(a) Work out \(0.7^2\). [1]

(b) Work out \(2\div0.04\). [1]

Write seven point two five million in figures. [1]

Calculate \(10-\left(\frac78\right)^3\times2\), correct to 1 decimal place. [2]

Write \(0.7\overline3\) as a fraction in its simplest form. [3]

Find the reciprocal of \(3\frac13\), as a fraction in its simplest form. [2]

Evaluate \(\frac16\div\frac27\). [2]

(a) Evaluate \(0.9\overline{24}-0.213\), giving the answer correct to 5 decimal places. [2]

(b) Express \(0.6\overline7\) as a fraction. [2]

Complete: \(\frac47=\frac{\square}{56}\). [1]

Calculate \(\frac{0.7-3.5^3}{4.2^2}\), giving your answer correct to 2 significant figures. [2]

Oranges cost 220 rupees per kilogram. Find the cost of 9 kg. [1]

Work out \(\frac59+0.2\overline8\), giving a fraction in simplest form. [4]

Calculate \(\frac{20.24-\sqrt[3]{30}}{6.5}\), correct to 1 decimal place. [2]

Work out \(\frac56-\frac23\times\frac38\). [3]

Write \(0.2\overline6\) as a fraction in simplest form. [3]

Write \(0.2\overline5\) as a fraction. [2]

Write \(0.3\overline{28}\) as a fraction in simplest form. [3]

(a) Work out \(\frac56-\frac7{12}\), giving a fraction in simplest form. [2]

(b) Work out \(1\frac13\div\frac8{15}\), giving a mixed number in simplest form. [3]

Work out \(\frac{16.71+46.13}{\sqrt{8.6^2-3.5^2}}\), correct to 2 significant figures. [2]

Calculate \(\frac{2.1^2-1.9}{0.5}\). [1]

Write \(0.\overline{24}\) as a fraction in simplest form. [2]

Temperature rises from \(-12^\circ\text C\) at 4 am to \(21^\circ\text C\) at 4 pm. Find the increase. [1]

Rajid drinks \(1/3\) of a full bottle on Monday and \(3/7\) of the full bottle on Tuesday. Find the fraction remaining. [3]

Calculate \(0.1\overline{14}+0.2\), giving a fraction. [3]

A train starts at 22:16 and travels for 5 hours 52 minutes. Find its finishing time. [1]

Calculate \((3.5^2-2.2^3)^{1/4}\). [1]

\(G=\frac45m^2n\). Find G when m=6 and n=15. [1]

Identify the calculation equivalent to \(n\div2\frac35\): \(n\times2\frac53\), \(n\times\frac5{13}\), \(n\times\frac{13}5\), \(\frac1n\times\frac{13}5\), \(\frac1n\times\frac5{13}\). [1]

Without a calculator, work out \(1\frac14-\frac56\). Show all working and give a fraction in simplest form. [3]

Calculate \(\sqrt{5.76}+2.8^3\). [1]

A night bus runs from 21:50 to 05:18 the next day. Find how many hours and minutes it runs. [1]

The temperature is −4°C at midnight and 25°C at noon. Find the difference. [1]

Without a calculator, work out \(2\frac14\div1\frac78\). Show working and give a mixed number in simplest form. [3]

Write two million two thousand and two in figures. [1]

Insert one pair of brackets to make \(5-4\times3-9-2=0\) correct. [1]

Write \(0.4\overline1\) as a fraction in simplest form, showing working. [2]

Without a calculator, work out \(\frac37-\frac1{14}\), showing all working. Give a fraction in simplest form. [2]

Write \(0.1\overline{46}\) as a fraction in simplest form, showing all working. [3]

Calculate.

(a) \(\sqrt[3]{343}-\sqrt{40.96}\) [1]

(b) \((192+4\times16)^{1.25}\) [1]

Jonah has \(\$750\). He spends \(\frac14\) on travel and some on food, leaving \(\$437.50\). Find the fraction of the original money spent on food. [3]

A concert starts at 19:50 and finishes 2 hours 42 minutes later. Find its finishing time. [1]

Without a calculator, work out \(5\frac13-3\frac47\). Show all working and give a mixed number in simplest form. [3]

Find the reciprocal of \(1\frac14\). [1]

Calculate \(\sqrt[3]{1+10.9\times0.4^2}\). [1]

Without a calculator, work out \(\frac27\div\frac6{11}\). Show all working and simplify. [2]

