Number - Using A Calculator
Question 1
Use a calculator to investigate these order of operations questions
a) $5+8-2$
a
$11$
Question ID: 10060010010
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b) $5-2+8$
a
$11$
Question ID: 10060010020
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c) $8\times2\div4$
a
$4$
Question ID: 10060010030
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d) $8\div4\times2$
a
$4$
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e) $10+20\times3$
a
$70$
Question ID: 10060010050
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f) $10\times3+20$
a
$50$
Question ID: 10060010060
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g) $20+40\div4$
a
$30$
Question ID: 10060010070
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h) $20\div4+40$
a
$45$
Question ID: 10060010080
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Question 2
Use a calculator to investigate these order of operations questions
a) $3+5\times2$
a
$13$
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b) $(3+5)\times2$
a
$16$
Question ID: 10060020020
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c) $20-8\div4$
a
$18$
Question ID: 10060020030
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d) $(20-8)\div4$
a
$3$
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e) $5\times2+3\times4$
a
$22$
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f) $5\times(2+3)\times4$
a
$100$
Question ID: 10060020060
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g) $60\div10-9\div3$
a
$3$
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h) $60\div(10-9)\div3$
a
$20$
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Question 3
Use the $x^2$, $x^3$ or $x^y$ button on your calculator for the following:
a) $5^2$
a
$25$
Question ID: 10060030010
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b) $27^2$
a
$729$
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c) $7^3$
a
$343$
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d) $19^3$
a
$6859$
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e) $13^4$
a
$28561$
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f) $6^5$
a
$7776$
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g) $5^8$
a
$390625$
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h) $21^7$
a
$1801088541$
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Question 4
Can you explain the order of operations your calculator uses here?
a) $-3^2$
a
The answer is $-9$. The calculator calculated $3^2$ first and then put a negative sign in front of it.
Question ID: 10060040010
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The answer is $-9$. The calculator calculated $3^2$ first and then put a negative sign in front of it.
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b) $(-3)^2$
a
The answer is $9$. The calculator calculated $-3\times-3$ to give an answer of $9$
Question ID: 10060040020
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The answer is $9$. The calculator calculated $-3\times\-3$ to give an answer of $9$
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c) $-2^4$
a
The answer is $-16$. The calculator calculated $2^4$ first and then put a negative sign in front of it.
Question ID: 10060040030
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The answer is $-16$. The calculator calculated $2^4$ first and then put a negative sign in front of it.
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d) $(-2)^4$
a
The answer is $16$. The calculator calculated $-2\times-2\times-2\times-2$ to give an answer of $16$
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The answer is $16$. The calculator calculated $-2\times\-2\times-2\times-2$ to give an answer of $16$
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e) $-1^3$
a
The answer is $-1$. The calculator calculated $1^3$ first and then put a negative sign in front of it.
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The answer is $-1$. The calculator calculated $1^3$ first and then put a negative sign in front of it.
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f) $(-1)^3$
a
The answer is $-1$. The calculator calculated $-1\times-1\times-1$ to give an answer of $-1$
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The answer is $-1$. The calculator calculated $-1\times\-1\times-1$ to give an answer of $-1$
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g) $3^2+5^2$
a
The answer is $34$. The calculator calculated $3^2$ and $5^2$ first and then found their sum.
Question ID: 10060040070
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The answer is $34$. The calculator calculated $3^2$ and $5^2$ first and then found their sum.
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h) $(3+5)^2$
a
The answer $64$. The calculator calculated the sum of $3$ and $5$ first and then squared the answer. This gave a different answer to the previous question.
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The answer $64$. The calculator calculated the sum of $3$ and $5$ first and then squared the answer. This gave a different answer to the previous question.
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Question 5
Use the $\sqrt\square$, $\sqrt[3]\square$ or $\sqrt[\square]\square$ button on your calculator for the following:
a) $\sqrt9$
a
$3$
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b) $\sqrt{324}$
a
$18$
Question ID: 10060050020
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c) $\sqrt[3]{216}$
a
$6$
Question ID: 10060050030
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d) $\sqrt[3]{-3375}$
a
$-15$
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e) $\sqrt[4]{6561}$
a
$9$
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f) $\sqrt[5]{16807}$
a
$7$
Question ID: 10060050060
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g) $\sqrt[6]{1.771561}$
a
$1.1$
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h) $\sqrt[11]{-177147}$
a
$-3$
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i) Can you explain the result you get from $\sqrt{-64}$ compared with $\sqrt[3]{-64}$?
a
$\sqrt{-64}$ gives a maths error whilst $\sqrt[3]{-64}=-4$. This is because your calculator cannot find the square roots of negative numbers. You may wish to investigate $\sqrt[4]\square$, $\sqrt[5]\square$, etc. where $\square$ is a negative number.
Question ID: 10060050090
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$\sqrt{-64}$ gives a maths error whilst $\sqrt[3]{-64}=-4$. This is because your calculator cannot find the square roots of negative numbers. You may wish to investigate $\sqrt[4]\square$, $\sqrt[5]\square$, etc. where $\square$ is a negative number.
