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Order of operations - class-VII

Description: order of operations
Number of Questions: 43
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Tags: use of brackets numbers multiplication and division of algebraic expressions brackets place value, ordering and rounding maths substitution equations and simple functions
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Subtract  $ - \frac{2}{3}{y^3}-\frac{2}{7}{y^2} - 5$ from $\frac{1}{3}{y^3} + \frac{5}{7}{y^2} - 2$, then the resultant value is . 

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. ${y^3} + {y^2} - 7$

  2. ${y^3} + {y^2} + 3$

  3. ${y^3} + {y^2} - 3$

  4. ${y^3} + {y^2} + 7$

Show answer
Correct Option: A

If r and s are zeroes of the polynomial $t^2-4t+3$, then $\dfrac{1}{r}+\dfrac{1}{s}-2rs+\dfrac{14}{3}$ is equal to

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. 0

  2. 1

  3. 2

  4. -1

Show answer
Correct Option: A
Explanation:
Quadratic Equation
If $\alpha$ and $\beta$ are the roots of the quadratic equation $ax^2+bx+c=0$
then $\alpha + \beta=\dfrac{-b}{a}$ and $\alpha\beta=\dfrac{c}{a}$

$f(t)=t^2-4t+3$
$r+s=4$
$rs=3$
Now,
$\dfrac{1}{r}+\dfrac{1}{s}-2rs+\dfrac{14}{3}=\dfrac{r+s}{rs}-2rs+\dfrac{14}{3}$

$=\dfrac{4}{3}-6+\dfrac{14}{3}=\dfrac{4-18+14}{3}=0$

State whether True or False.

Simplify: $(3y+4z)(3y-4z)+(2y+7z)(y+z) $.
The answer is $11y^2+9yz-9z^2$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$Multiplying\quad (3y+4z)(3y-4z),\quad (2y+7z)(y+z),\ =-16z^{ 2 }+12yz-12yz+9y^{ 2 }\quad +\quad 7z^{ 2 }+7yz+2yz+2y^{ 2 }\ =-9z^{ 2 }+9yz+11y^{ 2 }$

Simplify $(a + b) (c -d) + (a-  b) (c + d) + 2 (ac + bd)$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $4ac$

  2. $4ac - 4bd$

  3. $4bd$

  4. $4ac+4bd$

Show answer
Correct Option: A
Explanation:

$(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)$
$=a(c-d)+b(c-d)+a(c+d)-b(c+d)+2(ac+bd)$
$=ac-ad+bc-bd+ac+ad-bc-db+2ac+2bd$
$=4ac$

Simplify: $(x + y)(x^2 -xy + y^2)$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^3 - y^3$

  2. $x^3 + y^3$

  3. $x^3 + y^3 + 3ab$

  4. $x^3 + y^3-3ab$

Show answer
Correct Option: B
Explanation:

$(x + y)(x^2 - xy + y^2)$
$=x(x^2 - xy + y^2)+y(x^2 - xy + y^2)$
$=x^3-x^2y+xy^2+x^2y^-xy^2+y^3$
$=x^3+y^3$

The simplified form of the expression given below is :$\dfrac{\dfrac{y^4-x^4}{x(x+y)}-\dfrac{y^3}{x}}{y^2-xy+x^2}$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $1$

  2. $0$

  3. $-1$

  4. $2$

Show answer
Correct Option: C
Explanation:

The given expression $\dfrac { \dfrac { { y }^{ 4 }-{ x }^{ 4 } }{ x(x+y) } -\dfrac { { y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } }$ can be simplified as follows:

 
$\dfrac { \dfrac { { y }^{ 4 }-{ x }^{ 4 } }{ x(x+y) } -\dfrac { { y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } } \ =\dfrac { \dfrac { ({ y }^{ 2 })^{ 2 }-({ x }^{ 2 })^{ 2 } }{ x(x+y) } -\dfrac { { y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } } \ =\dfrac { \dfrac { ({ y }^{ 2 }-{ x }^{ 2 })({ y }^{ 2 }+{ x }^{ 2 }) }{ x(x+y) } -\dfrac { { y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } } \quad \quad \quad \quad \quad \quad \quad \left( \because \quad a^{ 2 }-b^{ 2 }=(a+b)(a-b) \right)$
$=\dfrac { \dfrac { ({ y }+x)(y-x)({ y }^{ 2 }+{ x }^{ 2 }) }{ x(x+y) } -\dfrac { { y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } } \ =\dfrac { \dfrac { (y-x)({ y }^{ 2 }+{ x }^{ 2 }) }{ x } -\dfrac { { y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } } \ =\dfrac { \dfrac { { y }^{ 3 }-xy^{ 2 }+yx^{ 2 }-{ x }^{ 3 }-{ y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } }$
$=\dfrac { \dfrac { -x(y^{ 2 }-xy+{ x }^{ 2 }) }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } } \ =-\dfrac { y^{ 2 }-xy+{ x }^{ 2 } }{ { y }^{ 2 }-xy+{ x }^{ 2 } } \ =-1$