Without a calculator, work out \(2\frac14-1\frac{11}{12}\). Show all working and give a fraction in simplest form. [3]

A train journey starts at 23:30 and finishes at 07:15 next day. Find its duration. [1]

Insert <, > or = in each gap: \(\frac27\;\ldots\;0.2861\), \(\frac{99}{900}\;\ldots\;11\%\), \(1^3\;\ldots\;4^0\). [2]

Without a calculator, work out \(\frac47\div8\). Show all your working and give your answer as a fraction in its simplest form. [2]

Without a calculator, work out \(2\frac17\div\frac59\). Show all your working and give a mixed number in its simplest form. [3]

Find the temperature 8°C colder than −5°C. [1]

Write \(0.6\overline{21}\) as a fraction in its simplest form. Show all your working. [3]

Without a calculator, work out \(\frac47\div1\frac5{21}\). Show all your working and give a fraction in its simplest form. [3]

Without a calculator, work out \(5\frac{11}{12}+2\frac14\). Show all your working and give a mixed number in its simplest form. [3]

Calculate \(\sqrt{42}+3^{0.4}\). [1]

Write \(0.5\overline{81}\) as a fraction in its simplest form. Show your working. [3]

Calculate \(7\frac3{11}\times3\frac3{10}\). [1]

Write the number 9 greater than \(-23\). [1]

Without a calculator, calculate \(3\frac18-1\frac34\). Show all working and give a mixed number in simplest form. [3]

Write \(0.4\overline2\) as a fraction in simplest form. Show all working. [3]

Without a calculator, calculate \(1\frac56\div\frac{11}{15}\). Show all working and give a mixed number in simplest form. [3]

Without a calculator calculate \(2\frac13\times\frac{11}{14}\). Show working and give a mixed number in simplest form. [3]

Calculate \(\sqrt5\times6^2\) to 2 decimal places. [2]

Calculate \(\frac{1-0.7}{0.45-0.38}\) to 4 significant figures. [2]

Without a calculator calculate \(3/7-2/21\). Show working and give a fraction in simplest form. [2]

Temperature is 4°C at noon and −9°C at midnight. Find the difference. [1]

Without a calculator calculate \(4\frac18-2\frac56\). Show all working and give a mixed number in simplest form. [3]

Figs cost 43 cents each. Lyra has \$5. Find the largest number she can buy and her change in cents. [3]

Find \(\frac{mk^3}{\sqrt3}\) when \(m=4,k=7\). [2]

Without a calculator calculate \(\frac29\div\frac56\). Show working and give a fraction in simplest form. [2]

(a) Find the lowest common multiple of 30 and 75. [2]

(b) Share \$608 in the ratio 4:5:7. [3]

(c) Calculate \(\frac{6.39\times10^4}{2.45\times10^6}\) and give the answer in standard form. [2]

(d) Write \(0.\dot2\dot7\) as a fraction. [1]

(e) A stone has volume \(45\text{ cm}^3\) and mass 126 g. Find its density, including units. Density = mass ÷ volume. [2]

Write 32 cm as a fraction of 2 m in simplest form. [2]

Without a calculator, calculate \(\frac13+\frac56\). Show all working and give a simplified mixed number. [2]

Find the sum of \(3^2\) and \(-3^2\). [1]

Without a calculator, calculate \(\frac59-\frac16\). Show all working and simplify. [2]

Convert \(0.2\dot4\) to a simplified fraction, showing working. [2]

Calculate \(\sqrt{15}+\frac{4.8}{2.2}\). [1]

Without a calculator, find \(\frac57-\frac23\). Show working and simplify. [2]

(a) Calculate \(2000\times1.2^3\). [1]

(b) Calculate \(2\frac18\times\frac6{17}\). [1]

(c) Calculate \(\frac{4.5\cos30^\circ}{\sqrt3}-2\). [1]

Convert \(0.4\dot1\dot9\) to a simplified fraction, showing all working. [3]

Joseph spends \(5/24\) of one week’s earnings on a \$56.50 jacket. Find his weekly earnings. [2]

Without a calculator, work out \(2\frac14\times3\frac23\). Show working and give a mixed number in simplest form. [3]

Write \(0.\dot3\dot7\) as a fraction. [1]

Without a calculator, work out \(1\frac38-\frac56\). Show working and give a fraction in simplest form. [3]

Write \(0.\dot0\dot4\) as a fraction in simplest form. [1]

