<section><h2><h2><strong>KS3 MATHS - Algebra - formulae</strong></h2></h2><p>Practise your algebra skills with this quiz.</p></section><section><h2><h2><p><span style="font-size:24px;">A piece of wood measures 150 cm.</span></p></h2><p><span style="font-size:24px;"> </span></p><h2><p><span style="font-size:24px;">The length, l, left over after cutting off t cm is 150 – t.</span></p></h2><h2><p><span style="font-size:24px;"> </span></p></h2><h2><p><span style="font-size:24px;">Calculate the value of l, if t = 35 cm.</span></p></h2></h2></section><section><h3><h2><p><span style="font-size:24px;">QUESTION</span></p></h2><h2><p><span style="font-size:24px;"> </span></p></h2><h2><p><span style="font-size:24px;">A piece of wood measures 210 cm.</span><span style="font-size:1.5em;"></span></p></h2><h2><p><span style="font-size:24px;"> </span></p></h2><h2><p><span style="font-size:24px;">Use the same formula to work out the length left over after cutting off t, if t = 200 mm.</span></p></h2></h3><p><p><strong><span style="font-size:16px;">That’s right!</span></strong></p><p></p><p>The length left over after cutting off t is 150 – t</p><p> </p><p>150 – 35 = 115 cm, which is the value of l.</p><p> </p><p>Now try another one.</p><p> </p></p></section><section><h3><h2><p><span style="font-size:22px;">QUESTION</span></p></h2><h2><p><span style="font-size:22px;"> </span></p></h2><h2><p><span style="font-size:22px;">You want to combine two pieces of wood. </span></p><p><span style="font-size:22px;"> </span></p><p><span style="font-size:22px;">The first piece measures 75 cm. You need to cut off x cm.</span></p><p><span style="font-size:22px;"> </span></p><p><span style="font-size:22px;">The second piece measures 88 cm. You need to cut off y cm.</span></p><p><span style="font-size:22px;"> </span></p><p><span style="font-size:22px;">Work out the overall length of leftover wood after x and y have been cut off, if x = 15 cm and y = 12 cm.</span></p></h2></h3><p><p><strong><span style="font-size:16px;">That’s right!</span></strong></p><p> </p><p>t = 200 mm which is the same as 20 cm.</p><p> </p><p>The length left over after cutting off t is 210 cm – t</p><p> </p><p>210 – 20 = 190 cm, which is the value of l.</p><p> </p><p>Now try another one.</p><p> </p></p></section><section><h3><h2><p><span style="font-size:26px;"><strong>You scored 3 out 3. Well done!</strong></span></p></h2><p> </p></h3><p><p><strong><span style="font-size:16px;">That’s right!</span></strong></p><p> </p><p>For the first piece of wood, the length left over after cutting off t is 75 cm – x</p><p> </p><ul><li>75 – 15 = 60 cm</li></ul><p> </p><p>For the second piece of wood, the length left over after cutting off y is 88 cm – y</p><p> </p><ul><li>88 – 12 = 76 cm</li></ul><p> </p><p>The overall length of leftover wood is 60 cm + 76 cm.</p><p> </p><ul><li>60 + 76 = 136 cm</li></ul><p> </p></p></section><section><h3><h2><p><span style="font-size:26px;"><strong>You scored 2 out 3. Well done!</strong></span></p></h2><p> </p></h3><p><p><strong><span style="font-size:16px;">Not quite.</span></strong></p><p> </p><p>For the first piece of wood, the length left over after cutting off t is 75 cm – x</p><p> </p><ul><li>75 – 15 = 60 cm</li></ul><p> </p><p>For the second piece of wood, the length left over after cutting off y is 88 cm – y</p><p> </p><ul><li>88 – 12 = 76 cm</li></ul><p> </p><p>The overall length of leftover wood is 60 cm + 76 cm.</p><p> </p><ul><li>60 + 76 = 136 cm</li></ul><p> </p></p></section><section><h3><h2><p><span style="font-size:24px;">QUESTION</span></p></h2><h2><p><span style="font-size:24px;"> </span></p></h2><h2><p><span style="font-size:24px;">Another piece of wood measures 120 cm.</span></p><p><span style="font-size:24px;"> </span></p><p><span style="font-size:24px;">Use the formula to work out the length left over after cutting off t if t = 100 mm.</span></p><p><span style="font-size:24px;"> </span></p><span style="font-size:24px;">Remember to convert your measurements if you need to.</span></h2></h3><p><p><strong><span style="font-size:16px;">Not quite.</span></strong></p><p> </p><p>t = 200 mm which is the same as 20 cm.</p><p> </p><p>The length left over after cutting off t is 210 cm – t</p><p> </p><p>210 – 20 = 190 cm, which is the value of l.</p><p> </p><p>Now try another one.</p><p> </p></p></section><section><h3><h2><p><span style="font-size:26px;"><strong>You scored 2 out 3. Well done!</strong></span></p></h2><p> </p></h3><p><p><strong><span style="font-size:16px;">That’s right.</span></strong></p><p> </p><p>t = 100 mm which is the same as 10 cm.</p><p> </p><p>The length left over after cutting off t is 120 cm – t</p><p> </p><p>120 – 10 = 110 cm, which is the value of l.