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Question 6
Use the keys $\frac\square\square$ to calculate the following:
a) $\frac14\times3$
a
$\frac34$
Question ID: 10060060010
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b) $\frac27\times\frac35$
a
$\frac{6}{35}$
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c) $\frac14\div\frac13$
a
$\frac34$
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d) $\frac{1+2}{5}$
a
$\frac{3}{5}$
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e) $\frac{2^3}{8}$
a
$1$
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f) $\left(\frac{2}{8}\right)^3$
a
$\frac{1}{64}$
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g) $\frac{4+5}{20-8}-\frac{3\times2}{4}$
a
$-\frac34$
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h) $\frac{2^2}{15\div3}-\left(\frac{4-3}{2^3}\right)^3$
a
$\frac{2043}{2560}$
Question ID: 10060060080
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Question 7
Use the keys $\square\frac\square\square$ to calculate the following. Leave your answer as a top heavy/improper fraction.
a) $1\frac25-1$
a
$\frac{2}{5}$
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b) $2\frac13+2$
a
$\frac{13}{3}$
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c) $5\frac17+\frac37$
a
$\frac{39}{7}$
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d) $3\frac12-\frac45$
a
$\frac{27}{10}$
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e) $3\frac49+1\frac39$
a
$\frac{43}{9}$
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f) $2\frac16-1\frac56$
a
$\frac{1}{3}$
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g) $4\frac25-2\frac34$
a
$\frac{33}{20}$
Question ID: 10060070070
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h) $2\frac{3+4}{8}-1+8\frac{2}{5-2}$
a
$\frac{253}{24}$
Question ID: 10060070080
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Question 8
Express each of the following answers as a top heavy/improper fraction, a mixed number and a decimal
a) $1+\frac12+2$
a
$\frac72$ $3\frac12$ $3.5$
Question ID: 10060080010
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b) $2.1+3.2$
a
$\frac{53}{10}$ $5\frac{3}{10}$ $5.3$
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c) $\frac45+2.4$
a
$\frac{16}{5}$ $3\frac{1}{5}$ $3.2$
Question ID: 10060080030
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d) $\frac45\times1.34$
a
$\frac{134}{125}$ $1\frac{9}{125}$ $1.072$
Question ID: 10060080040
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e) $2\frac15\div\frac14$
a
$\frac{44}{5}$ $8\frac{4}{5}$ $8.8$
Question ID: 10060080050
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f) $1.5\times\frac53+1\frac{9}{12}$
a
$\frac{17}{4}$ $4\frac{1}{4}$ $4.25$
Question ID: 10060080060
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g) $4.7+1.5\times5\frac15\div\frac12$
a
$\frac{203}{10}$ $20\frac{3}{10}$ $20.3$
Question ID: 10060080070
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h) $8\frac12\div\frac45-\frac{4+5}{10}-8.45^2$
a
$-\frac{24671}{400}$ $-61\frac{271}{400}$ $-61.6775$
Question ID: 10060080080
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Question 9
Type in the following and use your calculator to express as a fraction. Final answer should be impropert/top heavy where necessary
a) $1.\dot{1}$
a
$\frac{10}{9}$
Question ID: 10060090010
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b) $2.\dot{3}$
a
$\frac{7}{3}$
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c) $4.\dot{5}$
a
$\frac{41}{9}$
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d) $0.\dot{6}$
a
$\frac23$
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e) $0.8\dot{4}$
a
$\frac{38}{45}$
Question ID: 10060090050
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f) $8.2\dot{3}$
a
$\frac{247}{30}$
Question ID: 10060090060
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g) $0.\dot{2}\dot{3}$
a
$\frac{23}{99}$
Question ID: 10060090070
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h) $4.\dot{3}\dot{6}$
a
$\frac{48}{11}$
Question ID: 10060090080
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i) $8.\dot{2}3\dot{4}$
a
$\frac{914}{111}$
Question ID: 10060090090
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j) $35.\dot{6}7\dot{6}$
a
$\frac{35641}{999}$
Question ID: 10060090100
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k) $0.\dot{9}$
a
$1$
Question ID: 10060090110
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Question 10
Use the $\%$ button to find the answer to the following. Leave answers as decimals where necessary.
