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:
3.Simplify the following:
a)5a² -3b -3+ 9a²+6a-4b+2
4.Given that a=-4 and b=-½,evaluate:
5.Solve the following equations:
For non-integer solutions give fractions in simplified form.
a)7x − 4 = 17
b)3(6 − y) = 4y − 3
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 = −2x + 3
−6x + 2y = 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.