Without a calculator, work out \(\frac23\div1\frac37\). Show working and give a fraction in simplest form. [3]

Find the number 23 less than −1.6. [1]

(a) Write 72% as a fraction in simplest form. [1]

(b) Write 0.004 as a fraction in simplest form. [1]

Without a calculator, work out \(1\frac23\div7\frac12\). Show working and give a fraction in simplest form. [3]

Calculate \(\frac{4.87-2.7}{-0.2+\sqrt[3]{0.729}}\). [1]

Without a calculator, work out \(1\frac56+\frac25\). Show working and give a mixed number in simplest form. [3]

The temperature is −8.5°C at midnight and −1°C at 11 am. Work out the difference. [1]

Without a calculator, work out \(\frac13\div\frac76+\frac15\). Show working and give a fraction in simplest form. [4]

Put \(2.1\times10^{-1},\ 0.\dot2,\ 22\%,\ \sqrt{0.2},\ \frac{24}{1000}\) in increasing order. [2]

Without a calculator, work out \(\frac{11}{12}+\frac34\). Show working and give a mixed number in simplest form. [3]

(a) From \(=,\ne,>,<\), select every symbol that makes \(0.5\ \ldots\ 5\%\) correct. [1]

(b) Insert one pair of brackets to make \(7-3-1+2=7\) correct. [1]

Write \(0.\dot2\dot7\) as a fraction. [1]

Write \(0.2\dot6\) as a fraction. Show all working. [2]

Without a calculator, work out \(\frac{15}{28}\div\frac47\). Show all working and give a fraction in simplest form. [3]

Without a calculator, work out \(1\frac34-\frac{11}{12}\). Show working and give a simplest fraction. [3]

Without a calculator, work out \(\left(2\frac13-\frac78\right)\times\frac6{25}\). Show all working and give a simplest fraction. [4]

At noon Maseru’s temperature was 21°C. By midnight it had fallen by 26°C. Find the midnight temperature. [1]

Find y in \(y=mx+c\) when m = −3, x = −2 and c = −8. [2]

Without a calculator, work out \(3\frac14-2\frac23\). Show all working and give a simplest fraction. [3]

Write \(0.1\dot7\) as a simplest fraction, showing working. [3]

Without a calculator, work out \(2\frac23\times2\frac34\). Show working and give a simplest mixed number. [3]

Write two hundred thousand and seventeen in figures. [1]

Without a calculator, work out \(\frac56\div1\frac13\). Show working and give a simplest fraction. [3]

Insert one pair of brackets to make \(7-5-3+4=9\) correct. [1]

Calculate \(\frac4{\sqrt{.0025}}\). [1]

Without a calculator, work out \(1\frac17\times2\frac1{10}\). Show working and give a simplest mixed number. [3]

The temperature at07:00 is −3°C, which is11°C higher than at01:00. Find the temperature at01:00. [1]

Jodi swims22 pool lengths for charity and receives \$15 per length. Find the money raised. [1]

Without a calculator, work out \(3\frac18\div\frac5{12}\). Show all working and give a simplest mixed number. [4]

Write \(0.\dot2\dot3\) as a fraction. [1]

Without a calculator, work out \(\frac56+\frac23\). Show all working and give a simplest mixed number. [3]

Calculate \(\sqrt[3]{8.1^2-1.3^{0.8}}\). [1]

Write \(0.4\dot7\) as a fraction. Show all working. [2]

Without a calculator, work out \(2\frac14\div\frac37\). Show all working and give a simplest mixed number. [3]

Use your calculator to work out \(\sqrt{1-(\sin33^\circ)^2}\). [1]

Write \(0.\dot7\) as a fraction. [1]

Giulio’s reaction times in two games are \(1/3\) s and \(1/8\) s. Find the difference. [1]

(a) Calculate \(-12\div(-2)\). [1]

(b) Calculate \(\sqrt[3]{2^3+2}\). [1]

Without a calculator, work out \(\frac{12}{35}\times\frac79\). Show all working; give a simplest fraction. [2]

Calculate \(\frac{16.379-.879}{4.2}\times1.241\) to 2 significant figures. [2]

Without a calculator, work out \(\frac5{16}\times1\frac17\). Show all working; give a simplest fraction. [2]

The lowest temperature recorded at Scott Base, Antarctica, is −57.0 °C. The highest temperature is 63.8 °C more. Find the highest temperature. [1]

Write \(0.6\dot7\) as a fraction. Show all working; give the simplest form. [2]

