Answer the Following Questions

$10.00

Jamie purchases 8 basketballs for the same price, and also a backboard and rim for $115. His total bill is $295. Using ‘b’ to represent the cost of one basketball, write an algebraic equation to represent Jamie’s bill.

 

 

SKU: Math656432

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 -3b -3+ 9+6a-4b+2

b)2x²y-3+4xy²-7x²y+4y²x

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

 

4.Given that a=-4 and b=-½,evaluate:

a)3ab

b)4b+a²

 

5.Solve the following equations:

For non-integer solutions give fractions in simplified form.

a)7x − 4 = 17

b)3(6 − y) = 4y − 3

c)

maths

 

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:

180

 

 

01

 

 

 

 

 

 

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.

= −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.

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