Trigonometry
What is sin(θ)?
Opposite / Hypotenuse
A rectangle has a length of 12 cm and a width of 3 cm.
What is the perimeter and area of this rectangle.
P = 30 cm
A = 36 cm2
A survey question asks people how much time they spend commuting to their work or school each day, to the nearest minute.
What is this type of data called?
Numerical Continuous
Express 8a-3 using positive indices only
8/a3
Expand and simplify:
(3x + 4)(2x - 7)
6x2 - 13x - 28
A right-angle triangle ABC has the following sides:
AB = 9
BC = 12
AC = 15
Given ∠ABC is a right angle, what is ∠BAC?
53.13°
θ = sin-1(12/15)
θ = cos-1(9/15)
θ = tan-1(12/9)
Convert the following:
246 000 cm3 into m3
0.246 m3
A letter is chosen from the word JEOPARDY. What is the probability that a vowel is chosen?
(Y is not a vowel)
3/8
Simplify √48
4√3
Factorise the following:
x2 - 5x - 24
(x + 3)(x - 8)
A ship travels in a South-West direction for 3 km. What is the true bearing from the ship back to its origin?
045°T
What is the area and perimeter of a semicircle with a diameter of 7 cm? Give your answer to 2 d.p.
P = 17.99 cm
A = 19.24 cm2
What is the mean, median and mode of the following data set?
5, 5, 7, 10, 14, 15, 15, 15, 18, 18
Mean: 12.2
Median: 14.5
Mode: 15
Simplify and evaluate the following:
log39 + log327
5
Solve for x.
(x - 2)(x - 1) = 30
x = -4
x = 7
A bushwalker walks due south for 3 km from a resting place to a waterhole, then on a true bearing of 150°T for a further 4 km to their base camp.
Draw a diagram then find how far east the base camp is from the waterhole, to the nearest metre.
2000 m or 2.000 km
What is the surface area and volume of a cylinder with a radius of 4.5 cm and a length of 10 cm? Give your answer to 2 d.p.
SA = 409.98 cm2
V = 636.17 cm3
A bag contains 5 mauve (M) and 2 yellow (Y) marbles, and two marbles are chosen without replacement.
Draw a tree diagram and determine the probability of choosing two mauve marbles.
10/21
Solve for x
1252x = 25 . 5x+3
56x = 5x+5
x=1
Find the x-intercepts (if any exist) of a parabola that has a turning point of (-1, -8) and a y-intercept of (0, -6).
x = -3
x = 1
Rachael is building a ramp for her dog, who is struggling with the front step into the house. She starts designing the ramp to have an angle of elevation of 7.13°, but realises that she needs to change the angle of elevation to 5.71° to abide by Australian regulations. If the step is 15 cm high, how long does the ramp need to be? Give your answer to the nearest millimetre.
1500 mm or 150.0 cm
The Great Pyramid of Giza was built around 2300 BC, taking 26 years to complete. It is a square based pyramid with a base length of 440 cubits and a height of 280 cubits. The slanted length of the Pyramid is 356 cubits.
Find the visible surface area and the volume of the Great Pyramid. Give your answer to the closest whole number.
Visible SA = 313 280 cubits2
Volume = 18 069 333 cubits3
Twenty students were selected at random and asked whether they liked chocolate or lollies. Fifteen students like chocolate, twelve students like lollies and eight students like both.
Present this information in a two-way table, then find the probability a students doesn't like chocolate nor lollies.
8 7 15
4 1 5
12 8 20
P(no choc and no lollies) = 1/20
Solve for x
log4(16x) + 4x-1 = 350x2 ÷ 35x3
x = ±√3
A garden bed in the shape of a right-angle triangle has an area of 24 m2. The height of the triangle is 2 m longer than its base. Let x be the length of its base.
Draw a picture that represents this garden bed, then solve for x.
x = 6 m