Without a calculator, work out \(3\frac58-1\frac23\). Show all working; give a mixed number in simplest form. [3]

Calculate \(\frac58+\sqrt[3]{340}\). [1]

Write the temperature 7 °C below −3 °C. [1]

Without a calculator, work out \(\frac23+\frac14\times\frac23\). Show all steps and give a fraction in simplest form. [4]

Calculate \(\sqrt{256^{0.25}+4\times8}\). [1]

Without a calculator, work out \(\frac78+\frac16\). Show all working; give a mixed number in simplest form. [3]

Calculate \(\sqrt{17.8}-1.3^{2.5}\). [1]

Write \(0.\dot8\) as a fraction. [1]

Without a calculator, work out \(1\frac34\times\frac6{35}\). Show all working; give a fraction in simplest form. [3]

Write \(0.\dot6\dot3\) as a fraction. [1]

Marcia works from 08:20 to 11:15. Find how long she works, in hours and minutes. [1]

(a) Calculate \(\sqrt{2.38+6.4^2}\); write your full calculator display. [1]

(b) Round the answer in (a) to 4 decimal places. [1]

Without a calculator, work out \(\frac23-\frac1{12}\). Show all working; give a fraction in simplest form. [2]

At noon in Chamonix the temperature was 6°C. At midnight it was 11°C lower. Find the midnight temperature. [1]

Without a calculator, work out \(\frac23\div1\frac15\). Show all working; give a fraction in simplest form. [3]

Carlos works from 21:20 to 06:15 the next day. Find the duration. [1]

Without a calculator, work out \(\frac38\div2\frac14\). Show all working; give a fraction in simplest form. [3]

Without a calculator, work out \(\frac1{15}+\frac25\). Show all steps and give a fraction in simplest form. [2]

\(\frac7{11}\) of 198 kg. [1]

Change \(0.1\dot8\) to a fraction, showing working. [2]

Calculate \(\frac{5.39-.98}{.743-.0743}\). [1]

Without a calculator, work out \(\frac14\div\frac23\). Show all working and give a fraction. [2]

Write \(0.1\dot7\) as a fraction. Show all working. [2]

Without a calculator, work out \(3\frac13\div2\frac12\). Show all working and give a mixed number in simplest form. [3]

Without a calculator, work out \(1\frac23+\frac57\). Show all working and give a mixed number in simplest form. [3]

Calculate \(\sqrt{120}+3.8^2-25\). [1]

Without a calculator, work out \(\frac56-\frac12\). Show all steps; give a fraction in simplest form. [2]

Calculate \(\sqrt{\frac12(1-\cos48^\circ)}\). [1]

The temperatures at 10 am one January day were:

(a) Which place was coldest? [1]

(b) By 2 pm Helsinki warmed by 4 °C. Write its temperature at 2 pm. [1]

Write \(0.\dot6\dot3\) as a fraction in lowest terms. Show all working. [3]

Without a calculator, work out \(\frac{11}{12}-(\frac34-\frac23)\). Show all working and give a fraction in simplest form. [4]

Without a calculator, work out \(1\frac23-\frac{11}{15}\). Show steps and give a fraction in lowest terms. [3]

At noon in Maseru the temperature is 17°C. At midnight it is 20°C lower. Find the midnight temperature. [1]

Write \(0.\overline{48}\) as a fraction, showing working. [2]

(a) Write \(11/3\) as a mixed number. [1]

(b) Without a calculator, work out \(\frac14+\frac5{12}\). Show steps and simplify. [2]

Without a calculator, work out \(3\frac17-1\frac14\). Show steps and give a mixed number in lowest terms. [3]

Write \(0.8\overline7\) as a fraction, showing working. [2]

Write \(0.\dot4=0.444\ldots\) as a fraction. [2]

Without a calculator, work out \(1\frac7{12}+\frac{13}{20}\). Show all working and give a mixed number in simplest form. [3]

Without a calculator, work out \(\frac67\div1\frac23\). Show all working and give a fraction in lowest terms. [3]

Without a calculator, work out \(2\frac58\times\frac37\). Show working and give a mixed number in lowest terms. [3]

Calculate \(\frac{3.07+2^4}{5.03-1.79}\). [1]

Without a calculator, work out \(\frac1{12}\times1\frac15\). Show all working and give a fraction in lowest terms. [2]

Write \(0.3\dot2=0.3222\ldots\) as a fraction. [2]