a) $100\times50\%$
a
$50$
Question ID: 10060100010
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b) $140\times20\%$
a
$28$
Question ID: 10060100020
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c) $360\times15\%$
a
$54$
Question ID: 10060100030
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d) $4.5\times40\%$
a
$1.8$
Question ID: 10060100040
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e) Find $20\%$ of $540$
a
$108$
Question ID: 10060100050
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f) Find $17\%$ of $345$
a
$58.65$
Question ID: 10060100060
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g) $14\%$ of $83+82\%$ of $47$
a
$50.16$
Question ID: 10060100070
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h) $1.4\%$ of $62+55\times3.4\%$
a
$2.738$
Question ID: 10060100080
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i) $20\%+30\%$
a
$0.5$
Question ID: 10060100090
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j) $75\%-14\%$
a
$0.61$
Question ID: 10060100100
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Question 11
Use the Ran# button to generate a random number between:
a) $0$ and $1$
a
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Type in Ran# and press $=$. It will give you a decimal up to $3$ decimal places between $0$ and $1$
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b) $0$ and $1000$
a
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Type in Ran#$\times1000$ and press $=$. It will give you a number between $0$ and $1000$
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c) $1000$ and $2000$
a
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Type in Ran#$\times1000+1000$ and press $=$. It will give you a number between $1000$ and $2000$
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d) $500$ and $1500$
a
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Question ID: 10060110040
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Type in Ran#$\times1000+500$ and press $=$. It will give you a number between $500$ and $1500$
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e) $0$ and $100$
a
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Type in Ran#$\times100$ and press $=$. It will give you a number between $0$ and $100$, but may include a decimal place. If you want to generate a whole number, simply ignore the decimal
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Question 12
Use the FACT button to find the prime factorisation of the following: (your calculator may not necessarily have this button)
a) $6$
a
$2\times3$
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b) $12$
a
$2^2\times3$
Question ID: 10060120020
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c) $15$
a
$3\times5$
Question ID: 10060120030
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d) $20$
a
$2^2\times5$
Question ID: 10060120040
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e) $245$
a
$5\times7^2$
Question ID: 10060120050
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f) $60$
a
$2^2\times3\times5$
Question ID: 10060120060
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g) $2310$
a
$2\times3\times5\times7\times11$
Question ID: 10060120070
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h) $126$
a
$2\times3^2\times7$
Question ID: 10060120080
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i) $80262$
a
$2\times3^2\times7^3\times13$
Question ID: 10060120090
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j) $136458$
a
$2\times3^3\times7\times19^2$
Question ID: 10060120100
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k) $1$
a
As $1$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
Question ID: 10060120110
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l) $0$
a
As $0$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
Question ID: 10060120120
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m) $-2$
a
As $-2$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
Question ID: 10060120130
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n) $1.1$
a
As $1.1$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
Question ID: 10060120140
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Question 13
Use your calculators memory to work out the following calculations. You should not need to memorise or write down any intermediate answers yourself.
a) Calculate $3.2\times4.3$. Store this answer. Multiply the answer by $14$
a
$192.64$
Question ID: 10060130010
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b) Calculate $0.14\div18$. Store this answer. Multiply the answer by $180$
a
$1.4$
Question ID: 10060130020
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c) Calculate $\sqrt5$. Store this answer. Divide the answer by $7$. Store this answer. Multiply the new answer by $\sqrt{20}$.
a
$\frac{10}{7}$ or $1\frac37$
Question ID: 10060130030
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d) Calculate $\frac34\div1\frac13$. Store this answer. Squuare the answer. Store this answer. Divide the new answer by $8$. Store this answer. Multiply the answer by $4096$.
a
$162$
Question ID: 10060130040
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e) Calculate $10\div33$. Store this answer under A. Calculate $11\div100$. Store this answer under B. Find A$\times$B.
a
$\frac{1}{30}$
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f) Calculate $0.55^2+3$. Store this answer under A. Calculate $\sqrt{169}-18$. Store this answer under B. Calculate B$^2$-A.
a
$\frac{8679}{400}$ or $21\frac{279}{400}$ or $21.6975$
Question ID: 10060130060
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g) Calculate $5^2-3\times2\times2$. Store this answer. Calculate the square root of the answer. Store this answer. Add $5$ to the new answer. Store this answer. Divide the new answer by $4$. Round your answer to $2$ decimal places.
a
$2.15$
Question ID: 10060130070
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h) Calculate $\frac34-\frac23$. Store this answer under A. Calculate $18^2-22$. Store this answer under B. Calculate $(-3)^4-100$. Store this answer under C. Calculate A$^2$$\times$B$+$C.
a
$-\frac{1217}{72}$ or $-16\frac{65}{72}
Question ID: 10060130080
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Question 14
Use your calculator to find the answer to the following:
a) $5^3+18$
a
$143$
Question ID: 10060140010
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b) $5^7-3^7-1^7$
a
$75937$
Question ID: 10060140020
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c) $(-6.85)^2\times400$
a
$18769$
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d) $6^2-\frac23\times24$
a
$20$
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e) $\frac{4^2-6}{2^8}$
a
$\frac{5}{128}$
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f) $18\%$ of $50000$
a
$9000$
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g) $3\%$ of $6789$ $-$ $22\%$ of $80$
a
$\frac{18607}{100}$ or $186\frac{7}{100}$ or $186.07$
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h) $2(8.3+6.33)-4(3.1-1.1)^2-0.26$
a
$13$
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i) $\sqrt{27220+10\div2}-66$
a
$99$
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j) $3\frac45+\frac{\sqrt{48}}{\sqrt{243}}-3.2$
a
$\frac{47}{45}$ or $1\frac{2}{45}$
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k) $\frac{4}{7}$ of $455$ plus $33.5$
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$293.5$ or $293\frac12$ or $\frac{587}{2}$
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l) $\frac{9.2\div3.4}{8.6^2}\times62866\div(21-2\times8)$
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$460$
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Question 1
Use a calculator to investigate these order of operations questions
a) $5+8-2$
b) $5-2+8$
c) $8\times2\div4$
d) $8\div4\times2$
e) $10+20\times3$
f) $10\times3+20$
g) $20+40\div4$
h) $20\div4+40$
Question 2
Use a calculator to investigate these order of operations questions
a) $3+5\times2$
b) $(3+5)\times2$
c) $20-8\div4$
d) $(20-8)\div4$
e) $5\times2+3\times4$
f) $5\times(2+3)\times4$
g) $60\div10-9\div3$
h) $60\div(10-9)\div3$
Question 3
Use the $x^2$, $x^3$ or $x^y$ button on your calculator for the following:
a) $5^2$
b) $27^2$
c) $7^3$
d) $19^3$
e) $13^4$
f) $6^5$
g) $5^8$
h) $21^7$
Question 4
Can you explain the order of operations your calculator uses here?
