HSC Mathematics & Extension Mathematics Pre-test

HSC Mathematics & Extension Mathematics Pre-testYou must show all working to achieve full marks.Question One (Algebraic Expressions)Simplify:

a)

b)

c)

d)

e)

f)

g)

Question Two (Expanding Brackets)Expand and simplify where possible:

a)

b)

c)

Question Three (Equations)Solve:a)

b)

c)

Question Four (Factorising)Factorise each expression completely:

a)

b)

c)

d)

e)

f)

g)

h)

Question Five (Binomial Expansions)Expand and simplify:

a)

b)

c)

d)

Question Six (Quadratic Equations)Solve:a)

b)

c)

Question Seven (Algebraic Fractions)Simplify as far as possible:a)

b)

c)

d)

e)

Question Eight (Geometry)Prove that

Question Nine (Curve Sketching)On the axes given, sketch the following graphs, showing all important points:

a)

b)

c)

d)

e)

f)

g)

h)

Question Ten (Trigonometry)Find the value of the pronumeral in each example:

a)

b)

c)d) Find the height of the tree:

e)Find the length of x, correct to one decimal place.

f)Find the size of the marked angle, correct to the nearest degree.

A

B

E

C

D

x

y

y

x

y

x

y

x

y

x

y

x

y

x

y

x

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