Write \(0.3\dot6=0.3666\ldots\) as a fraction in simplest form. [3]

Write the temperature 5°C below −2°C. [1]

Without a calculator, work out \(\frac23-\frac14\). Show all steps and give a fraction in lowest terms. [2]

Write \(0.\overline2=0.222\ldots\) as a fraction. [2]

Without a calculator, work out \(\frac35+\frac16\). Show all steps and give a fraction in simplest form. [2]

(a) Write \$0.70 as a fraction of \$5.60, in lowest terms. [1]

(b) Write \(0.\overline{18}=0.181818\ldots\) as a fraction, in lowest terms. [2]

Without a calculator, work out \(\frac34+\frac23-\frac18\). Show all working and give a mixed number in simplest form. [4]

Calculate:

(a) \(2^3-\sqrt{10+4^2}\); [1]

(b) \(\frac{2\sqrt3\tan70^\circ}{3}\). [1]

Without a calculator, work out \(2\frac79\div\frac56\). Show each step and give a fraction in lowest terms. [4]

At noon the temperature is 4°C; at midnight it is −5.5°C. Find the difference. [1]

Use a calculator to work out \(\sqrt{10+0.6\times(8.3^2+5)}\). [1]

Without a calculator, calculate \(1\frac45\div\frac37\). Show working and give a fraction in lowest terms. [3]

Without a calculator, work out \(\frac45\div2\frac23\). Show all steps and give a fraction in simplest form. [3]

Write \(0.2\overline5=0.2555\ldots\) as a fraction. [2]

Without a calculator, work out \(1\frac78\div\frac59\). Show working and give a fraction in lowest terms. [3]

At midnight the temperature is −8°C; at noon it is 9°C. Find the rise. [1]

Express \(0.1\overline5=0.15555\ldots\) as a fraction. [2]

Find the difference between 8°C and −9°C. [1]

Without a calculator, evaluate \(\tfrac23+\tfrac16-\tfrac14\). Show working and give a fraction in lowest terms. [3]

Without a calculator, evaluate \(2\tfrac14-\tfrac{11}{12}\). Show working and give a fraction in lowest terms. [3]

Calculate \((2.07-1.89)/(5.71-3.92)\). [1]

Calculate \(\sqrt{3/4}+2^{-1}\), to 2 decimal places. [2]

\(y=2/x^2+x^2/2\). Find y when x = 6, as a simplified mixed number. [2]

Calculate \(\sqrt[3]{16}/1.3^2\). [1]

Order from smallest: \(\sqrt{0.1},\ 43/201,\ 2\tfrac12\%,\ 0.2\). [2]

Without a calculator, work out \(5/6-(1/2\times1\tfrac12)\), showing all steps. [3]

Kiev’s March 2011 average temperature was 3°C. In March 2012 it was 19°C lower. Find the March 2012 average. [1]

Without a calculator, work out \(1\tfrac14-7/9\), showing steps. [3]

Calculate \(1.35^7\) to 5 significant figures. [2]

Order \(\pi,\ 3.14,\ 22/7,\ 3.142,\ 3\) from smallest to largest. [2]

Without a calculator, find \(1/4+1/6\) as a fraction in its simplest form. Show working. [2]

Insert one pair of brackets to make \(6+5\times10-8=16\) correct. [1]

Calculate \((8.24+2.56)/(1.26-0.72)\). [1]

Without a calculator, find \(1\tfrac16\div\tfrac78\) in lowest terms, showing working. [3]

Order \(0.34,\ \sqrt{0.6},\ 0.6^2,\ 0.7^3\) from smallest to largest. [2]

In Munich the temperature at noon was 3°C and at midnight was −8°C. Write down the difference between the temperatures. [1]

Without a calculator, show all steps proving \(1\tfrac12\div\tfrac3{16}=8\). [2]

Without a calculator, work out \(\tfrac67\div1\tfrac23\), showing all steps. [3]

(a) Calculate \(\sqrt{5.7}-1.03^2\). Write all the digits displayed on your calculator. [1]

(b) Give your answer to (a) correct to 3 decimal places. [1]

(a) Calculate \(\sqrt{65}-1.7^2\) and give all the digits displayed. [1]

(b) Give your answer to 2 significant figures. [1]

(a) Use a calculator to find \(\sqrt{5\tfrac5{24}}\). [1]

(b) Find \(\cos40^\circ/7\). [1]

Calculate \((5.27-0.93)/(4.89-4.07)\) to 4 significant figures. [2]