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

< A-level Mathematics‎ | OCR‎ | C1‎ | Equations

## Manipulating Equations

### Collecting Like Terms

1. ${\displaystyle 2x}$
2. ${\displaystyle 4x^{2}}$
3. ${\displaystyle 3x^{3}+5x}$
4. ${\displaystyle 3zy+2y+2z}$
5. ${\displaystyle -x^{2}+4x^{2}y-4xy^{2}+7xy}$

### Multiplication

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

### Fractions

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

## Solving Equations

### Changing the Subject of an Equation

1. Solve for x.

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

1. Solve for z.

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

1. Solve for y.

${\displaystyle y=b^{2}}$

1. Solve for x.

${\displaystyle x={\sqrt {y+9}}}$

1. Solve for b.

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

Find the Roots of:

1. ${\displaystyle x=-2\ or\ 3}$
2. ${\displaystyle x=7\ or\ {\frac {3}{2}}}$
3. ${\displaystyle x=2\ or\ 3}$
4. ${\displaystyle x=-1\ or\ 0}$
5. ${\displaystyle x=-3\ or\ 4}$

## Simultaneous Equations

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