1. Number a. Using a calculator or otherwise 1 3 1 5 i. 3 1 4 18 5 ii. 0.1014 5.47 1.5 5.47 0.6 5.1 b. Bus tour tickets
. Algebra a. Write as a single fraction 3 4 11 3 4 1 b. 1 5 c. Factorize completely i. 36 6 6 ii. 5 1 4 3 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 15 1 8 8 35 8 7 Part b is deliberately omitted
4. Functions, relations a. Calculate i. 3 1 f ( ) 4 7; g( ) 1 16 1 g(0) g(5) 8 ii. 3 1 f ( ) 4 7; g( ) fg(5) f (8) 5 iii. f ( ) 4 7 f 1 (1) 4 7 1 4 7 1 b. Coordinate Geometry y y1 i. Gradient of PQ 1 7 ( 1) 6 1 y1 y 6 1 7 ii.,, 4,3 The midpoint of PQ iii. The equation of the perpendicular bisector y y m 1 1 1 y 3 4 1 y 1
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)
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.75 0.5 11units b. Circle measurements i. Calculating the diameter; Using Pythagoras theorem, any two sides of the square and AC as the diameter 11 11 AC 11 AC 11 11 AC 11 AC or 11 11 AC 4 AC AC 4 11 11 AC 11
ii. The area of the circle 1 radius 11 7.78 cm A r 7.78 A 190.06cm iii. The area of the square is 11cm iv. The area of the shaded region 190.06cm 11 17.7 4 cm 7. Statistics a. Draw the bar chart b. Range is Highest lowest 75 40 = 35
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
b. Copy and complete the table
9.. a. Variation i. k y k y k ii. k 6 3 6 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 6 8 0 4 ii. The minimum point is 3, 1 6 8 3 1 iii. iv. Draw the graph
v. Solving 6 8 5
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
ii. Calculate BC, using the cosine rule BC 90 310 90 310 cos 60 BC 76km iii. Calculate angle ABC using the sine rule 310 76 sin ABC sin 60 310sin 60 ABC 76 ABC sin 0.973 77 1 0 0 iv. The bearing of C measured from B 360 150 77 133 11. Vectors and Matrices a. Matrices i. c 0 0 b3 3 c 1 b 1 1 0 5 5 0 1 4 4 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 1 0 0 1
b. Vectors i. OP 4 1 ii. 3 QR 5 iii. The magnitude of QR 3 5 34 iv. Show that PQRS is a parallelogram PQRS is a parallelogram because QR = PS and QP = RS, opposite sides are equal