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

< A-level Mathematics‎ | OCR‎ | C1‎ | Equations

Manipulating Equations

Collecting Like Terms

1. $x+x$ 2. $x^{2}+3x^{2}$ 3. $3x+2x^{2}+2x-2x^{2}+3x^{3}$ 4. $zy+2zy+2z+2y$ 5. $8x^{2}+7xy+x^{2}-10x^{2}+4x^{2}y-4xy^{2}$ Multiplication

1. $2x\times 2x$ 2. $6xy\times 3xy$ 3. $6zb\times 3x\times 2ab$ 4. $3x^{2}\times 4xy^{2}\times 5x^{2}y^{2}z^{2}$ 5. $x^{2}{\sqrt {x}}$ Fractions

1. ${\frac {x}{2}}+{\frac {x}{2}}$ 2. ${\frac {x}{3}}+{\frac {x}{4}}$ 3. ${\frac {3xy}{15}}-{\frac {xy}{3}}+{\frac {6xy}{5}}$ 4. ${\frac {4x}{2}}-{\frac {4y}{4}}+{\frac {8z}{8}}$ 5. ${\frac {x}{y}}+{\frac {y}{x}}$ Solving Equations

Changing the Subject of an Equation

1. Solve for x.

$y=2x$ 1. Solve for z.

$x=3z+8$ 1. Solve for y.

$b={\sqrt {y}}$ 1. Solve for x.

$y=x^{2}-9$ 1. Solve for b.

$y={\frac {6b-7z}{6}}$ Find the Roots of:

1. $x^{2}-x-6=0$ 2. $2x^{2}-17x+21=0$ 3. $x^{2}-5x+6=0$ 4. $x^{2}+x=0$ 5. $-x^{2}+x+12=0$ Simultaneous Equations

Example 1

At a record store, 2 albums and 1 single costs £10. 1 album and 2 singles cost £8. Find the cost of an album and the cost of a single.

Taking an album as $a$ and a single as $s$ , the two equations would be:

$2a+s=10$ $a+2s=8$ You can now solve the equations and find the individual costs.

Example 2

Tom has a budget of £10 to spend on party food. He can buy 5 packets of crisps and 8 bottles of drink, or he can buy 10 packets of crisps and 6 bottles of drink.

Taking a packet of crisps as $c$ and a bottle of drink as $d$ , the two equations would be:

$5c+8d=10$ $10c+6d=10$ Now you can solve the equations to find the cost of each item.

Example 3

At a sweetshop, a gobstopper costs 5p more than a gummi bear. 8 gummi bears and nine gobstoppers cost £1.64.

Taking a gobstopper as $g$ and a gummi bear as $b$ , the two equations would be:

$b+5=g$ $8b+9g=164$ 