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And two examples of present value? 1. Karen wishes to have $5000 saved in 3 years time for a holiday. Interest is compounded monthly at 6% p.a. What lump sum does he need to invest now to reach his target amount? You can do this using the little PV formula. The "lump sum invested now" is the...

V = U + AT U + AT = V AT = V - U T = (V - U)/A

There are really two simple conversions to remember. Make sure these are among the first things you write down onto the formula sheet. 1 cm3 = 1 mL 1 m3 = 1 kL That's it. You can rewrite your number and then just change the unit. Of course, we're often asked to give the capacity in litres...

Yes, the angle of depression is outside the right angled triangle, but using the rule of alternate angles in parallel lines (horizontals), the angle of depression is the same as the angle inside the triangle at the other end of the line of sight. If that makes sense.

Try to work out as many angles as you can before getting started. ^JML = 75° because it's an alternate angle to the given angle of depression. ^MJL = 15° because it makes up the 90° angle with the angle of depression (or it makes up the 180° angle sum in ∆JML). Now in ∆JMK, we have ^MJK =...

This is a really nasty question. But it does specifically ask for one thing, the product of the class centre of the 30-39 group and its frequency. There are five scores in this group; 35, 30, 30, 31, 37, so the frequency is 5. The class centre is simply the average (or median) of the smallest...

There are 43 252 003 274 489 856 000 possible arrangements of colours on a Rubik's cube. Apparently.

The break even point is where the two lines intersect. You'll need to graph I = 80n as well as C = 150 + 2n. You could plot some points. For cost, C = 150 + 20n When n = 0, C = 150 When n = 1, C = 170 When n = 2, C = 190 When n = 3, C = 210, and so on. For income, I = 80n When n = 0, I = 0...

No idea. I'm not sure how you went from the question to the next line - unless 2^1/3 is a typo.

For the Mac users out there, you can try: Grapher Already on your computer! But you already knew that, right? /Applications/Utilities/Grapher Graphing Calculator http://www.pacifict.com/Home.html Will do pretty much anything, including solving equations. Take the tour. Costs a bit but well...

The largest integer smaller than 2000 with 7 prime factors is 1984. 1984 = 2 x 2 x 2 x 2 x 2 x 2 x 31 The smallest integer greater than 2000 with 7 prime factors is 2080. 2080 = 2 x 2 x 2 x 2 x 2 x 5 x 13 So the difference is 2080 – 1984 = 96. I used the "brute force" method. Is there a...

Well, probably New Century Maths 11 & 12. Try the Chapter Review exercises, and all the questions marked with >> which are challenging. Maths In Focus 11 & 12 have pretty basic questions, but the chapter summaries are good and I love the Challenge stages at the end of each chapter. But it's 9...

You're given an equation for cost (say C = 150 + 20n) and equation for income (say I = 80n). The easiest thing to do is graph the two straight lines. The point of intersection is the break even point. In this example, the point of intersection is (2.5,200). That means if you sold 2.5 items...

Yep ... everything.

Hey, I'm the far eastern suburbs and I ride up to the lower north shore or out to Haberfield pretty much every day. Next term I'll be riding down to Hurstville for work. Started mainly for exercise, but it's cheap and often quicker than driving, and it's a great way to lose weight and stay fit...

Areas of shapes, Triangle A = 1/2 bh, Trapezium A = 1/2 h(a + b), Circle, A = πr2, and so on. It's also worth writing down the useful conversions: 1 cm3 = 1 mL 1 m3 = 1 kL and: 1 nm = 1.852 km 1° = 60 nm (on a great circle) 1 h = 15° (for time difference)

(i) 0.15n (ii) 3 seedlings Next question: The region by the curve y = ln x, the co-ordinate axes, and the line y = ln 2 is rotated about the y-axis. Find the volume of the solid so formed.

Not all of them, but I do have 2005. Let me know if there are any mistakes.

Nowhere. All my own work. All care and no responsibility, etc, etc. In (i), I don't think it's wrong. Novirus costs $115 more than Funmaths, and your equation says that. Usually the question says write an expression for the cost of Funmaths (F) in terms of the cost of Novirus (x). That...

Of course, that's all that ever happens in Newcastle. Still, a nice portrayal of a sub-culture. They could have just as easily have called it Maroubra.