Pythagoras' Theorem
Algebraic Techniques
Equations
Financial Mathematics
Computation of Integers
100
Find the length of the Hypotenuse.
c=30
100
Simplify
-3(x-6)
-3x+18
100
Simplify and ,
4x + 4 = 20
x=4
100
An electrical store marks up all entertainment systems by 30%. If the cost price of one entertainment system is $8000, what will be its selling price?
= 30% of $8000
= 0.3 × 8000
= $2400
∴ selling price = 8000 + 2400 = $10400
100
Write the following as an improper fraction:
18 4/13
238/13
200
Find the value of the pronumeral (b), correct to 2 decimal places.
0.74
200
Expand and simplify:
-4(3x-2) + 2(3x+5)
18-6x
200
Solve the following pair of simultaneous equations using the elimination method:
2x-4y=6
5x+3y=-11
x = -1
y = -2
(-1, -2)
200
Charlie lent his brother $3,000 to help him buy a car. In 4 years his brother paid him back the $3,000 plus $660 in interest. What was the rate of interest?
r = 0.055
r = 5.5%
200
True or False: Are the following numbers equivalent?
(-2)^2 and -2^2
FALSE!!
300
Find the direct distance between the points A and B in each of the following, correct to one decimal place. 
Length of AB = 6.3 m (1dp)
300
Factorise the following:
6m + 15mn - 9mp
3m(2+5n-3p)
300
3/x - 33 = -3
x = 10
300
Ronaldo noticed that his new car loan papers stated that with an interest rate of 7.5%, he would pay $6,596.25 in interest over 5 years. How much did he borrow to pay for his car?
The principle amount, or the total amount borrowed, was:
$17590
300
Evaluate the following:
20 ÷ (6 × (-4 × 2) ÷ (-12) - (-1))
4
400
Find the distance, d units, from one corner to the opposite corner in the following rectangular prism. Give your answer correct to two decimal places. 
d = 0.34 (2dp)
400
Expand and simplify the following:
3a(2a+4b)-3b(4a+c)-3c(3a-2b)
6a^2 + 3bc - 9ac
3(2a^2+bc-3ac)
400
Solve the following equation:
-x^2-2x+4=2-2x [x<0]
x=-sqrt(2)
400
Victoria’s investment of $6000 is invested at 8.4% p.a. for 4 years. Calculate the final value of her investment if interest is compounded:
i] monthly
$8386.21
P=6000
R= 0.084/12 = 0.007
N= 4 x 12 = 48
A = P(1+R)^n
400
Evaluate the following:
(-1)^101.(-1)^1000 . root3 -1
1
500
Find the total length of the black dotted line, and leave the final result in surd form or with respect to 1dp.
Length of dotted line = 19.7 cm (1 dp)
500
Factorise the following:
-22x^2+66x^3-11x^0+11y
17x(14x^3-8x^2+58x+1)
500
Solve the following pairs of simultaneous equations using the substitution method or otherwise:
2x + y = 1
x^2 + y^2 = 1
x = 0 y = 1
x = 4/5 y = -3/5
500
It can be assumed that most cars depreciate at a rate of about 15% p.a. Calculate the projected value of each of the following cars at the end of 3 years, by using the rate of 15% p.a.
1) Bentley GT = $189 900
2) Audi A3 = $30 850
1) $116622
2) $18946
500
Convert the following recurring decimal to fraction form:
