Trigonometry, SMB-027
Trigonometry, SMB-026
Trigonometry, SMB-025
Trigonometry, SMB-024
Trigonometry, SMB-023
Using Pythagoras and showing your working, express `tan 30^{@}` as a fraction. (2 marks)
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Trigonometry, SMB-022
Trigonometry, SMB-021
Trigonometry, SMB-020
Trigonometry, SMB-019
Trigonometry, SMB-018
Trigonometry, SMB-017
Trigonometry, SMB-016
Trigonometry, SMB-015
Trigonometry, SMB-014
Trigonometry, SMB-013
Using Pythagoras and showing your working, express `cos 30^{@}` as a fraction. (2 marks)
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Trigonometry, SMB-012
Trigonometry, SMB-011
Trigonometry, SMB-010
Trigonometry, SMB-009
Trigonometry, SMB-008
Trigonometry, SMB-007
Trigonometry, SMB-006
Trigonometry, SMB-005
Trigonometry, SMB-004
Trigonometry, SMB-003
Trigonometry, SMB-002
Trigonometry, SMB-001
Rates of Change, SMB-010
Moses finds that for a Froghead eel, its mass is directly proportional to the square of its length.
An eel of this species has a length of 72 cm and a mass of 8250 grams.
What is the expected length of a Froghead eel with a mass of 10.2 kg? Give your answer to one decimal place. (3 marks)
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Rates of Change, SMB-009
The number of trees that can be planted along the fence line of a paddock varies inversely with the distance between each tree.
There will be 108 trees if the distance between them is 5 metres.
- How many trees can be planted if the distance between them is 6 metres? (2 marks)
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- What is the distance between the trees if 120 trees are planted? (1 mark)
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Rates of Change, SMB-008
It is known that the quantity of steel produced in tonnes `(S)`, is directly proportional to the tonnes of iron ore used in the process `(I)`.
If 16 tonnes or iron ore produces 10 tonnes of steel, calculate the tonnes of iron ore required to produce 48 tonnes of steel. (3 marks)
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Rates of Change, SMB-007
It is known that a quantity `P` kgs is proportional to the reciprocal of another quantity `Q` kgs such that `P prop 1/Q`.
If `P=12` when `Q=20`, calculate the estimated quantity of `Q` when `P=45` kgs, to the nearest gram. (3 marks)
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Rates of Change, SMB-006
The stopping distance of a car on a certain road, once the brakes are applied, is directly proportional to the square of the speed of the car when the brakes are first applied.
A car travelling at 70 km/h takes 58.8 metres to stop.
How far does it take to stop if it is travelling at 105 km/h? (3 marks)
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Rates of Change, SMB-005
Fuifui finds that for Giant moray eels, the mass of an eel `(M)` is directly proportional to the cube of its length `(l)`.
An eel of this species has a length of 15 cm and a mass of 675 grams.
What is the expected length of a Giant moray eel with a mass of 3.125 kg? Give your answer to one decimal place. (3 marks)
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Rates of Change, SMB-004
Jacques is a marine biologist and finds that the mass of a crab `(M)` is directly proportional to the cube of the diameter of its shell `(d)`.
If a crab with a shell diameter of 15 cm weighs 680 grams, what will be the diameter of a crab that weighs 1.1 kilograms? Give your answer to 1 decimal place. (3 marks)
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Rates of Change, SMB-003
The current of an electrical circuit, measured in amps (A), varies inversely with its resistance, measured in ohms (R).
When the resistance of a circuit is 28 ohms, the current is 3 amps.
What is the current when the resistance is 8 ohms? (2 marks)
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Rates of Change, SMB-002
It is known that at a constant speed, the distance travelled in kilometres `(d)` is directly proportional to the time of travel in hours `(t)`, or `d prop t`.
- If `d=75` when `t=5`, calculate the constant of variation `k`. (2 marks)
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- In the context of this question, what does the value of `k` represent? (1 mark)
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Rates of Change, SMB-001
It is known that a quantity `y` is inversely proportional to another quantity `x`.
If `y=3` when `x=1.8`, calculate the constant of variation `k`. (2 marks)
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Functions and Graphs, SMB-020
A circle has centre `(5,3)` and radius 3.
- Describe, with inequalities, the region that consists of the interior of the circle and more than 2 units above the `x`-axis. (2 marks)
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- Sketch the region. (1 mark)
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Functions and Graphs, SMB-019
Shade the region defined by `y+3x>3` on the graph below and verify your result. (3 marks)
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Functions and Graphs, SMB-018
Functions and Graphs, SMB-017
Functions and Graphs, SMB-016
Functions and Graphs, SMB-015
State the inequality that defines the domain of the function `g(x) = 2/sqrt(5-x)` ? (2 marks)
Functions and Graphs, SMB-014
What is the domain of the function `g(x) = log_2(x^2-3)`? (2 marks)
Functions and Graphs, SMB-013
- Factorise the expression `x^2-x-6`. (1 mark)
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- What is the domain of the function `f(x) = log_2(x^2-x-6)`? (2 marks)
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Functions and Graphs, SMB-012
What is the domain of the function `f(x) = log_10(3-2x)`? (2 marks)
Functions and Graphs, SMB-011
What is the domain of the function `g(x) = log_2(x+1)`? (2 marks)
Functions and Graphs, SMB-010
A function has the equation `h(x)=-1-(x-3)^2`.
State the domain and range of `h(x)`. (2 marks)
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Functions and Graphs, SMB-009
A function has the equation `f(x)=2x^2+1`.
State the range of `f(x)`. (2 marks)
Functions and Graphs, SMB-008
A function has the equation `f(x)=4-(x+1)^2`.
State the domain and range of `f(x)`. (3 marks)
Functions and Graphs, SMB-007
A function has the equation `g(x)=x^2-1`.
State the range of `g(x)`. (2 marks)
Functions and Graphs, SMB-006
State the domain of the function `f(x) = x^2 + log_10(x)`. (2 marks)
Functions and Graphs, SMB-005 MC
The domain of the function `f (x) = log_2 (2x + 1)` is
- `-1/2<x<0`
- `text{All}\ x`
- `x> -1/2`
- `– oo<x<-1/2`
Functions and Graphs, SMB-004 MC
What is the domain of the function `f(x) = log_10(4-x)`?
- `x < 4`
- `x <= 4`
- `x > 4`
- `x >= 4`
Functions and Graphs, SMB-003
State the domain and range of `y = -sqrt(12-x^2)`. (2 marks)
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Functions and Graphs, SMB-002
A function has the equation `f(x)=(x-2)^2-5`.
State the range of `f(x)`. (2 marks)
Functions and Graphs, SMB-001
`f(x)` is defined by the equation `f(x)=3-x^2`.
- Find the coordinates of the `x`-intercepts of `f(x)`. (1 mark)
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- State the domain and range of `f(x)`. (2 marks)
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Polynomials, SMB-017
Sketch `y=-(x+2)(x-1)^2` on the graph below, clearly showing all intercepts. (3 marks)
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Polynomials, SMB-016
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