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Calculate the length of side $a$ of the right-angled triangle given $b=\\var{b}$ and $c=\\var{c}$

\n

\n

\n

$a$= [[0]]

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

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\n

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

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

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\n

(give your answer to 2 decimal places)

\n

$a=$ [[0]]

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

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[[0]] degrees

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

\n

[[0]] 

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What is the value of $n$ if $\\simplify[!all]{ x^n/x^{a}=x^{b} }$

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[[0]]

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Calculate the value of $x$ when $\\simplify[noLeadingMinus, !cancelTerms]{ {a}x = {b}({c}+{d}x) }$

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$x$ = [[0]]

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Calculate the value of $y$ when $\\simplify[!all, noLeadingMinus]{ {a}/y={b}/(y-{c}) }$

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$y$ = [[0]]

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Write the following expression in its simplest form:

\n

\\[\\simplify[!all]{ {a}p+{b}+{c}p^2+{d}p+{f}+{g}p^2 }\\]

\n

[[0]]

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

\n

Calculate $R$ if $\\alpha = \\var{a}$, $T=\\var{b}^{\\circ}$C and $R_0=\\var{c} \\Omega$.

\n

[[0]]

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

\n

[[0]]

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Factorise the expression $x^2 +\\var{c}x +\\var{d}$ . Please include brackets but your expression can be written in either order.

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Calculate the values of $x$ when $\\simplify{ {a}x^2 + {b}x +{c} =0 }$

\n

Enter the lowest value first, giving your answers to 2 decimal places.

\n

$x=$ [[0]] , [[1]]

\n

\n

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Transpose (rearrange) the following to make $x$ the subject of the formula 

\n

\\[z=a + \\frac{\\sqrt{kx}}{y}\\]

\n

$x=$ [[0]]

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The following expression can be simplified to the form $a^n$, determine the value of $n$ for $\\displaystyle \\frac{a^\\var{b} \\times a^\\var{c}}{(a^\\var{d})^\\var{f}}$

\n


$n=$ [[0]]

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Expand and simplify the expression $\\simplify[!all]{ (x+{a})(x+{b}) }$

\n

[[0]]

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Solve the simultaneous equations

\n

$\\simplify{{a}x + {b}y = {c}}$

\n

and

\n

$\\simplify{{d}x + {f}y = {g}}$

\n

\n

$x=$ [[0]]

\n

$y=$ [[1]]

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A chemical mix comprises of two parts, A and B, mixed at a ratio of $\\var{a}$:$\\var{b}$. 

\n

How much of part B is required for $\\var{c}$ g of part A?

\n

[[0]] g

\n

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If 1 mile = 1.609 km, convert $\\var{a}$ mph to m/s.

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Evaluate $\\simplify[!collectNumbers,alwaysTimes]{ {a}+({b}+{c}) * {d} }$

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The temperature in a test chamber drops from $\\var{a}$oC to $\\var{b}$oC. What is the total change in temperature in degrees Celcius?

\n

[[0]] Celcius

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Supplier A has an offer for a pack of $\\var{a}$ screws for £$\\var{b}$. Supplier B has an offer for $\\var{c}$ screws for £$\\var{d}$.

\n

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

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Evaluate the following, writing your answer in the simplest form:

\n

\\[\\simplify[!collectNumbers]{ {a}/{b}+ {c}/{d} }\\]

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Evaluate the following, writing your answer in the simplest form:

\n

\\[\\simplify[!collectNumbers]{ {a}/{b} } \\times \\simplify[!collectNumbers]{ {c}/{d} }\\]

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The value of a car is initially £$\\var{a}$. If the value decreases by $\\var{b}$% each year, what is the value of the car after $\\var{c}$ years?

\n

£[[0]]

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Calculate $\\var{a}$% of $\\var{b}$

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\n

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

\n

$\\var{a}$

\n


[[0]] 

\n


[[1]] 

\n

 

\n

\n

\n

\n

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A delivery lorry leaves the depot at $\\var{a}$:$\\var{b}$ and takes $\\var{c}$ minutes to reach its destination. It spends $\\var{d}$ minutes unloading the cargo and then travels for $\\var{f}$ minutes back to the depot. At what time does the lorry arrive back at the depot?

\n

[[0]]:[[1]]

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

\n

$\\frac{\\var{a1}}{\\var{a2}}$ of A, $\\frac{\\var{b1}}{\\var{b2}}$ of B and $\\frac{\\var{c1}}{\\var{c2}}$ of C

\n

Complete the missing ratio for A

\n

[[0]] A : $\\var{b3}$ B : $\\var{c3}$ C

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