a) $-3^2$
b) $(-3)^2$
c) $-2^4$
d) $(-2)^4$
e) $-1^3$
f) $(-1)^3$
g) $3^2+5^2$
h) $(3+5)^2$
Question 5
Use the $\sqrt\square$, $\sqrt[3]\square$ or $\sqrt[\square]\square$ button on your calculator for the following:
a) $\sqrt9$
b) $\sqrt{324}$
c) $\sqrt[3]{216}$
d) $\sqrt[3]{-3375}$
e) $\sqrt[4]{6561}$
f) $\sqrt[5]{16807}$
g) $\sqrt[6]{1.771561}$
h) $\sqrt[11]{-177147}$
i) Can you explain the result you get from $\sqrt{-64}$ compared with $\sqrt[3]{-64}$?
Question 6
Use the keys $\frac\square\square$ to calculate the following:
a) $\frac14\times3$
b) $\frac27\times\frac35$
c) $\frac14\div\frac13$
d) $\frac{1+2}{5}$
e) $\frac{2^3}{8}$
f) $\left(\frac{2}{8}\right)^3$
g) $\frac{4+5}{20-8}-\frac{3\times2}{4}$
h) $\frac{2^2}{15\div3}-\left(\frac{4-3}{2^3}\right)^3$
Question 7
Use the keys $\square\frac\square\square$ to calculate the following. Leave your answer as a top heavy/improper fraction.
a) $1\frac25-1$
b) $2\frac13+2$
c) $5\frac17+\frac37$
d) $3\frac12-\frac45$
e) $3\frac49+1\frac39$
f) $2\frac16-1\frac56$
g) $4\frac25-2\frac34$
h) $2\frac{3+4}{8}-1+8\frac{2}{5-2}$
Question 8
Express each of the following answers as a top heavy/improper fraction, a mixed number and a decimal
a) $1+\frac12+2$
b) $2.1+3.2$
c) $\frac45+2.4$
d) $\frac45\times1.34$
e) $2\frac15\div\frac14$
f) $1.5\times\frac53+1\frac{9}{12}$
g) $4.7+1.5\times5\frac15\div\frac12$
h) $8\frac12\div\frac45-\frac{4+5}{10}-8.45^2$
Question 9
Type in the following and use your calculator to express as a fraction. Final answer should be impropert/top heavy where necessary
a) $1.\dot{1}$
b) $2.\dot{3}$
c) $4.\dot{5}$
d) $0.\dot{6}$
e) $0.8\dot{4}$
f) $8.2\dot{3}$
g) $0.\dot{2}\dot{3}$
h) $4.\dot{3}\dot{6}$
i) $8.\dot{2}3\dot{4}$
j) $35.\dot{6}7\dot{6}$
k) $0.\dot{9}$
Question 10
Use the $\%$ button to find the answer to the following. Leave answers as decimals where necessary.
a) $100\times50\%$
b) $140\times20\%$
c) $360\times15\%$
d) $4.5\times40\%$
e) Find $20\%$ of $540$
f) Find $17\%$ of $345$
g) $14\%$ of $83+82\%$ of $47$
h) $1.4\%$ of $62+55\times3.4\%$
i) $20\%+30\%$
j) $75\%-14\%$
Question 11
Use the Ran# button to generate a random number between:
a) $0$ and $1$
b) $0$ and $1000$
c) $1000$ and $2000$
d) $500$ and $1500$
e) $0$ and $100$
Question 12
Use the FACT button to find the prime factorisation of the following: (your calculator may not necessarily have this button)
a) $6$
b) $12$
c) $15$
d) $20$
e) $245$
f) $60$
g) $2310$
h) $126$
i) $80262$
j) $136458$
k) $1$
l) $0$
m) $-2$
n) $1.1$
Question 13
Use your calculators memory to work out the following calculations. You should not need to memorise or write down any intermediate answers yourself.
a) Calculate $3.2\times4.3$. Store this answer. Multiply the answer by $14$
b) Calculate $0.14\div18$. Store this answer. Multiply the answer by $180$
c) Calculate $\sqrt5$. Store this answer. Divide the answer by $7$. Store this answer. Multiply the new answer by $\sqrt{20}$.
d) Calculate $\frac34\div1\frac13$. Store this answer. Squuare the answer. Store this answer. Divide the new answer by $8$. Store this answer. Multiply the answer by $4096$.
e) Calculate $10\div33$. Store this answer under A. Calculate $11\div100$. Store this answer under B. Find A$\times$B.
f) Calculate $0.55^2+3$. Store this answer under A. Calculate $\sqrt{169}-18$. Store this answer under B. Calculate B$^2$-A.
g) Calculate $5^2-3\times2\times2$. Store this answer. Calculate the square root of the answer. Store this answer. Add $5$ to the new answer. Store this answer. Divide the new answer by $4$. Round your answer to $2$ decimal places.
h) Calculate $\frac34-\frac23$. Store this answer under A. Calculate $18^2-22$. Store this answer under B. Calculate $(-3)^4-100$. Store this answer under C. Calculate A$^2$$\times$B$+$C.
Question 14
Use your calculator to find the answer to the following:
a) $5^3+18$
b) $5^7-3^7-1^7$
c) $(-6.85)^2\times400$
d) $6^2-\frac23\times24$
e) $\frac{4^2-6}{2^8}$
f) $18\%$ of $50000$
g) $3\%$ of $6789$ $-$ $22\%$ of $80$
h) $2(8.3+6.33)-4(3.1-1.1)^2-0.26$
i) $\sqrt{27220+10\div2}-66$
j) $3\frac45+\frac{\sqrt{48}}{\sqrt{243}}-3.2$
k) $\frac{4}{7}$ of $455$ plus $33.5$
l) $\frac{9.2\div3.4}{8.6^2}\times62866\div(21-2\times8)$
Answers
Question 1
a) $11$
b) $11$
c) $4$
d) $4$
e) $70$
f) $50$
g) $30$
h) $45$
Question 2
a) $13$
b) $16$
c) $18$
d) $3$
e) $22$
f) $100$
g) $3$
h) $20$
Question 3
a) $25$
b) $729$
c) $343$
d) $6859$
e) $28561$
f) $7776$
g) $390625$
h) $1801088541$
Question 4
a) The answer is $-9$. The calculator calculated $3^2$ first and then put a negative sign in front of it.
b) The answer is $9$. The calculator calculated $-3\times-3$ to give an answer of $9$
c) The answer is $-16$. The calculator calculated $2^4$ first and then put a negative sign in front of it.
d) The answer is $16$. The calculator calculated $-2\times-2\times-2\times-2$ to give an answer of $16$
e) The answer is $-1$. The calculator calculated $1^3$ first and then put a negative sign in front of it.
f) The answer is $-1$. The calculator calculated $-1\times-1\times-1$ to give an answer of $-1$
g) The answer is $34$. The calculator calculated $3^2$ and $5^2$ first and then found their sum.
h) The answer $64$. The calculator calculated the sum of $3$ and $5$ first and then squared the answer. This gave a different answer to the previous question.
Question 5
a) $3$
b) $18$
c) $6$
d) $-15$
e) $9$
f) $7$
g) $1.1$
h) $-3$
i) $\sqrt{-64}$ gives a maths error whilst $\sqrt[3]{-64}=-4$. This is because your calculator cannot find the square roots of negative numbers. You may wish to investigate $\sqrt[4]\square$, $\sqrt[5]\square$, etc. where $\square$ is a negative number.
Question 6
a) $\frac34$
b) $\frac{6}{35}$
c) $\frac34$
d) $\frac{3}{5}$
e) $1$
f) $\frac{1}{64}$
g) $-\frac34$
h) $\frac{2043}{2560}$
Question 7
a) $\frac{2}{5}$
b) $\frac{13}{3}$
c) $\frac{39}{7}$
d) $\frac{27}{10}$
e) $\frac{43}{9}$
f) $\frac{1}{3}$
g) $\frac{33}{20}$
h) $\frac{253}{24}$
Question 8
a) $\frac72$ $3\frac12$ $3.5$
b) $\frac{53}{10}$ $5\frac{3}{10}$ $5.3$
c) $\frac{16}{5}$ $3\frac{1}{5}$ $3.2$
d) $\frac{134}{125}$ $1\frac{9}{125}$ $1.072$
e) $\frac{44}{5}$ $8\frac{4}{5}$ $8.8$
f) $\frac{17}{4}$ $4\frac{1}{4}$ $4.25$
g) $\frac{203}{10}$ $20\frac{3}{10}$ $20.3$
h) $-\frac{24671}{400}$ $-61\frac{271}{400}$ $-61.6775$
Question 9
a) $\frac{10}{9}$
b) $\frac{7}{3}$
c) $\frac{41}{9}$
d) $\frac23$
e) $\frac{38}{45}$
f) $\frac{247}{30}$
g) $\frac{23}{99}$
h) $\frac{48}{11}$
i) $\frac{914}{111}$
j) $\frac{35641}{999}$
k) $1$
Question 10
a) $50$
b) $28$
c) $54$
d) $1.8$
e) $108$
f) $58.65$
g) $50.16$
h) $2.738$
i) $0.5$
j) $0.61$
Question 11
a) Various Answers!
b) Various Answers!
c) Various Answers!
d) Various Answers!
e) Various Answers!
