Indices
Surds
Pythagoras
Linear Relationships
Problem Solving 1
100
5x^0 = ?
5
100
Simplify
2sqrt(8)
4sqrt(2)
100
Prove that a triangle with side lengths 3,4,5 units contains a right angle
32 + 42 = 52
9 + 16 = 25
100
c represents the y intercept.
(What is the question?)
What does the c represent in the general form of the equations of a straight line y = mx + c ?
100
Marty has 6 more pogs then Jen has. After he gives 10 pogs to Jen, how many more pogs will Jen have than Marty?
Jen has 14 more pogs than Marty has.
200
Simplify
3^-2
1/9
200
Simplify
3sqrt(50)-sqrt(50)
15sqrt(2)
200
Find the value of the pronumeral in the following triangle. Give your answer in simplified, exact form.
c=4sqrt(5)
200
The gradient of the straight line connecting these two points is 3.
(What are the two points?)
What is the gradient of the line connecting these two points? multiple correct answers. e.g. (0,0) and (1, 3)
200
What number between 121 and 149 is exactly divisible by both 3 and 5?
The number is 135
300
Simplify
2^2 + 3^2 + 2^0 + 0^2
4 + 9 + 1 + 0 = 14
300
Simplify
(21sqrt(2))/(7sqrt(18))
1
300
An isosceles triangle has a size length of 4 cm for the hypotenuse. Find the length of the shortest side in exact form.
2sqrt(2) cm
300
What is the scenario which shows how much the electrician charges for a repair visit? The rule is c = 80 + 2m
The electrician charges an $80 call out fee and then $2 per minute. What is the rule (equation) which shows the total cost to visit someone's house for a repair?
300
The number 6 has exactly four different factors: 1, 2, 3 and 6. How many different factors does the number 36 have?
9 different factors
400
Simplify
(16x^4)^(1/4)
2x
400
4sqrt3(sqrt12−sqrt3)
12
400
Pythagoras can be used to find the distance between two points on the Cartesian plane.
A triangle has vertices at A (3, 7), B (6, 4) and C (3, 4).
What is the length of the longest size in exact form?
from Point A to Point B
c^2 = 3^2 + 3^2
c=sqrt(18)
400
Equation 1 has a zero gradient. Equation 2 has an undefined gradient. Both equations intersect at the point (-1,5)
(What are the two equations?)
What is the gradient of equations 1 and 2 below and and at what point do they intersect?
1. y=5
2. x = -1
400
The area of a square is 36 square cm. A rectangle has the same perimeter as the square. The length of the rectangle is twice its width. What is the area of the rectangle in square cm?
The rectangle is 32 square cm.
500
What value of x makes this equation true (no calculator allowed)
3^x= 1/81
1/81 = 1/3^-4
x = -4
500
What is the meaning (or origin) of the term 'surd'
500
Apart from 3,4,5, name a Pythagorean Triple
500
y = 2x - 3 is the equation passing through these two points
(What two points?)
several answers possible e.g. 1. (0,-3) 2. (2, 1)
500
When two people shake hands with one another , that counts as one 'handshake'. Every person in the room shakes hands with each other person once. There are a total of 15 'handshakes'. How many people are in the room?
6 people in the room