**1.** Evaluate the following:

Give any fractions in simplified form.

a) 6² – 8 × 2 ÷ (4 – 8)

b)5/6 ÷ 4/3

**2.** Complete the following:

Fraction | Decimal | Percentage |

2/5 | ||

0.65 | ||

42% | ||

1.75 |

**3.**Simplify the following:

a)5*a²* -3*b* -3+ 9*a²*+6*a*-4*b*+2

b)2*x²y*-3*x²*+4*xy²*-7*x²y*+4*y²x*

c)*m*(*m*-5)+2(*m*-1)

**4.**Given that *a=*-4 and *b=-½,*evaluate:

a)3*ab*

b)4*b+a²*

**5.**Solve the following equations:

For non-integer solutions give fractions in simplified form.

a)7*x* − 4 = 17

b)3(6 − *y*) = 4*y* − 3

c)

**6.**Jamie purchases 8 basketballs for the same price, and also a backboard and rim for $115. His total bill is $295.

a)Using ‘b’ to represent the cost of one basketball, write an algebraic equation to represent Jamie’s bill.

b)How much does one basketball cost?

**7.** The length of a circular curve is given by the formula:

Where: L = length of curve in centimeters (cm)

r = radius of curve in centimetres (cm)

θ = angle of curve in degrees (q)

π = constant = 3.142…..

(most calculators have a ‘π’ button, if possible use this instead of entering the rounded number given here)

a) Transpose the equation to make* r* the subject.

b) A student sitting in an exam finds themselves ‘clock watching’. The student estimates that the minute hand of the clock moves a distance of 20 cm round the face of the clock in 10 minutes.

Based on the student’s estimation, how long is the minute hand?

Hint: how many degrees (out of 360q) make up 10 minutes on a clock face?

**8.** a) Solve the following simultaneous equations using a method of your choice.

*y *= −2*x* + 3

−6*x* + 2*y* = 1

**9.** A manufacturing plant produces fixed size square and circular metal panels.

The mass of a square panel is 13kg and that of a circular panel is 22 kg.

Use algebraic techniques to find how many of each panel there are in a truck loaded with 65 panels of total mass 1205 kg.

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