Question 12
a) $2\times3$
b) $2^2\times3$
c) $3\times5$
d) $2^2\times5$
e) $5\times7^2$
f) $2^2\times3\times5$
g) $2\times3\times5\times7\times11$
h) $2\times3^2\times7$
i) $2\times3^2\times7^3\times13$
j) $2\times3^3\times7\times19^2$
k) As $1$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
l) As $0$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
m) As $-2$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
n) As $1.1$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
Question 13
a) $192.64$
b) $1.4$
c) $\frac{10}{7}$ or $1\frac37$
d) $162$
e) $\frac{1}{30}$
f) $\frac{8679}{400}$ or $21\frac{279}{400}$ or $21.6975$
g) $2.15$
h) $-\frac{1217}{72}$ or $-16\frac{65}{72}
Question 14
a) $143$
b) $75937$
c) $18769$
d) $20$
e) $\frac{5}{128}$
f) $9000$
g) $\frac{18607}{100}$ or $186\frac{7}{100}$ or $186.07$
h) $13$
i) $99$
j) $\frac{47}{45}$ or $1\frac{2}{45}$
k) $293.5$ or $293\frac12$ or $\frac{587}{2}$
l) $460$
Question 1
Use a calculator to investigate these order of operations questions
a) $5+8-2$
b) $5-2+8$
c) $8\times2\div4$
d) $8\div4\times2$
e) $10+20\times3$
f) $10\times3+20$
g) $20+40\div4$
h) $20\div4+40$
Question 2
Use a calculator to investigate these order of operations questions
a) $3+5\times2$
b) $(3+5)\times2$
c) $20-8\div4$
d) $(20-8)\div4$
e) $5\times2+3\times4$
f) $5\times(2+3)\times4$
g) $60\div10-9\div3$
h) $60\div(10-9)\div3$
Question 3
Use the $x^2$, $x^3$ or $x^y$ button on your calculator for the following:
a) $5^2$
b) $27^2$
c) $7^3$
d) $19^3$
e) $13^4$
f) $6^5$
g) $5^8$
h) $21^7$
Question 4
Can you explain the order of operations your calculator uses here?
a) $-3^2$
b) $(-3)^2$
c) $-2^4$
d) $(-2)^4$
e) $-1^3$
f) $(-1)^3$
g) $3^2+5^2$
h) $(3+5)^2$
Question 5
Use the $\sqrt\square$, $\sqrt[3]\square$ or $\sqrt[\square]\square$ button on your calculator for the following:
a) $\sqrt9$
b) $\sqrt{324}$
c) $\sqrt[3]{216}$
d) $\sqrt[3]{-3375}$
e) $\sqrt[4]{6561}$
f) $\sqrt[5]{16807}$
g) $\sqrt[6]{1.771561}$
h) $\sqrt[11]{-177147}$
i) Can you explain the result you get from $\sqrt{-64}$ compared with $\sqrt[3]{-64}$?
Question 6
Use the keys $\frac\square\square$ to calculate the following:
a) $\frac14\times3$
b) $\frac27\times\frac35$
c) $\frac14\div\frac13$
d) $\frac{1+2}{5}$
e) $\frac{2^3}{8}$
f) $\left(\frac{2}{8}\right)^3$
g) $\frac{4+5}{20-8}-\frac{3\times2}{4}$
h) $\frac{2^2}{15\div3}-\left(\frac{4-3}{2^3}\right)^3$
Question 7
Use the keys $\square\frac\square\square$ to calculate the following. Leave your answer as a top heavy/improper fraction.
a) $1\frac25-1$
b) $2\frac13+2$
c) $5\frac17+\frac37$
d) $3\frac12-\frac45$
e) $3\frac49+1\frac39$
f) $2\frac16-1\frac56$
g) $4\frac25-2\frac34$
h) $2\frac{3+4}{8}-1+8\frac{2}{5-2}$
Question 8
Express each of the following answers as a top heavy/improper fraction, a mixed number and a decimal
a) $1+\frac12+2$
b) $2.1+3.2$
c) $\frac45+2.4$
d) $\frac45\times1.34$
e) $2\frac15\div\frac14$
f) $1.5\times\frac53+1\frac{9}{12}$
g) $4.7+1.5\times5\frac15\div\frac12$
h) $8\frac12\div\frac45-\frac{4+5}{10}-8.45^2$
Question 9
Type in the following and use your calculator to express as a fraction. Final answer should be impropert/top heavy where necessary
a) $1.\dot{1}$
b) $2.\dot{3}$
c) $4.\dot{5}$
d) $0.\dot{6}$
e) $0.8\dot{4}$
f) $8.2\dot{3}$
g) $0.\dot{2}\dot{3}$
h) $4.\dot{3}\dot{6}$
i) $8.\dot{2}3\dot{4}$
j) $35.\dot{6}7\dot{6}$
k) $0.\dot{9}$
Question 10
Use the $\%$ button to find the answer to the following. Leave answers as decimals where necessary.
