(1,3) and is parallel to the line with equation 2x y 4.

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1 Question 1 A straight line passes through the point The equation of the straight line is (1,3) and is parallel to the line with equation 4. A. B E. 4 Question The equation has A. no real solutions B. one rational solution one irrational solution two rational solutions E. two irrational solutions Question 3 The minimum value of 8 is A. 16 B E. 4

2 Question 4 The graph of a quadratic function is shown below. If the rule of the function shown above is a( b) c, then which of the following is true? A. a 0, b 0 and c 0 B. a 0, b 0 and c 0 a 0, b 0 and c 0 a 0, b 0 and c 0 E. a 0, b 0 and c 0 Question 5 The line with equation = m 5 is a tangent to the parabola with equation: = The possible values of m are: A. B. R E.

3 Question 6 Which one of the following relations is not a function? A. B. E. Question 7 The maimal domain of f () 3 1 is ( 4) A. B. E. R\{ 4} R\{ 1} R\{3} R\{4} R\{ 4, 1}

4 Question 8 The range of the function f :[1, ) R, f () 1 is given b A. [ 1, ) B. (0, ) [0, ) (1, ) E. [1, ) Question 9 If A. B. E. f () then f (a 1) is equal to a a 1 a a a a 3 a a

5 Question 10 The graph of the function g is shown below. The function g can be described as A. one-to-one B. one-to-man man-to-one man-to-none E. man-to-man Question 11 The function g: R R, g() 3 1 has an inverse g 1 with rule given b A. B. E. 3( 1)

6 Question The inverse function of the function shown above is given b A. B E. -1

7 Question 13 The graph of the function f () is shown below The rule for f could be A. 1 f ( ) 1 ( ) B. 1 f ( ) 1 ( ) 1 f ( ) ( 1) 1 f ( ) ( 1) E. 1 f ( ) 1 ( ) Question 14 When the polnomial The value of d is p() 3 3 d is divided b, the remainder is 11. A. 0 B E. 1

8 Question 15 The graph of the function g is shown below. g() The rule for g is A. B. E. g() 1 3 ( 3)3 1 g() 1 3 ( 3)3 1 g() ( 3) 3 1 g() ( 1) 3 3 g() 3( 1) 3 3

9 Question 16 The graph of the function a 3 b c d is shown below The values of a, b, c and d are given b A. a 6, b 3, c 1and d B. a 0.5, b 1, c and d 6 a 0.5, b 6, c 1and d 3 a 1, b 1, c 3and d 6 E. a 1, b, c 5and d 6 Question 17 The inverse of the matri is A B E

10 Question 18 The point with co-ordinates (a, b) is transformed under the matri according to the matri equation: = The values of a and b are: A. a = 3 and b = B. a= 9 and E.

11 Question 1 The flight path of a water bird is shown on the graph below. C A O B The bird takes off from the edge of a wharf at point A and enters the water. It snatches up a fish at point B; the lowest point on the bird s flight path, before fling to perch on top of a mast at point The bird s path is described b the function f with the rule: where represents the horizontal distance in metres, of the bird from the edge of the wharf. The variable represents the vertical distance in metres, of the bird from the water where the -ais represents the surface of the water. a. What is the height, in metres, of the wharf above the water? b. What horizontal distance in metres; correct to decimal places, from the wharf did the bird i. enter the water ii. eit from the water. 1 1 marks

12 c. Epress the rule for f in turning point form. = a( h) + k d. Find the distance, in metres, of the fish at point B i. horizontall from the wharf. ii. verticall below the wharf at point A. 1 1 marks The top of the mast is 7m verticall above the surface of the water. e. Find the horizontal distance, in metres, of the top of the mast from the wharf. marks

13 f. For the function f which represents the path of the bird s flight, write down i. the domain ii. the range. 1 1 marks g. Define completel the function f. marks Total s

14 Question Concrete guttering links a road surface and a nature strip along a suburban street. The road surface and the nature strip are both horizontal surfaces. A cross-section of the gutter is shown below. nature strip concrete gutter road surface The cross-section of the gutter can be represented b the function g : , a R, g( ) ( ) where the -ais represents the level of the road surface and the -ais passes through the point where the gutter meets the nature strip. The unit of measurement is the centimetre. a. Factorise ( ). b. On the set of aes below, sketch the graph of Indicate clearl on our graph g(). aes intercepts the coordinates of an turning points (epress coordinates correct to one decimal place where appropriate) the coordinates of the endpoints. 5 marks

15 c. Hence write down the value of a. The graph of the cubic function ( ) has two turning points. d. Eplain wh the graph of the function g has onl one turning point. e. What is the range of the function g? Epress values correct to 1 decimal place where appropriate. f. What is the vertical height of the nature strip above the road surface? g. What is the maimum height that the water collecting in the gutter can reach before it floods onto the road? Epress our answer correct to 1 decimal place.

16 A straight stick of length 30cm is thrown into the gutter. It rests against two points on the gutter which on the graph of g() coincide with the points (40, 3) and (60,0). nature strip straight stick road surface h. Find the length of the stick that protrudes (sticks out) past the end of the gutter. Epress our answer in cm correct to 1 decimal place. marks Total 13 marks

17 Question 3 Pinevale Secondar College is located close to the intersection point P of two major highwas. Relative to a set of co-ordinate aes, the route followed b these two highwas can be modelled b the linear equations: c, i. Write these simultaneous equations as a matri equation of the form A. X = K where X =. ii. Write down in eact form the inverse of matri A, A -1 iii. Solve the matri equation to determine the coordinates of point P,the intersection of the two highwas. marks a. The Pinevale Railwa station is located at the point S with co-ordinates (333, 176). The co-ordinates of Melbourne Central relative to this same set of aes are: ( 7, 64). Assuming that the railwa line runs in a straight line from S to Melbourne Central, determine: i. the gradient of this line ii. the angle that it makes with the positive -ais. Give our answer to the nearest degree.

18 iii. the co-ordinates of M, the midpoint of the line connecting S to Melbourne Central.. ( = 3 marks) b. Another railwa line runs through M and is at right angles to the Pinevale Melbourne Central line. Find the equation representing this railwa line. 3 marks T

1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.

1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3. Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient