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

Manipulating Equations

Collecting Like Terms

1. 2x
2. 4x²
3. 3x³ + 5x
4. 3zy + 2y + 2z
5. − x² + 4x²y − 4xy² + 7xy

Multiplication

1. 4x²
2. 18x²y²
3. 36ab²xz
4. 60x⁵y⁴z²
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.

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

2. Solve for z.

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

3. Solve for y.

   y = b²

4. Solve for x.

   $x = \sqrt {y + 9}$

5. Solve for b.

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

Solving Quadratic Equations

Find the Roots of:

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

Simultaneous Equations

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