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Question 1.
1. Evaluate
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Marks
4.51  174
.
correct to 2 significant figures.
15.6  219
.
2. Simplify fully
50 +
98 – 9 2
3. Rationalise the denominator of
1
2
8
62
2
4. Solve 3x² + 4x – 1 = 0 , giving answers in simplest surd form.
3
5. Factorise x3 – 27
1
Question 2.
(Start a new page)
1. Solve | 3x – 4 | = 1 – 5x
2. Solve
2x  1
3x  4
–
= 5
3
2
3. Solve and graph the solution on a number line:
3
3
3
| 2x + 7 | < 5
4. Simplify fully
x 2  49
2 x 2  13x  7
3
2
Question 3.
(Start a new page)
Marks
1. Determine whether the function f(x) = 7x5 + 5x is odd, even
or neither. (Reasons must be shown)
2. If f(x) =
x2 + 1
for x  0
1
for 0 < x < 2
3 – x
for x > 2
2
(a) Evaluate f( –1 ) – f( 5 )
1
(b) Draw a neat sketch of this function over the domain –3  x  3
3
2. On separate diagrams, draw a neat sketch of the following
( showing all essential features)
(a) y = 3x
2
(b) y = 6x – x2
2
4. State the natural domain of y =
Question 4.
1
x2
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1. Find the value of x correct to 2 decimal places
xm
2
2
15·6m
57º
2. Find the exact area of  ABC where AC = 6m, BC = 8m
and ACB = 45º.
2
3
3.
Marks
P
16m
17m
39º
Find the size of PQR to the
nearest minute
2
R
Q
3. A man walks 7km on a bearing of 200º T from town A to town B.
He then walks 3km due north from town B to town C.
(a) Draw a diagram showing his journey.
1
(b) Calculate the distance and bearing of town C from town A.
4
Question 5.
(Start a new page)
1. A (–2,–1), B (7,2) and C (–3,4) are the vertices of a triangle.
(a) Calculate the length of AB in simplest form.
2
(b) Show that the equation of AB is x – 3y – 1 = 0.
2
(c) Find the perpendicular distance from point C to the line AB.
2
(d) Hence find the exact area of  ABC ( in simplest form).
1
2. Shade the region that simultaneously satisfies
x + y  5
and
y  2
3
3. The lines 3x + 4y = 9 and 2x – 3y = –11 meet at point P.
(a) Find the coordinates of P.
3
(b) Find the equation of the circle with centre P and radius 4 units.
1
4. Find the value of k for which the lines 5x – 2y = 0
and 3x + ky = 7 are parallel.
3
4
Question 6.
(Start a new page)
Marks
1. Find the exact value of sec 135º.
2. Given sin A =
1
3
and tan A < 0, find the exact value of cos A.
7
2
3. Solve the following for 0º  x  360º
(a) cos x ( 2sin x + 1) = 0
3
(b) sin x = cos x
2
4. Fully simplify the following:
sin A
1  sin A
+
sin A
1  sin A
5. Draw a neat sketch of y = cos x
showing all essential features.
Question 7.
3
for 0º  x  360º
2
(Start a new page)
1. For the arithmetic series 56 + 53 + 50 + .......
(a) Find an expression in simplest form for the nth term.
2
(b) What is the value of the first negative term of the series?
3
2. The second and sixth terms of a geometric series are 2 and
2
125
3
respectively. Calculate the common ratio and the first term.
3. The cost of constructing a multi-storey building is $60 000 for the
first floor, $65 000 for the second floor and an extra $5 000 for each
successive floor.
Calculate the cost of the building if it has 30 floors.
3
5