Pythagoras' Theorem
In a right-angled triangle, the two shortest sides are 4.2 cm and 3.8 cm. Calculate the length of the hypotenuse correct to 2 decimal places.
5.66cm
State the gradient of the equation y =-2x + 2.
A card is drawn at random from a standard deck of 52 cards. Calculate the probability of selecting a king.
1/13
Express the ratio 16:40 in simplest form.
2:5
Complete the following to make this equation true.
13 × (15 − 1) = 180 + ?
2
Katie goes on a hike. She walks 2.5 km north, then 3.1 km east, she then walks in a straight line back to her starting point. How far was the last leg of her hike?
3.98km
Determine the equation of the straight line with the gradient of 6 and y-intercept of 7.
y = 6x + 7
A bag contains four purple balls and two green balls. State the probability of selecting a purple ball.
Jan raised $15 for a charity fundraising event, while her friend Lara raised $25. Calculate the ratio of the amount Jan raised to the amount Lara raised.
3 : 5
How many faces does a rectangular prism have?
6
A ladder that is 7 m long leans up against a vertical wall. The top of the ladder reaches 6.5 m up the wall. Determine how far the foot of the ladder is from the wall, correct to 2 decimal places.
2.60m from the foot of the wall.
Calculate the gradient of the line that passes through the points (1,−2) and (3,−10).
m = -4
A letter is chosen at random from the letters in the word PROBABILITY. Determine the probability that the letter is a vowel.
4/11
A recipe for a cake says the butter and flour needs to be combined in the ratio 3 : 7. Determine the amount of butter that should be mixed with 350g of flour.
150g
Anne bought 20 pens and Jo bought 30 pens. Each pen costs the same amount, and the pens cost $75 altogether. How much did Jo pay for her pens?
$45
The side length of an equilateral triangle is 1 m. Calculate the height of the triangle in metres, correct to 2 decimal places.
0.87m
Determine the y-intercept of the line y=54−3x
c = 54
The experimental probability of tossing a heads is given as Pr(Heads) = 0.8. What is the probability of getting a Tails?
Pr(Tails) = 0.2
The estimated volume of Earth’s salt water is 1,285,600,000 cubic kilometres. The estimated volume of fresh water is about 35,000,000 cubic kilometres. Simplify this ratio.
6428 : 175
A store is having a 25% off sale. What would be the reduced price of an item that was originally $120?
$90
Katie goes on a hike. She walks 2.5 km north, then 3.1 km east, she then walks in a straight line back to her starting point. How far did Katie walk?
9.58km
The temperature of water in a kettle is 15°C before the temperature increases at a constant rate using the formula T = 5s + 15, where T= temperature and s= seconds.
How long will it take the kettle to get to 100°C?
17 seconds
Calculate the expected number of threes if a fair die is rolled 120 times.
20
The ratio of gold to other metals in 18-carat gold is 18∶6. How many grams of gold are in a 2.5g bracelet?
1.875g of gold
If 3 hours of parking costs $13.50, how much will it cost to park from 9 am until 2 pm?
$22.50