The perimeter of a square with side lengths of a is given by the formula P = 4a.
Find the value of P, if the length of each side is 7 \text{ cm}.
The area of a square with side lengths of s is given by the formula A = s^{2}. Find the value of A if the length of each side is 6 \text{ cm}.
The area of a rectangle is given by the formula A=\text{ Length }\times \text{ Width}. If the length of a rectangle is 2 \text{ cm} and its width is 3 \text{ cm}, find its area.
The perimeter of a triangle with sides of lengths x, y, \text{and } z is given by the formula P = x + y + z
Find P if the lengths of its three sides are x = 6\text{ cm, }y = 3\text{ cm and } z = 7 \text{ cm.}
The perimeter of a rectangle is given by the formula P = 2 \times \left(l + w\right) , where l is the length and w is the width. If the width of a rectangle is 10 \text{ cm} and its length is 5 \text{ cm}, find its perimeter.
The area of a triangle is given by the formula A = \dfrac{1}{2} \times \text{base} \times\text{height}. If the base of a triangle is 5 \text{ cm} and its height is 8 \text{ cm}, find its area.
Evaluate the following expressions given the values of its variables:
a + b + c; if a = 10, b = 15, and c = 11
k r; if k = 5 and r = 6
4 r \times 3 s + 38; if r = - 5 and s = 3
4 x - 9 y - 7; if x = 2 and y = 4
14.5 - 4 x; if x is equal to 4.2
6 r \times 4 s; if r = - \dfrac{1}{6} and s = 7
\left(u + v\right) \left(w - y\right); if u = 5, v = 8, w = 2 and y = 10
y^{2}; if y = 4
r^{2}; if r = - 2
\left( r h\right)^{2}; if r = 2 and h = 3
7 a^{2}; if a = - 3
3 x^{2} + 5; if x = 2
25 - z^{2}; if z = 8
v^{2} + u; if u = - 49 and v = 2
s \left(12 - t\right); if s = - 3 and t = 10
y^{3} + 4 y z - 2 x^{2}; if y = 2, x = - 4 and z = 1
\dfrac{1}{2} y^{2} - 6 z + 1; if y = - 2 and z = \dfrac{5}{6}
x \left(2 - 4 y^{2}\right); if x = - 2 and y = - 2
8 p^{2} + 5 q^{3}; if p = 3 and q = - 2
\dfrac{2 p + 4}{3 q + 5}; if p = 2 and q = 4
\dfrac{3 a}{2 b - 6}; if a = 4 and b = 14
\dfrac{p + 4}{q}; if p = - 8 and q = - 8
\sqrt{\dfrac{3 p}{2 q}}; if p = 12 and q = 2
5 y - z^{2} + 9; if y = 7 and z = 4
\dfrac{x^{2}}{3} + \dfrac{y^{3}}{2}; if x = - 4 and y = 3
The equation of a straight line is given by the formula y = m x + c. Given that m = 6, x = - 4 and c = 9, find the value of y.
Complete the table of values given the formula:
q = 2 p - 3
| p | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| q |
q = - 2 p - 3
| p | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| q |
The area of a rhombus is given by the formula A = \dfrac{1}{2} x y, where x \text{ and } y are the lengths of the diagonals.
If the diagonals of a rhombus have lengths of 2\text{ cm} and 4\text{ cm}, find the area of the rhombus.
The volume of a rectangular prism is given by the formula V = l \times w \times h, where l, w and h are the dimensions of the prism.
Given that a rectangular prism has a length of 4\text{ cm}, a width of 8\text{ cm} and a height of 5\text{ cm}, find its volume.
The simple interest generated by an investment is given by the formula I = \dfrac{P \times R \times T}{100}.
Given that P = \$1000, R = 6 and T = 7, find the interest generated.
The surface area of a rectangular prism is given by formula S = 2 \left( l w + w h + l h\right), where l, w and h are the dimensions of the prism.
Given that a rectangular prism has a length of 8\text{ cm}, a width of 7\text{ cm} and a height of 9\text{ cm}, find its surface area.
Evaluate the expression r s if:
r = 3 and s = - 5
r = - 5 and s = 3.2
r = \dfrac{1}{5} and s = - 35
The value of a variable, T, is defined by the formula T = a + \left(n - 1\right) d. Given that a = 6, \\ n = 5 and d = 8, find the value of T.
The sum of n terms in an arithmetic sequence is defined by the formula \\ S = \dfrac{n}{2} \left( 2 a + \left(n - 1\right) d\right). Given that n = 10, a = 3 and d = 9, find the value of S.
Converting a measure of temperature from Celsius to Fahrenheit is given by the formula F = 32 + \dfrac{9 C}{5}
Given that C = 15, evaluate F.
The formula relating density D, mass M and volume V is D = \dfrac{M}{V}.
Calculate the density of a material that has a mass of 6.16 \text{ g} and a volume of 5.6 \text{ cm}^3.
For many 3 dimensional shapes, we can find the number of edges, E, on the shape by using the formula: E = V + F - 2 where V is the number of vertices and F is the number of faces.
Find the number of edges of a 3 dimensional shape which has:
7 vertices and 7 faces
8 vertices and 6 faces
Sally bought a television series online. The television series was 7.2 gigabytes large and took 2 hours to download. The formula b = 8 B converts gigabytes, B, to gigabits b. Find the size of the television series in gigabits.
The area, A, of triangle is given by the formula:
A = \dfrac{b h}{2}
where h is the height of the triangle and b is the length of its base.
Find the area of a triangle that has a base of 7 \text{ cm} and a height of 5 \text{ cm}
Find the area of a triangle that has a base of 25 \text{ cm} and a height of 16 \text{ cm}
In physics, Newton's second law states that F = m a, where F is the force of on object (measured in Newtons), m is the mass of the object (in kilograms) and a is the acceleration of that object (measured in \text{m/s}^2).
Calculate the force imparted by an object with a mass of 830 grams and an acceleration of 9\text{ m/s}^2.
Calculate the force created from an object with a mass of 660 grams and an acceleration of 13\text{ m/s}^2.
Find the value of x^{2} - 9 x + 18 if:
x = 2
x = 4
x = -1
x = 0
Evaluate the expression \left( 2 a + 9\right) \left( 5 b - 7\right) if:
a = 1 and b = 6
a = - 9 and b = - 1
Find the largest whole number value of p that makes the expression 81 - p^{2} positive.
Conversion from Fahrenheit to Celsius is defined by the formula C = \dfrac{5}{9} \left(F - 32\right).
The temperature inside a freezer is 86 \degree F. Convert this temperature to Celsius.
Pythagoras' theorem states that the length of the hypotenuse of a right-angled triangle is equal to the root of the sum of the squares of the other two sides.
We can represent this using the formula c = \sqrt{a^{2} + b^{2}}, where c is the length of the hypotenuse and a and b are the other two side lengths.
Find the exact length of the hypotenuse of a right-angled triangle which has other side lengths of 6 \text{ cm} and 8 \text{ cm}.
Find the length of the hypotenuse of a right-angled triangle which has other side lengths of 8.4 \text{ m} and 7.2 \text{ m}. Round your answer to one decimal place.
The volume of a sphere can be calculated using the formula V = \dfrac{4}{3} \pi r^{3}, where r is the radius of the sphere.
Given that a sphere has a radius of 2\text{ cm}, calculate its volume correct to two decimal places.
Newton's second law of motion states that a = \dfrac{F}{m}, where F is the force acting on an object (in Newtons), m is the mass of the object (in kilograms) and a is the acceleration of that object (in \text{m/s}^2).
Calculate the acceleration of an object with a mass of 25 kilograms and a force of 775 Newtons acting on it.
Energy can be measured in many forms. A quantity of energy is given in units of Joules (\text{J}).
