Number and Arithmetic
Write 0.000047 in standard form
4.7\times10^{-5}
True or false: \mathbb{I}\subset\mathbb{Q}\subset \mathbb{R}
True
Fully factorise: 3x^2-75
3(x-5)(x+5)
State the gradient and y-intercept of y=\frac{3x-6}{2}
m=3/2, \text{ y-int}=-3
In Minecraft, what is the only material that can't be destroyed by the Ender Dragon?
Obsidian
Evaluate -2^4-(-3)^0+\sqrt{64}\times2^{-2}
-15
\mathbb{U}=\{1,2,...,15\}
A=\{\text{ multiples of 3 }\}
B=\{\text{ factors of 12 }\}
Find A\cap B
A\cap B=\{3,6,12\}
Simplify:
\frac{2x^2-8x}{x^2-2x-8}
\frac{2x}{x+2}
Rearrange the follwing to find the gradient and y-intecept.
3x+2y=12
m=-3/2, \text{ y-int}=6
What is the name of the fictional metal that Captain America's shield is made from?
Vibranium
$5000 is invested at 6% simple interest. After how many years will the investment exceed $7000?
7 years ($7100)
If n(A\cupB)=45, n(A)=27, n(B)=30
find n(A\capB)\text{ and hence } n(A \text{ only})
n(A\capB)=12
n(A \text{ only})=15
Solve: \frac{3x-1}{4}-\frac{x+2}{3}=2
x = 5
Find the intersection point for the lines l_1: y=2x-3\text{ and }l_2:y=-x+6
(3,3)
What is the name of the paradox where travelling back in time and killing your own grandfather would prevent your own birth, making the act impossible?
The Grandfather Paradox
Find the HCF and LCM of 12, 30 and 72. Hence find the smallest number divisble by all three that is also a perfect square.
HCF = 6, LCM = 360
Smallest perfect square = 3600
In a survey of 60 people: everyone likes at least one of tea, coffee, or juice. 35 like tea, 30 like coffee, 28 like juice. 14 like tea and coffee, 11 like coffee and juice, 9 like tea and juice. How many like all three?
1
A rectangle has perimeter 52cm. Its length is (2x+5) and width is (x+3). Find x and hence the area.
x = 6, length = 17cm, width = 9cm, area = 153cm²
For y=-2(x-3)^2+8 , state the vertex, axis of symmetry, y-int and x-ints.
Vertex: (3,8)
AOS: x = 3
X-ints: x = 1, 5
Y-int: y = -10
In Death Note, what are the three rules you must follow when using the Death Note?
Write a person's name, picture their face, they die within 40 seconds
A car's fuel consumption is 7.8L per 100km. Petrol costs $2.67/L. How much does a 430km trip cost?
$88.64
In a group of 50 students: 30 study French, 25 study Spanish, 10 study neither. How many study both? How many study French only?
Both = 15, French only = 15
This year Sam is twice as old as Tia. Three years ago the product of their ages was 44. Form and solve a quadratic to find their current ages.
Tia = 7 years old, Sam is 14 years old.
A parabola has vertex (-2, 5) and y-intercept (0, 1). Find the equation in the form
y=a(x-h)^2+k
y=-(x+2)^2+5
In the original Star Wars trilogy, what is the name of the chess-like holographic game played aboard the Millennium Falcon?
Dejarik (also Holochess)