Hence, $\dfrac { \dfrac { { y }^{ 4 }-{ x }^{ 4 } }{ x(x+y) } -\dfrac { { y }^{ 3 } }{ x }  }{ { y }^{ 2 }-xy+{ x }^{ 2 } }=-1$  

In the equation $4x+y=10$, if the value of $x$ ins increased by $3$, then what would be the effect on the corresponding value of $y$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. The value of $y$ is decreased by $12$

  2. The value of $y$ is decreased by $2$

  3. The value of $y$ is increased by $3$

  4. The value of $y$ will be $3$ times as large

Show answer
Correct Option: A

Evaluate $\sqrt {13+\sqrt {44+10^2}}$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $12$

  2. $5$

  3. $25$

  4. None

Show answer
Correct Option: B
Explanation:

$\sqrt {13+\sqrt {44+10^2}}\$

$=\sqrt{13+\sqrt {44+100}}\$
$=\sqrt {13+144}\$
$=\sqrt {13+12}\$
$=\sqrt {25}=5$

If $f(x)=x^2+x+5$ then find $f(1)$
maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $7$

  2. $5$

  3. $4$

  4. None of the above

Show answer
Correct Option: A
Explanation:
$f(x)=x^2+x+5$

Put $x=1$

$\Rightarrow$$f(1)=1+1+5$

$\Rightarrow$$f(1)=7$

$x^2+y^2 =100$ find $x$ if $y=6$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\pm 8$

  2. $\pm \sqrt 8$

  3. $\pm 64$

  4. $\pm 4$

Show answer
Correct Option: A
Explanation:

$x^2+y^2=100\y=6\x^2+6^2=100\x^2=100-36\x^2=64\x=\pm 8$

If ${a}^{2}+{b}^{2}+{c}^{2}-ab-bc-ca=0$, then

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $a+b=c$

  2. $b+c=a$

  3. $c+a=b$

  4. $a=b=c$

Show answer
Correct Option: D
Explanation:
Given,

$a^2+b^2+c^2-ab-bc-ca=0$

$\Rightarrow 2(a^2+b^2+c^2-ab-bc-ca)=2(0)$

$\Rightarrow 2a^2+2b^2+2c^2-2ab-2bc-2ca=0$

$\Rightarrow (a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)=0$

$(a-b)^2+(b-c)^2+(c-a)^2=0$

$\Rightarrow a-b=b-c=c-a=0$

$\therefore a=b=c$

If $\displaystyle b=6-\left [ \frac{4b+3}{2a-5} \right ]$, express a in terms of b.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle a=\frac{33-b}{2\left ( 6-b \right )}$

  2. $\displaystyle a=\frac{b-33}{2\left ( 6-b \right )}$

  3. $\displaystyle a=\frac{33-b}{2\left ( b-6 \right )}$

  4. none of the above

Show answer
Correct Option: A
Explanation:

Given,
$ b = 6 - \left[ \frac { 4b+3 }{ 2a-5 }  \right]  $
$ => \left[ \frac { 4b+3 }{ 2a-5 }  \right] = 6 - b $
$ => 4b + 3 = (6-b)(2a-5) $
$ => 4b + 3 = 12a - 30 - 2ab +5b $
$ => 12a - 33  -2ab + b = 0 $
$ =>  a(12 -2b) = 33 - b $
$ => 2a(6-b) = 33-b $
$ => a = \frac {33-b}{2(6-b)} $

Given $\displaystyle b=\frac{2a}{a-2}$ and $\displaystyle c=\frac{3b-4}{4b+3}$, express c in terms of a.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle c=\frac{2a+8}{11a+6}$

  2. $\displaystyle c=\frac{2a-8}{11a-6}$

  3. $\displaystyle c=\frac{2a+8}{11a-6}$

  4. none of the above

Show answer
Correct Option: C
Explanation:

Given, $ c = \frac {3b-4}{4b + 3} $

But, $ b = \frac {2a}{a-2} $
Hence, $ c = \frac {3(\frac {2a}{a-2} )-4}{4(\frac {2a}{a-2} ) + 3} $
$ => c = \frac {6a-4a + 8}{8a +3a - 6} $
$ => c = \frac {2a+8}{11a -6} $

The value of $100 - { ( 7 $of $8 + 4 ) \div 5 } $ is

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $92$

  2. $78$

  3. $96$

  4. $88$

Show answer
Correct Option: D
Explanation:

We apply BODMAS rule to find the value of the given expression. According to BODMAS rule, if an expression contains brackets we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.


