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Revision QuestionsPreliminary Course

1 Given that 5sin13

and that is acute, derive values for cosand tan .

2 A fair coin is tossed 3 times. By using a probability tree, or otherwise, find the probability that the result is:a. All tailsb.

2 tails

c. At least one head3 Find the equation of the line with gradient 2

3 that bisects the interval AB where A has coordinates 3,4

and B is 5, 2 .

4 If 2 3x , write 1x

with a rational denominator.

5 Find derivatives of:a. 915 8x b. 7 4

7 4

x

x

6 Two straight roads from C to A and C to B make an angle of 146 at C. If the distance from C to A is 23km andfrom C to B is 18.5km, then find the shortest distance from A to B correct to one decimal place.

7 Find 24d xdx

8 Derive the equation of the tangent to 23 5y x at the point where 1x 9 Solve for x :

a. 7 40 3x x b. 26 42x x c. 2 11 30 0x x d. 22 5 2 0x x

10 The curve 3 2 2y x x x cuts the x axis at A, B and C. Find the coordinates of A, B and C.a. Find the equation of the tangent to the curve at Cb. This tangent cuts the y axis at N. Calculate the area of ANC

11 Write down the factors of 23 10x x 12 Solve and graph the values of x satisfying 4 4x 13 2,2 , 3,4A B and 1,0C are points on the number plane. A line, k, passes through C parallel to AB.

a. Calculate the length of ABb. Find the gradient of AB and hence the equation of the line ABc. Calculate the acute angle made by the line AB and the positive direction of the x axisd. Find the equation of the line k

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14 1Jennifer, during a bushwalk, walks 1.2km on a bearing of 178 to T, then turns due East and walks a further1.6km to V . Calculate Jillians distance from her starting point, S (correct to 2

significant figures)

15 Find the size of each interior angle of a regular octagon.a. A square, ABCD, is drawn alongside a regular octagon using one side (CD) of

the octagon as a side of the square. Calculate the size of ADP , giving

adequate reasons.

16 Find the largest angle in a triangle with sides 9cm, 11cm and 17cm.17 Show that a triangle whose sides satisfy 2 0x y , 2 5x y and 3 20x y is both right angled and

isosceles.

18 Solve for 5: 42

xx x

19 Solve and graph the values of x for which 2 3 4x x 20 Georges top drawer contains 5 white socks and 3 red. George chooses two socks at random. Find the

probability that George has selected:

a. Two white socksb. One white sockc. No white socksd. At least one white socke. Two of the same colour

21 AB CD .Given that 35EAB ,

120AEG , calculate the value for y , giving full reasons.

22 A function is defined such that 4 for 0

4 for 0 5

1 for 5

x

f x x x

x

a. Write down the values of 2 , 0 , 3 , 6f f f f b. Hence, or otherwise, sketch y f x for 2 6x

23 Find the equation of the normal to 12 5

yx

at the point where 2x

24 Sketch the region where both 29y x and 3 3x y hold simultaneously.25 In Ashs gloveboxthere are 5 twenty-cent pieces and 4 fifty-cent pieces. He chooses two coins at random.

Find the probability that the coins chosen are:

a. Both twenty-cent piecesb. Neither twenty-cent piecesc. At least one twenty-cent piece.

A

B C

D

P

C

A B

E

GD