MATHS JEOPARDY

Pythagoras' Theorem

100

^{Find the length of the Hypotenuse.}

c=30

200

^{Find the value of the pronumeral (b), correct to 2 decimal places.}

0.74

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)

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)

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)

Algebraic Techniques

100

Simplify

-3(x-6)

-3x+18

200

Expand and simplify:

-4(3x-2) + 2(3x+5)

18-6x

300

Factorise the following:

6m + 15mn - 9mp

3m(2+5n-3p)

400

Expand and simplify the following:

3a(2a+4b)-3b(4a+c)-3c(3a-2b)

6a^2 + 3bc - 9ac

3(2a^2+bc-3ac)

500

Factorise the following:

-22x^2+66x^3-11x^0+11y

17x(14x^3-8x^2+58x+1)

Equations

100

Simplify and ,

4x + 4 = 20

x=4

200

Solve the following pair of simultaneous equations using the elimination method:

2x-4y=6

5x+3y=-11

x = -1
y = -2

(-1, -2)

300

3/x - 33 = -3

x = 10

400

Solve the following equation:

-x^2-2x+4=2-2x [x<0]

x=-sqrt(2)

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

Financial Mathematics

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



 

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%

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

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

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

Computation of Integers

100

Write the following as an improper fraction:

18 4/13

238/13

200

True or False: Are the following numbers equivalent?

(-2)^2 and -2^2

FALSE!!

300

Evaluate the following:

20 ÷ (6 × (-4 × 2) ÷ (-12) - (-1)) 

4

400

Evaluate the following:

(-1)^101.(-1)^1000 . root3 -1

1

500

Convert the following recurring decimal to fraction form: