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Demo Version

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Evaluate $6-(3+1) \\div 4$

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The temperature in a test chamber drops from 27oC to -18oC. What is the total change in temperature in degrees Celcius?

\n

[[0]] Celcius

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\n

\$\\frac{2}{3}\\times \\frac{4}{5}\$

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\$\\frac{3}{4}+\\frac{7}{12}\$

The following proportion can be written as a ratio of A:B:C.

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$\\frac{1}{2}$ of A, $\\frac{2}{5}$ of B and $\\frac{1}{10}$ of C

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Complete the missing ratio for A

\n

[[0]] A : 4 B : 1 C

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An epoxy laminating resin for carbon fibre composites comprises of two parts, A and B, mixed at a ratio of 100:30.

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How much of part B is required for 150 g of part A?

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[[0]] g

\n

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Calculate 18% of 46

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The value of a car is initially £12000. If the value decreases by 15% each year, what is the value of the car after 3 years?

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£[[0]]

Supplier A has an offer for a pack of 25 screws for £2.34. Supplier B has an offer for 60 screws for £5.75.

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What is the cost per screw at the cheapest supplier (answer in pence)?

A delivery lorry leaves the depot at 09:45 and takes 87 minutes to reach its destination. It spends 14 minutes unloading the cargo and then travels for 72 minutes back to the depot. At what time does the lorry arrive back at the depot?

\n

[[0]]:[[1]]

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Round the following number to 2 significant figures, and to 2 decimal places

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$\\var{a}$

\n

[[0]]

\n

[[1]]

\n

\n

\n

\n

\n

\n

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If 1 mile = 1.609 km, convert 30 mph to m/s.

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Write the following expression in its simplest form: $2p-4+p^2+11p+2-3p^2$

\n

[[0]]

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Calculate the value of $x$ when $3x = 3(6-2x)$

\n

$x$ = [[0]]

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Calculate the value of $y$ when $\\frac{3}{y}=\\frac{5}{(y-6)}$

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$y$ = [[0]]

Expand and simplify the expression $(x-2)(x+5)$

\n

[[0]]

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Factorise the expression $x^2 - 2x - 15$ . Please include brackets but your expression can be written in either order.

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Calculate the values of $q$ when $5q^2 + 13q -6 =0$

\n

Enter the lowest value first:

\n

$q=$ [[0]] , [[1]]

\n

\n

What is the value of $n$ if $\\frac{x^n}{x^4}=x^2$

\n

[[0]]

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The following expression can be simplified to the form $a^n$, determine the value of $n$ for $\\displaystyle \\frac{a^2 \\times a^5}{(a^3)^3}$

\n

$n=$ [[0]]

The resistance $R$ of a wire at temperature $T^{\\circ}$C is given by $R=R_0(1+\\alpha T)$.

\n

Calculate $R$ if $\\alpha = 6.8\\times 10^{-4}$, $T=89^{\\circ}$C and $R_0=33 \\Omega$.

\n

[[0]]

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If the current $I=2$A and voltage $V=5$V, calculate the power P, dissipated in a circuit if $I=\\frac{P}{V}$

\n

[[0]] W

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Transpose (rearrange) the following to make $a$ the subject of the formula $\\displaystyle N = \\sqrt{\\frac{a+x}{y}}$

\n

$a=$ [[0]]

Solve the simultaneous equations

\n

$2x + 3y = 12$

\n

and

\n

$3x + 4y = 17$

\n

\n

$x=$ [[0]]

\n

$y=$ [[1]]

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Calculate the length of side $a$ of the right-angled triangle given $b=4$ and $c=5$

\n

\n

\n

$a$= [[0]]

If a triangle has two angles measuring $30^{\\circ}$ and $55^{\\circ}$, what is the size of the missing third angle?

\n

[[0]] degrees

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Calculate the length of side $a$ of the right-angled triangle given $\\theta=30^{\\circ}$ and $b=2$

\n

\n

\n

$a=$ [[0]]

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Calculate the angle $\\theta$ (in degrees) of the right-angled triangle given $a=5$ and $c=10$

\n

\n

$\\theta =$ [[0]] degrees

Convert {a}$^{\\circ}$ into radians (give your answer to 2 decimal places).

\n

[[0]]

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Calculate the vertical component of the force shown in the diagram below

\n

\n

\n

[[0]] N

Differentiate $x^3$ with respect to $x$

\n

[[0]]

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Differentiate $4\\sin({x})$ with respect to $x$

\n

hint - include brackets within your answer (as shown in the question)

\n

[[0]]

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Differentiation

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Differentiate $e^{2x}$ with respect to $x$

\n

[[0]]

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Integrate $9x + 8$ with respect to $x$

\n

\n

[[0]] $+c$

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Integrate $\\sin({x}) + 3x$ with respect to $x$

\n

hint - include brackets within your answer as shown in the question

\n

[[0]] $+c$

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Integrate $e^{5x}$ with respect to $x$

\n

[[0]] $+c$

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A survey of a company's employees was undertaken to find out how far people commuted to work. The chart shows the results of the survey.

\n

\n

How many people travel 30 miles or more?

\n

[[0]]

The mass of seven components is recorded as follows:

\n

23.3, 25.1, 24.2, 20.9, 26.0, 25.2, 23.7.

\n

What is the mean mass of the group of components?

\n

[[0]]

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The mass of seven components is recorded as follows:

\n

23.3, 25.1, 24.2, 20.9, 26.0, 25.2, 23.7.

\n

What is the median for this sample of components?

\n

[[0]]

\n

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The following table shows the monthly financial data for a small business.

\n

\n

Calculate the actual net profit:

\n

[[0]]

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An experiment yields the following data. A line of best fit has been plotted to give the relationship between the two variables.

\n

\n

What is the equation of the straight line?

\n

$y=$[[0]]

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A car accelerates from 17.9 m/s to 31.3 m/s in 8 seconds as it moves along a straight slip road onto a motorway. Given the acceleration is constant, what is the acceleration of the car? You will need to use one of the following kinematic equations:

\n

\$v^2 = u^2 + 2as\$
\$v = u + at\$
\$s = \\frac{1}{2}(u+v)t\$
\$s = ut + \\frac{1}{2}at^2\$

\n

where $u$ is the initial velocity, $v$ is the final velocity, $t$ is time, $s$ is displacement and $a$ is acceleration.

\n

[[0]] $m/s^2$

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An object of mass 5 kg is dropped from a height of 3 m. Using the principle of conservation of energy, calculate the object's velocity when it impacts the floor.

\n

\n

Assume g = 9.81 $m/s^2$

\n

\n

[[0]] $m/s$

\n

\n

\n

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A horizontal force of 10 N acts on an object of mass 5 kg on a rough horizontal surface.

\n

Given the object is on the point of slipping, what is the coefficient of friction between the object and the surface?

\n

The equation for static friction is $F=\\mu R$ where $F$ is the frictional force in the direction of intended motion, $\\mu$ is the coefficient of friction, and $R$ is the resultant force perpendicular to the contact surface.

\n

Assume $g = 9.81$ m/s$^2$

\n

$\\mu=$ [[0]]

The figure below shows a crane 15 m long with a mass 200 kg at one end, 10 m from the cabin.

\n

\n

\n

What is the mass of the counterpoise required if the system is to remain in equilibrium?

\n

[[0]] kg

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