a) $100\times50\%$
b) $140\times20\%$
c) $360\times15\%$
d) $4.5\times40\%$
e) Find $20\%$ of $540$
f) Find $17\%$ of $345$
g) $14\%$ of $83+82\%$ of $47$
h) $1.4\%$ of $62+55\times3.4\%$
i) $20\%+30\%$
j) $75\%-14\%$
Question 11
Use the Ran# button to generate a random number between:
a) $0$ and $1$
b) $0$ and $1000$
c) $1000$ and $2000$
d) $500$ and $1500$
e) $0$ and $100$
Question 12
Use the FACT button to find the prime factorisation of the following: (your calculator may not necessarily have this button)
a) $6$
b) $12$
c) $15$
d) $20$
e) $245$
f) $60$
g) $2310$
h) $126$
i) $80262$
j) $136458$
k) $1$
l) $0$
m) $-2$
n) $1.1$
Question 13
Use your calculators memory to work out the following calculations. You should not need to memorise or write down any intermediate answers yourself.
a) Calculate $3.2\times4.3$. Store this answer. Multiply the answer by $14$
b) Calculate $0.14\div18$. Store this answer. Multiply the answer by $180$
c) Calculate $\sqrt5$. Store this answer. Divide the answer by $7$. Store this answer. Multiply the new answer by $\sqrt{20}$.
d) Calculate $\frac34\div1\frac13$. Store this answer. Squuare the answer. Store this answer. Divide the new answer by $8$. Store this answer. Multiply the answer by $4096$.
e) Calculate $10\div33$. Store this answer under A. Calculate $11\div100$. Store this answer under B. Find A$\times$B.
f) Calculate $0.55^2+3$. Store this answer under A. Calculate $\sqrt{169}-18$. Store this answer under B. Calculate B$^2$-A.
g) Calculate $5^2-3\times2\times2$. Store this answer. Calculate the square root of the answer. Store this answer. Add $5$ to the new answer. Store this answer. Divide the new answer by $4$. Round your answer to $2$ decimal places.
h) Calculate $\frac34-\frac23$. Store this answer under A. Calculate $18^2-22$. Store this answer under B. Calculate $(-3)^4-100$. Store this answer under C. Calculate A$^2$$\times$B$+$C.
Question 14
Use your calculator to find the answer to the following:
a) $5^3+18$
b) $5^7-3^7-1^7$
c) $(-6.85)^2\times400$
d) $6^2-\frac23\times24$
e) $\frac{4^2-6}{2^8}$
f) $18\%$ of $50000$
g) $3\%$ of $6789$ $-$ $22\%$ of $80$
h) $2(8.3+6.33)-4(3.1-1.1)^2-0.26$
i) $\sqrt{27220+10\div2}-66$
j) $3\frac45+\frac{\sqrt{48}}{\sqrt{243}}-3.2$
k) $\frac{4}{7}$ of $455$ plus $33.5$
l) $\frac{9.2\div3.4}{8.6^2}\times62866\div(21-2\times8)$
Answers
Question 1
a) $11$
b) $11$
c) $4$
d) $4$
e) $70$
f) $50$
g) $30$
h) $45$
Question 2
a) $13$
b) $16$
c) $18$
d) $3$
e) $22$
f) $100$
g) $3$
h) $20$
Question 3
a) $25$
b) $729$
c) $343$
d) $6859$
e) $28561$
f) $7776$
g) $390625$
h) $1801088541$
Question 4
a) The answer is $-9$. The calculator calculated $3^2$ first and then put a negative sign in front of it.
b) The answer is $9$. The calculator calculated $-3\times-3$ to give an answer of $9$
c) The answer is $-16$. The calculator calculated $2^4$ first and then put a negative sign in front of it.
d) The answer is $16$. The calculator calculated $-2\times-2\times-2\times-2$ to give an answer of $16$
e) The answer is $-1$. The calculator calculated $1^3$ first and then put a negative sign in front of it.
f) The answer is $-1$. The calculator calculated $-1\times-1\times-1$ to give an answer of $-1$
g) The answer is $34$. The calculator calculated $3^2$ and $5^2$ first and then found their sum.
h) The answer $64$. The calculator calculated the sum of $3$ and $5$ first and then squared the answer. This gave a different answer to the previous question.
Question 5
a) $3$
b) $18$
c) $6$
d) $-15$
e) $9$
f) $7$
g) $1.1$
h) $-3$
i) $\sqrt{-64}$ gives a maths error whilst $\sqrt[3]{-64}=-4$. This is because your calculator cannot find the square roots of negative numbers. You may wish to investigate $\sqrt[4]\square$, $\sqrt[5]\square$, etc. where $\square$ is a negative number.