The kinetic energy, E, of an object in motion is calculated using the following formula:
E = \dfrac{m v^{2}}{2}
where m is the mass of the object in kilograms and v is the speed of the object in metres per second. Find the kinetic energy, E, of an object with a mass of 6 \text{ kg}, travelling at a speed of 19 \text{ m/s}.
For x = 5 and y = 4, evaluate \sqrt{ 2 x^{2} + 4 y + 6} correct to two decimal places.
Evaluate \dfrac{11 s - 39}{3 r} when r = - 1.6 and s = 2.8. Round your answer to three decimal places.
The Mostellar formula can be used to calculate the body surface area (BSA) in \text{ m}^2. The formula is given by \text{BSA}=\sqrt{\dfrac{WH}{3600}}, where W is the mass of the subject in \text{kg} and H is their height in \text{cm}.
Calculate the BSA for each of the following, rounding your answers to two decimal places where necessary:
A child with a height of 120 \text{ cm} and a mass of 30 \text{ kg}.
An adult with a height of 1.75 \text{ m} and a mass of 72 \text{ kg}.
A child with a height of 96 \text{ cm} and a mass of 15.7 \text{ kg}.
A baby with a mass of 3.5 \text{ kg} and a length of 55 \text{ cm}.
When the heating system in a house is on a setting of s, the temperature, T, of the house within the first 30 minutes can be estimated by using the formula T = a + \dfrac{s t}{10}, where a is the initial temperature and t is the number of minutes since turning the heating system on.
Calculate the temperature of the room after 18 minutes if the initial temperature is - 3 degrees Celsius and the setting on the heater is 5.
Tobias operates his air conditioning unit using a remote with three buttons. The first one raises the temperature by 4 degrees, the second decreases it by 7 degrees and the third increases it by 3 degrees. The air conditioner always starts at 21 degrees.
We can model the temperature setting with the equation: T = 4 u - 7 v + 3 w + 21, where u, v and w represent the number of times Tobias presses the first, second and third buttons.
What will the temperature setting be if Tobias presses the first button 11 times, the second 14 times and the third 10 times?
Dave and Maria are contestants on a game show which has three rounds.
Their final scores are based on their performance in each round and are calculated using the formula:
\text{Score }= a - b + 5 \left(c + 6\right)
where a, b and c are their point scores for the first, second and third rounds.
Dave receives the following scores for each round:
Calculate his final score.
| \text{Round } 1 | \text{Round } 2 | \text{Round } 3 |
|---|---|---|
| -12 | 3 | -5 |
Maria receives the following scores for each round:
Calculate her final score.
| \text{Round } 1 | \text{Round } 2 | \text{Round } 3 |
|---|---|---|
| -12 | 20 | 1 |
In this game show, the winner is the contestant who has the lowest final score.
Which contestant won this game?
The period of a pendulum can be calculated by using the formula T = 2 \pi \sqrt{\dfrac{L}{g}}, where L is the length of the pendulum in metres and g is the acceleration due to gravity.
Calculate the period of a pendulum which is 3 \text{ m} long. Take the acceleration due to gravity to be 10 \text{ m/}\text{s}^2. Round your answer to two decimal places.
Calculate the period of a pendulum which is 5.6 \text{ m} long. Take the acceleration due to gravity to be 9.8 \text{ m/}\text{s}^2. Round your answer to two decimal places.
The volume of a sphere can be calculated using the rule V = \dfrac{4}{3} \pi r^{3}, where r is the radius of the sphere.
We can rearrange the formula to find the radius for a given volume: r = \sqrt[3]{\dfrac{3 V}{4 \pi}}.
Calculate the radius of a sphere with a volume of 180 \text{ mm}^3 to two decimal places.
Valerie stands at the top of a cliff and launches a tennis ball across the valley. To estimate the vertical position, y metres, of the ball compared to herself she uses the formula: y = 14.7 t - \dfrac{9.8}{2} t^{2} where t is the number of seconds since the ball was launched.
Find the vertical position of the ball after:
2 seconds
3 seconds
8 seconds
At which of the above times is the ball above Valerie?