Since 'of' stands for multiplication, therefore the given expression becomes 
$100-[(7\times 8+4)\div 5]$ and apply BODMAS rule as shown below:
$ \Rightarrow 100-[(56+4)\div 5]\ \Rightarrow 100-(60\div 5)\ \Rightarrow 100-12\ \Rightarrow 88$
Hence, the value of $100-[(7\times 8+4)\div 5]$ is $88$.

The value of $12\div \dfrac {1}{2}+0.5\times \dfrac {5}{2}-2$ is

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. 23.25

  2. 12.25

  3. 13.25

  4. none

Show answer
Correct Option: A
Explanation:

 

$12\div \dfrac {1}{2}+0.5\times \dfrac {5}{2}-2 = 24 + 1.25 - 2 = 23.25$

Find the value of $\displaystyle \frac{2}{1+\frac{1}{1-\frac{1}{2}}}\times\frac{3}{\frac{5}{6}of\frac{3}{2}\div 1\frac{1}{4}}$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. 4

  2. 3

  3. 2

  4. 1

Show answer
Correct Option: C
Explanation:

Given exp.$\displaystyle \frac{2}{1+\frac{1}{\frac{1}{2}}}\times\frac{3}{\frac{15}{12}\div \frac{5}{4}}=\frac{2}{1+2}\times\frac{3}{\frac{15}{12}\times\frac{4}{5}}=\frac{2}{3}\times\frac{3}{1}=2$

If $a$ and $ b $ are any two real numbers with opposite signs, which of the following is the greatest?

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle (a-b)^{2}$

  2. $\displaystyle (|a|-|b|)^{2}$

  3. $\displaystyle |a^{2}-b^{2}|$

  4. $\displaystyle a^{2}+b^{2}$

Show answer
Correct Option: A
Explanation:

$(a-b)^2=a^2+b^2-2ab$

as a and b are of oppsite sign ab<0 and -2ab>0,it means $(a-b)^2>a^2+b^2-2|a||b|=(|a|-|b|)^2>(|a2+b^2|)>(|a^2-b^2|)$

What is the value of $((x^3-2)\div2^2)\times 4+16$?

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^3+14$

  2. $x^3-14$

  3. $-x^3+14$

  4. $x^3+16$

Show answer
Correct Option: A
Explanation:

$((x^3-2)\div2^2)\times 4+16$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $((x^3-2)\div2^2)\times 4+16$
$=$ $\dfrac{x^3-2}{4}\times 4+16$
$=$ $x^3+14$

Simplify: $3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^3-3x^2+x+1$

  2. $x^3-3x^2+5x-1$

  3. $x^3+x^2-5x+1$

  4. $x^3+3x^2+5x-1$

Show answer
Correct Option: B
Explanation:

$3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$
$=$ $3x.x^2+3x.1-[2x.x^2+2x.x-2x.1+1]-x^2$
$=$ $3x^3+3x-2x^3-2x^2+2x-1-x^2$
$=$ $x^3-3x^2+5x-1$

Find the value of the expression using BODMAS rule: $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $-9x-12$

  2. $-9x-4x^2$

  3. $-9x-5$

  4. $-4x-5$

Show answer
Correct Option: C
Explanation:

$4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
$=$ $4-x+(4\times -2x)-9$
$=$ $4-x-8x-9$
$=$ $-9x-5$

Simplify using BODMAS rule: $[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^3+199x^2-x+1$

  2. $2x^3+199x^2-x+1$

  3. $2x^3-199x^2-x+1$

  4. $2x^3+199x^2-x-1$

Show answer
Correct Option: B
Explanation:

$[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$
$=$ $\dfrac{(100+x)(x^4)}{x^2}\times 2-x-x^2+1$
$=$ $200x^2+2x^3-x-x^2+1$
$=$ $2x^3+199x^2-x+1$

