Surds
Simplify root 90
3 root 10
2x2 - 18
2(x-3)(x+3)
Expand and simplify:
(x+6)2 - (x-6)2
(x+6)2 - (x-6)2
= x2 +12x + 36 - (x2 -12x + 36)
= 24x
A plane climbs at a constant angle of 4 degrees after take-off.
Find its altitude (vertical height, to the nearest metre) when it has flown a horizontal distance of 500 metres.
tan (4) = x/500
x = 500 tan(4) = 35 metres
You get paid $21.25 per hour for a 38-hour working week.
Any overtime that you work is paid at the rate of time-and-a-half.
Last week, you worked 45 hours.
How much did you get paid?
45 - 38= 7 hours
$21.25*38 + 1.5*21.25*7
= $1030.63
root 5 + root 20
3 root 5
x2 - 7x + 12
(x-4)(x-3)
Solve the following pair of simultaneous equations:
7x - 3y = 22
3x - 7y = -2
x = 4
y = 2
Fabrizio ties a 4 metre rope to the top of a vertical pole.
He pulls the rope tight and pegs it into the ground 2 metres from the base of the pole.
Find the angle that the rope makes with the ground.
(Hint: Draw a diagram first.)
cos (angle) = 2/4
Angle = cos-1(0.5)
Angle = 60 degrees
You take a loan of $1000 over 4 years at 5% simple interest.
How much interest do you pay?
I=Prn
I=1000*0.05*4
I=$200
root 128 + root 18 - root 50
6 root 2
(x + 3)2 - 16
(x-1)(x+7)
Old MacDonald's farmyard has pigs and chickens. Altogether, there are 60 heads and 200 legs.
(Old MacDonald is not home. )
How many pigs are in the yard?
p + c = 60
4p + 2c = 200
Solve...
There are 40 pigs in the yard.
Natalia is standing on top of a 12 metre cliff. She spots Arrielle in a boat 23 metres from the base of the cliff.
Calculate Natalia's angle of depression to Arrielle (to the nearest minute).
27˚33'
What is the simple interest rate if you borrow $500 for two years and pay $80 interest?
I=Prn
80=500*2*r
80/(500*2) = r
r = 0.08 or 8%
Rationalise 15 root 2 / root 3
5 root 6
5x2 + 13x - 6
(x+3)(5x-2)
Chiara was counting coins in the cafe. She has 22 coins, each of which is either a one-dollar coin or a two-dollar coin. She has a total of $35.
How many of each type of coin does she have?
Nine $1 coins and thirteen $2 coins
Esmerelda walks for 490 metres on a true bearing of 140 degrees from the campsite to the waterfall.
How far south is the waterfall from the campsite?
(Answer to the nearest metre.)
490cos(40) = 375 metres
Fabrizio works a normal week of 30 hours and is paid at an hourly rate of $10 per hour.
Overtime is paid at time-and-a-half.
Last week, Fabrizio earned $375.
How many hours did Fabrizio work last week?
Normal week: $10*30 = $300
$375 - $300 = $75
Time-and-a-half rate = 1.5 * $10 = $15
$75/15 = 5 hours overtime
Total hours worked = 30 + 5 = 35 hours
Rationalise 4 / root 5 + 1
root 5 - 1
Simplify: x2 - 9 / 2x2 + 5x - 3
x - 3 / 2x - 1
The shortest side of an isosceles triangle is 14 cm shorter than another side. Its perimeter is 88 cm.
What is the area of the triangle?
(Do not round early!! Answer to the nearest square centimetre.)
325 square centimetres
Charlotte travels 7 km due east of her starting point, and then 3 km due south.
Calculate the bearing from her current position to her starting point (nearest degree)
293˚
You invest $5600 in a bank account for 3 years.
The interest rate is 9% p.a. compounded monthly.
What amount is in your bank account at the end of 3 years?
A = P(1+r)n
A = 5600(1+9%/12)3*12
A = $7328.41