A-level Mathematics/OCR/C1/Equations/Solutions

Manipulating Equations

Collecting Like Terms

1.

Here we only have $x$ terms, so we can add them together:

$x+x=2x$

2.

We have a similar situation to problem 1, but this time with $x^2$ terms. We can combine them by adding their coefficients:

$x^2+3x^2=(1+3)x^2=4x^2$

3.

Here we have three different terms in the mix ($x$, $x^2$ and $x^3$) so we need to be a little more careful. We can only combine coefficients if they represent the same term. Separate the expression into terms of $x$, $x^2$ and $x^3$ as follows:

$(3x+2x)+(2x^2-2x^2)+3x^3$

Now combine the coefficients of the like terms:

$(3+2)x+(2-2)x^2+3x^3=5x+3x^3$

4.

This is another case with three distinct terms ($zy$, $z$ and $y$). Combine the coefficients of like terms:

$\begin{array}{cc}zy+2zy+2z+2y& =(1+2)zy+2z+2y\\ & =3zy+2z+2y\end{array}$

5. $-x^2+4x^{2}y-4x{y}^2+7xy$

Multiplication

1. $4x^2$
2. $18x^2{y}^2$
3. $36a{b}^{2}xz$
4. $60x^5{y}^4{z}^2$
5. $\sqrt{x^5}$

Fractions

1. $x$
2. $\frac{7x}{12}$
3. $\frac{16xy}{15}$
4. $2x-y+z$
5. $\frac{x^2+y^2}{xy}$

Solving Equations

Changing the Subject of an Equation

1. Solve for x.

$x=\frac{y}{2}$

1. Solve for z.

$z=\frac{x-8}{3}$

1. Solve for y.

$y=b^2$

1. Solve for x.

$x=\sqrt{y+9}$

1. Solve for b.

$b=\frac{6y+7z}{6}$

Solving Quadratic Equations

Find the Roots of:

1. $x=-2or3$
2. $x=7or\frac{3}{2}$
3. $x=2or3$
4. $x=-1or0$
5. $x=-3or4$

Simultaneous Equations

1. $a=4,s=2$
2. $c=\frac{2}{5},d=1$
3. $b=7,g=12$

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