Use the BODMAS rule to reduce the expression: $x-1[(x^2+x-2)(x^2-1^2)\div (x-1)^2]$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^3+2x^2-x-2$

  2. $x^3-2x^2-x-2$

  3. $-x^3+2x^2-x-2$

  4. $x^3+2x^2+x-+$

Show answer
Correct Option: A
Explanation:

$x-1[(x^2+x-2)(x^2-1^2)\div (x-1)^2]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $\frac{x-1(x^2+x-2)(x+1)(x-1)}{(x-1(x-1)}$
$=$ $x^3+x^2-2x+x^2+x-2$
$=$ $x^3+2x^2-x-2$

Solve: $12-[5y+2x(y^2-2x+2)+6y-(y^2-1)]\times 2$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $8x^2+y^2-4xy^2-8x-22y+10$

  2. $8x^2+2y^2+4xy^2-8x-22y+10$

  3. $8x^2+2y^2-4xy^2-8x-22y+10$

  4. $8x^2+2y^2-4xy^2-8x+22y+10$

Show answer
Correct Option: C
Explanation:

$12-[5y+2x(y^2-2x+2)+6y-(y^2-1)]\times 0.1$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $12-[5y+2xy^2-4x^2+4x+6y-y^2+1]\times 2$
$=$ $12- [2xy^2-4x^2+4x+11y-y^2+1]\times 2$
$=$ $12-[4xy^2-8x^2+8x+22y-2y^2+2]$
$=$ $12-4xy^2+8x^2-8x-22y+2y^2-2$
$=$ $8x^2+2y^2-4xy^2-8x-22y+10$

Expand the expression using BODMAS rule: $x^2-x[(-x)(-2+x)]\div x+x^3-3x^2$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^3-x^2-2x$

  2. $-x^3-x^2-2x$

  3. $x^3-x^2+2x$

  4. $x^3+x^2+2x$

Show answer
Correct Option: A
Explanation:

$x^2-x[(-x)(-2+x)]\div x+x^3-3x^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $-2x^2-x[\dfrac{(-x)(-2+x)}{x}]+x^3$
$=$ $-2x^2-x[2-x]+x^3$
$=$ $x^3-2x^2-2x+x^2$
$=$ $x^3-x^2-2x$

Reduce the following expression using BODMAS rule: $2y-1(y-y^2)+5y[(-2y)(y^2-1)]$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $10y^4+11y^2+y$

  2. $-10y^4+11y^2-y$

  3. $-10y^4+11y^2+y$

  4. $-10y^4-11y^2+y$

Show answer
Correct Option: C
Explanation:

$2y-1(y-y^2)+5y[(-2y)(y^2-1)]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $2y-y+y^2+5y[-2y^3+2y]$
$=$ $y+y^2-10y^4+10y^2$
$=$ $-10y^4+11y^2+y$

Simplify the expression: $4x^3[(3x-x^2)-1]+(x^2)[x+1]$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $-4x^5-12x^4-3x^3+x^2$

  2. $-4x^5+12x^4+3x^3+x^2$

  3. $-4x^5+12x^4-3x^3-x^2$

  4. $-4x^5+12x^4-3x^3+x^2$

Show answer
Correct Option: D
Explanation:

$4x^3[(3x-x^2)-1]+(x^2)[x+1]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $4x^3[(3x-x^2)-1]+(x^2)[x+1]$
$=$ $4x^3[3x-x^2-1]+x^3+x^2$
$=$ $12x^4-4x^5-4x^3+x^3+x^2$
$=$ $-4x^5+12x^4-3x^3+x^2$

Find the value of $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $15x^{12}-12x-4$

  2. $15x^4-12x-4$

  3. $15x^4+12x-4$

  4. $5x^4-12x-4$

Show answer
Correct Option: B
Explanation:

$5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
$=$ $5x[2x^3+2x^4-x^3]-\dfrac{4x^2}{x^2}-12x$
$=$ $5x[x^3+2x^4]-4-12x$
$=$ $5x^4+10x^4-12x-4$
$=$ $15x^4-12x-4$

Use the BODMAS rule to simplify the expression: 

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $-x^4-4x^3-x^2+xy^2$

  2. $-x^4+4x^2-x^2+xy^2$

  3. $-x^4+4x^3+x^2+xy^2$

  4. $-x^4+4x^3-x^2+xy^2$

Show answer
Correct Option: D
Explanation:

