Notes in 0) Maths Bridging Programme

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Status	Last Update	Fields
Published	11/11/2024	Rational Numbers
Published	11/11/2024	Integers
Published	11/11/2024	Real Numbers
Published	11/11/2024	Irrational Numbers
Published	11/11/2024	Complex Numbers
Published	11/11/2024	Expression (Definition?)
Published	11/11/2024	{{c1::image-occlusion:rect:left=.1439:top=.0305:width=.3234:height=.1583:oi=1}}{{c2::image-occlusion:rect:left=.2071:top=.6108:width=.3406:height=.153…
Published	11/11/2024	Equation (Definition?)
Published	11/11/2024	Identity (Definition)
Published	11/11/2024	Formula (Definition)
Published	11/11/2024	Completing the Square - What step is missing?1) \(2x^2+20x+32=0\)2) {{c1::\(2[x^2+10x+16]=0\)}}3) \(2[(x+5)^2-9]=0\)4) \(2(x+5)^2 -18=0…
Published	11/11/2024	Completing the square can be used to find the {{c1::Turning Point}} of a graph e.g. \(y=x^2+6x+5\)\((x+3)^2-4 =0\)
Published	11/11/2024	\[\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]What is the name of the part inside the \(\sqrt{}\)? (Quadratic Equation)
Published	11/11/2024	{{c1::image-occlusion:rect:left=.4483:top=.473:width=.2171:height=.1288:oi=1}}{{c2::image-occlusion:rect:left=.4489:top=.6239:width=.2081:height=.1442…
Published	11/11/2024	What happens when you multiply or divide by a negative number in an equalitye.g. dividing both sides of \(-2x<16\) by \(-2\)
Published	11/11/2024	Curved Brackets ( ) show what type of inequality?
Published	11/11/2024	Square Brackets [ ] show what type of inequality?
Published	11/11/2024	How to solve the below equations with the Elimination Method?e.g.\(3x+y=11\)\(2x+y=8\)
Published	11/11/2024	How to solve the below equations with the Substitution Method?e.g.\(3x+y=11\) \(2x+y=8\)
Published	11/11/2024	Exponential Functions Properties e.g. \(y=a^x\)- y-intercept at {{c1::(0,1)}}- Tends to {{c2::infinity}} as x increases- Tends to {{c2::zero}} as x de…
Published	11/16/2024	Solve \(log_28=x\)
Published	11/11/2024	Show the following as a log:\(2^x=8\)
Published	11/11/2024	Log Rules\(log_ax+log_ay=\)
Published	11/11/2024	Log Rules\(log_ax-log_ay=\)
Published	11/11/2024	Log Rules\(klog_a(x)=\)
Published	11/11/2024	For the function \(y=e^x\) (known as the exponential function) what is the gradient when \(y=9\)
Published	11/11/2024	\(e^{ln\ x} \)=
Published	11/11/2024	\(ln(e^x)=\)
Published	11/11/2024	What is the Range of the mapping \(f(x)=x-5\) if the domain is \(\{-4, 3, 9, 12\}\)
Published	11/11/2024	If the domain and range for a mapping look like the below can it be called a function?a -> pb -> c -> qd -> q
Published	11/11/2024	If the domain and range for a mapping look like the below can it be called a function?a -> q & rb -> pc -> qd -> r
Published	11/11/2024	If the domain and range for a mapping look like the below can it be called a function?a -> pb -> pc -> qd -> r
Published	11/11/2024	If the domain and range for a mapping look like the below can it be called a function?a -> pb -> qc -> r
Published	11/12/2024	Make the mapping \(f(x) = \frac1x\) a well defined function
Published	11/13/2024	Make the mapping  \(f(x) = \sqrt{x}\) a well defined function
Published	11/13/2024	Is \(ln(x)\) a positive or negative when \(0<x<1\)
Published	11/12/2024	For function \(f(x)=e^x+4\) find the Domain when the Range is \(f(x)>5\)
Published	11/12/2024	What type of function can have an inverse function?e.g. Many-to-One, One-to-One, etc
Published	11/20/2024	Find the inverse of the function\(f(x)=\sqrt{x-2}\)
Published	11/16/2024	\[f(x)=e^x\]What is the derivative of the function?
Published	11/16/2024	\[f(x)=ln(x)\]What is the derivative of the function?
Published	11/16/2024	\[f(x)=sin(x)\]What is the derivative of the function?
Published	11/16/2024	\[f(x)=cos(x)\]What is the derivative of the function?
Published	11/16/2024	\[f(x)=tan(x)\]What is the derivative of the function?
Published	11/12/2024	What is the gradient of the curve \(y=2x^2+6\) at point \((2,14)\)
Published	11/12/2024	What is the equation of the tangent to the curve \(y=2x^2+6\) at point \((2,14)\)The gradient of the tangent is 8
Published	11/12/2024	What is the equation of the normal line to the curve \(y=2x^2+6\) at point \((2,14)\)The gradient of the tangent is \(8\)
Published	11/16/2024	\[f(x)=-sin(x)\]What is the derivative of the function?