</p></p></section><section><h3><h2><p><span style="font-size:26px;"><strong>You scored 1 out 3. Keep trying!</strong></span></p></h2><p> </p></h3><p><p><strong><span style="font-size:16px;">Not quite.</span></strong></p><p> </p><p>t = 100 mm which is the same as 10 cm.</p><p> </p><p>The length left over after cutting off t is 120 cm – t</p><p> </p><p>120 – 10 = 110 cm, which is the value of l.</p></p></section><section><h3><h2><p><span style="font-size:24px;">QUESTION</span></p></h2><h2><p><span style="font-size:24px;"> </span></p></h2><h2><p><span style="font-size:24px;">Another piece of wood measures 30 cm.</span></p><p><span style="font-size:24px;"> </span></p><p><span style="font-size:24px;">The length, l, left over after cutting off t cm is 30 – t.</span></p><p><span style="font-size:24px;"> </span></p><p><span style="font-size:24px;">Calculate the value of l, if t = 10 cm.</span></p></h2></h3><p><p><strong><span style="font-size:16px;">Not quite.</span></strong></p><p> </p><p>The length left over after cutting off t is 150 – t</p><p> </p><p>150 – 35 = 115 cm, which is the value of l.</p><p> </p><p>Now try another one.</p><p> </p></p></section><section><h3><h2><span style="font-size:24px;">QUESTION</span></h2><h2><span style="font-size:24px;"> </span></h2><h2><span style="font-size:24px;">A piece of wood measures 215 cm.</span></h2><h2><span style="font-size:24px;"> </span></h2><h2><span style="font-size:24px;">Use the formula to work out the length left over after cutting off t, if t = 70 cm.</span></h2></h3><p><p><strong><span style="font-size:16px;">That’s right!</span></strong></p><p> </p><p>The length left over after cutting off t is 30 – t</p><p> </p><p>30 – 10 = 20 cm, which is the value of l.</p><p> </p><p>Now try another one.</p><p> </p></p></section><section><h3><h2><span style="font-size:24px;"><strong>You scored 2 out of 3. Well done!</strong></span></h2><p> </p></h3><p><p><strong><span style="font-size:16px;">That’s right!</span></strong></p><p> </p><p>t = 70</p><p> </p><p>The length left over after cutting off t is 215 – t</p><p> </p>215 – 70 = 145 cm, which is the value of l.</p></section><section><h3><h2><p><span style="font-size:26px;"><strong>You scored 1 out 3. Keep trying!</strong></span></p></h2><p><span style="font-size:26px;"> </span></p></h3><p><p><strong><span style="font-size:16px;">Not quite.</span></strong></p><p> </p><p>t = 70</p><p> </p><p>The length left over after cutting off t is 215 – t</p><p> </p><p>215 – 70 = 145 cm, which is the value of l.</p><p> </p></p></section><section><h3><h2><p><span style="font-size:22px;">QUESTION</span></p></h2><h2><p><span style="font-size:22px;"> </span></p></h2><h2><p><span style="font-size:22px;">A piece of wood measures 10 cm. We need to cut off some of the wood.</span></p><p><span style="font-size:22px;"> </span></p><ul><li><span style="font-size:22px;">To make a formula, we call the amount of wood which we cut off, t</span><br /></li></ul><ul><li><span style="font-size:22px;">In this case, t = 2 cm – this means we want to cut 2 cm off the wood.</span><br /></li></ul><ul><li><span style="font-size:22px;">Now we want to find out the length of wood which is left over after cutting off t.</span><br /></li></ul><ul><li><span style="font-size:22px;">We call the left-over wood, l</span></li></ul><p><span style="font-size:22px;"> </span></p><p><span style="font-size:22px;">The length, l, left over after cutting off t is the original length of wood, 10 cm, minus t, which we know is 2 cm.</span></p><p><span style="font-size:22px;"> </span></p><p><span style="font-size:22px;">l = 10 – t</span></p><p><span style="font-size:22px;"> </span></p><p><span style="font-size:22px;">What is the value of l?</span></p></h2></h3><p><p><strong><span style="font-size:16px;">Not quite.</span></strong></p><p> </p><p>The length left over after cutting off t is 30 – t</p><p> </p><p>30 – 10 = 20 cm, which is the value of l.</p><p> </p><p>Now try another one.</p><p> </p></p></section><section><h3><h2><p><span style="font-size:26px;"><strong>You scored 1 out 3. Keep trying!</strong></span></p></h2><p> </p></h3><p><p><strong><span style="font-size:16px;">That’s right!</span></strong></p><p> </p><p>t = 2</p><p> </p><p>The length left over after cutting off t is 10 – 2</p><p> </p><p>10 – 2 = 8 cm, which is the value of l.</p><p> </p></p></section><section><h3><h2><p><span style="font-size:26px;"><strong>Keep trying!</strong></span></p></h2><p> </p></h3><p><p><strong><span style="font-size:16px;">Not quite.</span></strong></p><p> </p><p>t = 2</p><p> </p><p>The length left over after cutting off t is 10 – 2</p><p> </p><p>10 – 2 = 8 cm, which is the value of l.</p></p></section>