1.

Simplify.
-1 +

2.

Consider the sequence
1, 3, 6, 10, ...

(a)

Find the 10th term.

(b)

Write down an expression for the nth term.

3.

Solve for x and y:

4.

Make t the subject of the formula.

5.

Two mechanics take 4 hours to repair a car. If each of them worked alone, one of them could do the job in 1 hour less time than the other. How long would it take the slower one to complete the job alone? Express your answer to the nearest tenth of an hour.

6.

A tank contains 430 L of water, correct to the nearest liter. The water is completely drained off in 1 h 20 min, correct to the nearest minute. Find the limits between which the average rate of draining in liters per minute must be, correct to 3 significant figures.

7.

Draw a graph of y = x² + 2x - 1 from x = -4 to x = 2

(a)

From the graph, find the solution of
x² + 2x - 1 = -x + 1 for -3 x 2

(b)

Find the coordinates of the point at which the gradient of a tangent to the curve is equal to -1.

8.

The maximum load of a horizontal beam that is supported at both ends varies directly as the width and the square of the height and inversely as the length between the supports. A beam 16 m long, 0.2 m wide, and 0.08 m high supports a load of 480 kg. What is the maximum load supported by a beam 6 m long, 0.1 m wide, and 0.06 m high?

9.

Two circles with centers at O and P intersect at A and B. The radius of the smaller circle is 4 cm.
AOB = 120^o, APO = 60^o. Find the area of the shaded portion to the nearest tenth of a cm. Take = 3.14.

sin 60^o =
cos 60^o =
sin 180^o = 0
cos 180^o = 1

10.

Town A is 16 km from Town B on a bearing of 58^o. Town C is 18 km from Town B on a bearing of 178°.

(a)

Find the distance between Town A and Town C to 3 significant figures.

(b)

Find the bearing of Town C from Town A to the nearest degree.

11.

f(x) = 3 - 4x
g(x) = 2x² - 5x
h(x) = f(x) + g(x)

(a)

Express h(x) in terms of x

(b)

Find h[f(-2)]

(c)

Find f^-1[g(4)]

12.

O is the center of a circle. A, B, C, and D are points on the circumference of the circle. PQ is a tangent to the circle at point D.
BOD = 118^o and CBD = 42^o.
Find x and y

13.

O is the center of a circle. A, B, C, and D are points on the circumference of the circle. PQ is a tangent to the circle at point D.
AED = 45^o and EDF = 65^o.
Find w, x, y, and z.

14.

= {x: x is an integer, 0 < x 10}
A = {x: x is an even number}
B = {x: 3 x < 7}
List the members of (A B) (A B)'

15.

Twenty four cows are in a field. Twelve of the cows are black, the rest are brown. Six of the cows have horns and fifteen of the cows have a white face. There is only one cow that is black with horns and a white face. Two of the cows are black with horns and do not have a white face. Two of the cows have horns and a white face but are not black. Eight of the cows are entirely black. How many cows are black with a white face but do not have horns?

16.

A particle moves in a straight line. The distance d in meters traveled and the time t in seconds is given by the following:

Plot d against t and estimate the speed of the particle at 1 second.

17.

An object starts from rest and increases its speed steadily to a maximum speed at 5 seconds and 50 m from its starting point. It moves at this speed for 7 seconds and then slows down at a steady rate until it stops after another 3 seconds. Find the distance it traveled in the last 10 seconds.

18.

The vertices of the ABC are A(1, 1), B(3, 1) and C(1, 2). ABC is transformed to A₁B₁C₁ by a shear with y axis invariant and factor 2. Give the vertices of A₁B₁C₁.

19.

The height of 100 plants in cm is given in the following table:

Height (cm)	2.0	4.0	8.0	10.0	12.0	14.0	16.0	18.0
Number of plants less than this height	0	6	24	40	60	78	92	100

Graph this data and use the graph to find:

(a)

The median height.

(b)

The interquartile range.

20.

Below is a wedge whose ends form identical right angled triangles. If the volume of the wedge is 900 cm³, find the lengths of the three edges at the end of the wedge (AB, BC, and AC).