Published	11/16/2024	\[f(x)=-cos(x)\]What is the derivative of the function?
Published	11/16/2024	What can you find by calculating the first differential \((\frac{dy}{dx})\) of an equation?
Published	11/16/2024	What can you find by calculating the second differential \((\frac{dy^2}{d^2x})\) of an equation?
Published	11/16/2024	If \(f''(x)>0 \) at a stantionary point, it is a local {{c1::minimum}} turning point
Published	11/16/2024	If \(f''(x)<0 \) at a stantionary point, it is a local {{c1::maximum}} turning point
Published	11/16/2024	Find the stationary points of the curve \(y=2x^2+4x+10\)
Published	11/16/2024	Solve the following quadratic inequality\[(5-2x)(x+2)\ge0\]
Published	11/16/2024	How many terms does this equation have?\[\frac{a^3}{5}*2+3bc\]
Published	11/16/2024	Solve the following quadratic inequality\[(x+5)(x-3)<0\]
Published	11/16/2024	The curve \(y=x^3+6x^2-15x\) has a stationary point at \((1,-8)\). What is the nature of the turning point?\(\frac{dy}{dx}=3x^2+12x\)
Published	11/20/2024	What step is missing from solving this equation \(3^{2x-1}-7=74\)\(3^{2x-1}=81\){{c1::\(log(3^{2x-1})=log(81)\)}}\(2x-1*log(3)=log(81)\)\((1+\fra…
Published	11/20/2024	The function \(f(x)=x^2\) has a range of \(f(x)>36\)State two possible domains for the function
Published	11/20/2024	What type of function is this mapping (Domain is all Real Numbers)\[f(x)=\frac{4}{x+1}\]
Published	11/20/2024	What type of function is this mapping (Domain is all Real Numbers)\[f(x)=\pm{x}\]
Published	11/20/2024	What type of function is this mapping (Domain is all Real Numbers)\[f(x)=x^2+5\]
Published	11/20/2024	\(f(x)=3x-4\) and has a domain of \(0\le x<3\)What is the domain of \(f^{-1}\)
Published	11/20/2024	\(f(x)=3x-4\) and has a domain of \(0\le x<3\)What is the range of \(f^{-1}\)
Published	11/20/2024	Show \(u=2i+3j\) as a column vector
Published	11/20/2024	What do you get when you multiply a vector by a scalare.g.\(u=4i+2j\)\(2u = 8i+4j\)
Published	11/20/2024	How can you find the magnitude (i.e. size/length) of a vectore.g.\(v = \begin{bmatrix} x \\ y \\ z\end{bmatrix}\)
Published	11/20/2024	What is the dot product (or scalar product) of these two vectors\(u = \begin{bmatrix} 3 \\ 5 \end{bmatrix} \ \ \ \ v = \begin{bmatrix} -1 \\ 4 \end{bm…
Published	11/20/2024	If the dot product of two vectors is equal to 0, then the two vectors are {{c1::perpendicular}}
Published	11/20/2024	What happens when you multiply an \(m\times n \) by an \(n\times k \) matrix
Published	11/20/2024	What happens when you multiply a \(n\times m \) matrix by a \(n\times k \) matrix
Published	11/20/2024	Solve:\[\begin{bmatrix} 3 & 2 \\ 5 & 1 \end{bmatrix} \times \begin{bmatrix} 1 & 4 \\ 3 & 6 \end{bmatrix}\]
Published	11/20/2024	A, B & C are three matrices. Is the following true?\[A(BC)=(AB)C\]
Published	11/20/2024	Is the following true when multiplying matrices?\[AB\ne BA\]
Published	11/20/2024	What is the result when a \(n\times n \) matrix is multiplied by \(I_n\) (\(n\times n\) identity matrix)
Published	11/20/2024	What is the determinant of \[\begin{bmatrix} 2 & 1 \\ 1 & 4 \end{bmatrix}\]
Published	11/20/2024	A matrix with a determinant of 0 has no {{c1::inverse}}
Published	11/20/2024	What is the inverse of \[A=\begin{bmatrix} 2 & 1 \\ 1 & 4 \end{bmatrix}\]\(det(A)=7\)
Published	11/20/2024	Re-write the simultaneous equations as one matrix equation\(7x+5y=3\)\(x+3y=2\)
Published	11/20/2024	How would you solve this matrix equation?\[\begin{bmatrix} 7 & 5 \\ 1 & 3 \end{bmatrix}\times \begin{bmatrix} x \\ y \end{bmatrix} =\begin{bma…
Published	11/20/2024	Re-write \(\frac{log(y)}{log(3)}\)
Status	Last Update	Fields