. Vectors i. OP 4 1 ii. 3 QR 5 iii. The magnitude of QR iv. Show that PQRS is a parallelogram PQRS is a parallelogram because QR = PS and QP = RS, opposite sides are equal
b UVW is a right-angled triangle, therefore VW is the diameter of the circle. Centre of circle = Midpoint of VW = (8 2) + ( 2 6) = 100
Circles 6F a U(, 8), V(7, 7) and W(, ) UV = ( x x ) ( y y ) = (7 ) (7 8) = 8 VW = ( 7) ( 7) = 64 UW = ( ) ( 8) = 8 Use Pythagoras' theorem to show UV UW = VW 8 8 = 64 = VW Therefore, UVW is a right-angled
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