Question 6
a) $\frac34$
b) $\frac{6}{35}$
c) $\frac34$
d) $\frac{3}{5}$
e) $1$
f) $\frac{1}{64}$
g) $-\frac34$
h) $\frac{2043}{2560}$
Question 7
a) $\frac{2}{5}$
b) $\frac{13}{3}$
c) $\frac{39}{7}$
d) $\frac{27}{10}$
e) $\frac{43}{9}$
f) $\frac{1}{3}$
g) $\frac{33}{20}$
h) $\frac{253}{24}$
Question 8
a) $\frac72$ $3\frac12$ $3.5$
b) $\frac{53}{10}$ $5\frac{3}{10}$ $5.3$
c) $\frac{16}{5}$ $3\frac{1}{5}$ $3.2$
d) $\frac{134}{125}$ $1\frac{9}{125}$ $1.072$
e) $\frac{44}{5}$ $8\frac{4}{5}$ $8.8$
f) $\frac{17}{4}$ $4\frac{1}{4}$ $4.25$
g) $\frac{203}{10}$ $20\frac{3}{10}$ $20.3$
h) $-\frac{24671}{400}$ $-61\frac{271}{400}$ $-61.6775$
Question 9
a) $\frac{10}{9}$
b) $\frac{7}{3}$
c) $\frac{41}{9}$
d) $\frac23$
e) $\frac{38}{45}$
f) $\frac{247}{30}$
g) $\frac{23}{99}$
h) $\frac{48}{11}$
i) $\frac{914}{111}$
j) $\frac{35641}{999}$
k) $1$
Question 10
a) $50$
b) $28$
c) $54$
d) $1.8$
e) $108$
f) $58.65$
g) $50.16$
h) $2.738$
i) $0.5$
j) $0.61$
Question 11
a) Various Answers!
b) Various Answers!
c) Various Answers!
d) Various Answers!
e) Various Answers!
Question 12
a) $2\times3$
b) $2^2\times3$
c) $3\times5$
d) $2^2\times5$
e) $5\times7^2$
f) $2^2\times3\times5$
g) $2\times3\times5\times7\times11$
h) $2\times3^2\times7$
i) $2\times3^2\times7^3\times13$
j) $2\times3^3\times7\times19^2$
k) As $1$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
l) As $0$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
m) As $-2$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
n) As $1.1$ is not a prime number, there is no prime factorisation. Therefore your calculator will show an error.
Question 13
a) $192.64$
b) $1.4$
c) $\frac{10}{7}$ or $1\frac37$
d) $162$
e) $\frac{1}{30}$
f) $\frac{8679}{400}$ or $21\frac{279}{400}$ or $21.6975$
g) $2.15$
h) $-\frac{1217}{72}$ or $-16\frac{65}{72}
Question 14
a) $143$
b) $75937$
c) $18769$
d) $20$
e) $\frac{5}{128}$
f) $9000$
g) $\frac{18607}{100}$ or $186\frac{7}{100}$ or $186.07$
h) $13$
i) $99$
j) $\frac{47}{45}$ or $1\frac{2}{45}$
k) $293.5$ or $293\frac12$ or $\frac{587}{2}$
l) $460$
Solutions
Question 1
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h)
Question 2
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f)
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h)
Question 3
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Question 4
a) The answer is $-9$. The calculator calculated $3^2$ first and then put a negative sign in front of it.
b) The answer is $9$. The calculator calculated $-3\times\-3$ to give an answer of $9$
c) The answer is $-16$. The calculator calculated $2^4$ first and then put a negative sign in front of it.
d) The answer is $16$. The calculator calculated $-2\times\-2\times-2\times-2$ to give an answer of $16$
e) The answer is $-1$. The calculator calculated $1^3$ first and then put a negative sign in front of it.
f) The answer is $-1$. The calculator calculated $-1\times\-1\times-1$ to give an answer of $-1$
g) The answer is $34$. The calculator calculated $3^2$ and $5^2$ first and then found their sum.
h) The answer $64$. The calculator calculated the sum of $3$ and $5$ first and then squared the answer. This gave a different answer to the previous question.
Question 5
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i) $\sqrt{-64}$ gives a maths error whilst $\sqrt[3]{-64}=-4$. This is because your calculator cannot find the square roots of negative numbers. You may wish to investigate $\sqrt[4]\square$, $\sqrt[5]\square$, etc. where $\square$ is a negative number.
Question 6
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Question 7
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Question 8
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Question 9
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Question 10
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Question 11
a) Type in Ran# and press $=$. It will give you a decimal up to $3$ decimal places between $0$ and $1$
b) Type in Ran#$\times1000$ and press $=$. It will give you a number between $0$ and $1000$
c) Type in Ran#$\times1000+1000$ and press $=$. It will give you a number between $1000$ and $2000$
d) Type in Ran#$\times1000+500$ and press $=$. It will give you a number between $500$ and $1500$
e) Type in Ran#$\times100$ and press $=$. It will give you a number between $0$ and $100$, but may include a decimal place. If you want to generate a whole number, simply ignore the decimal
Question 12
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Question 13
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Question 14
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