Probability
Measurement
Algebra
Networks
Mixed Bag
100
A bag contains 3 red, 5 blue, and 2 green marbles. A marble is drawn at random. Express the probability of drawing a blue marble as a fraction, a decimal, and a percentage.
P(blue) = 5/10 = 1/2 = 0.5 = 50%
100
Convert 3.5 km to metres, then to centimetres.
3.5 km = 3500 m = 350 000 cm
100
Simplify: 3x + 5y − x + 2y
2x + 7y
100
How many vertices and how many edges?
3 vertices, 5 edges
100
A spinner has 8 equal sectors numbered 1 to 8. What is the probability of spinning a number greater than 5? Express as a fraction and percentage.
3/8 = 37.5%
200
A = people who like apples
B = people who like bananas
If someone is selected at random, the probability they like neither fruit is...
2/18 or 1/9
200
Find the circumference of a circle with radius 8 cm.
Circumference = 2π × 8 ≈ 50.27 cm.
200
Expand and simplify: 2(3x − 4) + 5(x + 1)
11x − 3
200
A network has 5 vertices and 7 edges. Using Euler's Rule, how many faces does the planar graph have?
4
200
Factorise fully: 6x² + 9x
3x(2x + 3)
300
A survey of 30 students found that 18 study maths, 12 study science, and 6 study both. Draw a Venn diagram description in your head: let M = maths, S = science. How many students study maths or science (i.e. M ∪ S)?
24 students.
300
A right-angled triangle has shorter lengths 9 cm and 12 cm. Find the area of the triangle
Hypotenuse = √(81 + 144) = √225 = 15 cm.
Area = ½ × 9 × 12 = 54 cm².
300
If p = 3 and q = −2, evaluate: 2p² − 3q + 1
25
300
How many odd vertices?
4: A, B, D, E
300
A composite shape is formed by placing a semicircle on top of a rectangle. The rectangle is 10 cm wide and 8 cm tall. Find the total area of the shape. (Give your answer to 2 decimal places.)
Total ≈ 119.27 cm².
400
A bag contains 4 red and 3 blue balls. Two balls are drawn without replacement. Using a tree diagram, find the probability that both balls are the same colour.
3/7
400
A cylinder has a radius of 4 cm and a height of 10 cm. Find the total surface area.
351.86 cm²
400
Solve for x: 4(x − 3) = 2(x + 5)
x = 11
400
Can A - D - B - C - D be classified as a WALK, a PATH, a CIRCUIT or a TRAIL? (Clue: it may be more than one of these)
It is a WALK and a TRAIL (a trail is a walk where edges are not repeated)
400
A graph has 4 vertices, each connected to every other vertex. How many edges does it have?
6
500
In a class of 28 students, 15 play sport, 10 do drama, and 7 do neither. A student is chosen at random. Given that the student does drama, find the probability they also play sport.
P(sport | drama) = 4/10 = 2/5.
500
Find the volume of
25.42 cubic centimetres
500
A rectangle has length (2x + 3) cm and width (x − 1) cm. Its perimeter is 28 cm. Find the area.
area = 33 cm²
500
Can this graph have a Eulerian Trail, a Eulerian Circuit, or both?
There are exactly two odd vertices.
This means it can have a Eulerian Trail.
Because it does not have zero odd vertices, there is no Eulerian Circuit.
500
Find the perimeter of this shape, correct to two decimal places:
12.03m