Equations
The formula C=5/9(F-32) is used to convert temperatures between Fahrenheit (F) and degrees Celsius (C).
Convert 3o C to the equivalent temperature in Fahrenheit.
37.4o F
Simplify 40:60:12
7:10:2
What is the equation of the line with gradient -2 that passes through the point (0, 5)?
y=-2x+5
The top of the Sydney Harbour Bridge is measured to be 138.4m above sea level.
What is the percentage error in this measurement? (3dp)
0.036%
The mean, median and mode of the list of positive integers are all equal. What is the value of x?
3, 4, 5, 6, 6, 7, x
x=11
There are 2/3 as many netballs in the Sports Hall as in the Gymnasium. If there are a total of 150 netballs, how many fewer netballs are in the Sports Hall than in the Gymnasium?
30
At IGA Wahroonga, the ratio of the number of apples to the number of oranges is 1 : 4 and the ratio of the number of oranges to the number of lemons is 5 : 2. What is the ratio of the number of apples to the number of lemons?
5:8
Expand and simplify 7(5x-4)-(3x+2)
32x-30
A square sheet of metal with dimensions 15cm by 15cm has a 1cm square cut out of each corner. The remainder of the square is folded to form an open box. Calculate the volume of the box
169 cubic centimetres
The following scores are arranged in ascending order. The median is the same as the range. Find the value of x.
x, 2, 2, 4, 5, 5
x=2
A 2 metre length of ribbon is cut into two pieces. One length is 80cm shorter than the other.
What are the lengths of the two pieces?
1.4 m and 0.6m
The scale on a plan is 1:1000000. A length on the plan is measured to be 4.75cm?
What is the actual distance in kilometres?
47.5 km
What is the x-intercept of the line x+3y+6=0?
(-6,0)
A garden is in the shape of a rhombus whose side length is 30 metres and one diagonal is 48 metres. Find the area of the garden
864 square metres
A set of 70 scores has an interquartile range of 30.
If each score is increased by 5, what will be the interquartile range of the new scores?
30
In a triangle the largest angle is twice the smallest angle and the other angle is 20o larger than the smallest angle.
What is the size of each of the three angles?
40o,60o,80o
Peter rides his bike at a speed of 27 km/h.
What is this speed in m/s?
7.5m/s
Factorise x2 +4x - 45
(x+9)(x-5)
A container in the shape of a cylinder has a diameter of 40cm and height of 85cm. If the container is one-third filled, what is the amount of water in the container, to the nearest litre?
36L
A number is chosen from the set of positive integers between 1 and 10 inclusive.
Let A be the set of integers greater than 5 and B be the set of odd numbers between 1 and 10 inclusive.
Which of the following statements is true?
A) n(A)=4 D) A and B ={5, 7, 9}
B) n(AUB)=10 E) A' and B' = {2, 4}
C) P(B|A)=0.5
E
Make y the subject: 3xy-2y=7
y=7/(3x-2)
Brothers Marco and Matthew start riding from home into town, which is 30km away. Marco rode at 10km/h and Matthew took 20 minutes longer to complete the trip. Assuming that they both rode at a constant speed, how fast was Matthew riding?
9km/h
Expand and simplify:
(m-3)2 -(m-3)(m+3)
18-6m
A designer is creating a tiled pattern using regular polygons.
For one part of the design, she chooses a regular polygon whose interior angle sum is 1980°.
Using this information, determine how many sides the polygon has.
13
At a second hand book sale there are 2000 books. There are 800 children's books and the remainder are adults' books. Half of the 1100 non-fiction books are for adults. A book is chosen at random. What is the probability that it is fiction, given that it is a children's book?5
5/16