$xy^2+x^3-x[x^2-x][2x]+(x-1)x^2$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $xy^2+x^3+[-x^3+x^2]2x+x^3-x^2$
$=$ $xy^2+x^3-x^4+2x^3+x^3-x^2$
$=$ $xy^2+4x^3-x^4-x^2$
$=$ $-x^4+4x^3-x^2+xy^2$

Simplify the expression: $x^2\times(x-1)+[(2x+2)\times 4x]-1$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^3+7x^2+8x+1$

  2. $x^3-7x^2+8x-1$

  3. $x^3+7x^2+8x-1$

  4. $x^3+7x^2-8x-1$

Show answer
Correct Option: C
Explanation:

$x^2\times(x-1)+[(2x+2)\times 4x]-1$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $x^2\times(x-1)+[(2x+2)\times 4x]-1$
$=$ $x^3-x^2+8x^2+8x-1$
$=$ $x^3+7x^2+8x-1$

$24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$ using BODMAS rule to reduce the expression.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^2+23x+46$

  2. $-x^2+23x+46$

  3. $-x^2-23x+46$

  4. $-x^2+23x-46$

Show answer
Correct Option: B
Explanation:

$24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$
$=$ $24x+24-x^2+24-x-2$
$=$ $-x^2+46+23x$
$=$ $-x^2+23x+46$

Solve the expression using BODMAS rule: $3x(x-2)+x(x^2\times 2x)-12x$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $2x^5-3x^2-18x$

  2. $2x^5+3x^2-18x$

  3. $2x^5+3x^2+18x$

  4. $-2x^5-3x^2-18x$

Show answer
Correct Option: B
Explanation:

$3x(x-2)+x(x^2\times 2x)-12x$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $3x(x-2)+x(x^2\times 2x)-12x$
$=$ $3x^2-6x+x^3\times2x^2-12x$
$=$ $3x^2-6x+2x^5-12x$
$=$ $2x^5+3x^2-18x$

If $1\le a\le 2$, then $\sqrt { a-2\sqrt { a-1 }  } -\sqrt { a+2\sqrt { a-1 }  } =$.......

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $2$

  2. $2\sqrt{a-1}$

  3. $-2$

  4. $1$

Show answer
Correct Option: C
Explanation:

$\sqrt{a - 2 \sqrt{a - 1}} - \sqrt{a + 2 \sqrt{a - 1}}$

$\Rightarrow \sqrt{(\sqrt{a - 1})^2 - 2 (1) \sqrt{a - 1} + 1^2} - \sqrt{(\sqrt{(a - 1)})^2 + 2 \sqrt{a - 1} + 1^2}$
$\Rightarrow \sqrt{(\sqrt{a - 1} - 1)^2} - \sqrt{(\sqrt{a - 1} + 1)^2}$
$\Rightarrow (\sqrt{a - 1} - 1) - ( \sqrt{a - 1} + 1)$
$= -2$

A number x is decreased by m% and some other number y is increased by m%. If both the results are equal, find m in terms of x and y. Also, find m if $\displaystyle 2x=3y$.


maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=10$

  2. $\displaystyle m=\frac{100\left ( x-y \right )}{x-y};m=20$

  3. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=30$

  4. $\displaystyle m=\frac{100\left ( x-y \right )}{x+y};m=20$

Show answer
Correct Option: D
Explanation:

Given $ \frac {100 - m}{100} \times x = \frac {100 + m}{100} \times y $
$ => 100x - mx = 100y + my $
$ => 100x - 100y = mx + my $
$ => 100 (x-y) = m (x + y) $
$ => m = \frac {100(x-y)}{x+y} $

When , $ 2x = 3y => x = \frac {3y}{2} $
We have, $ m = \frac {100(\frac {3y}{2} -y)}{\frac {3y}{2} +y} $
$ => m =\frac {100(\frac {y}{2})}{\frac {5y}{2}} $
$ => m =\frac {100}{5} = 20 $

 Make b the subject of formula : $\displaystyle a=\frac{1+b^2}{1-b^2}$. 

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle b=\sqrt{\frac{a+1}{a-1}}$

  2. $\displaystyle b=\sqrt{\frac{a-1}{a+1}}$

  3. $\displaystyle b=2\sqrt{\frac{a-1}{a+1}}$

  4. $\displaystyle b=2\sqrt{\frac{a+1}{a-1}}$

Show answer
Correct Option: B
Explanation:

Given, $ a = \frac {1 +{b}^{2}}{1 - {b}^{2}} $
$ => a -a{b}^{2} = 1 +{b}^{2} $
$ => a- 1 = {b}^{2} (1 + a) $
$ =>{b}^{2} = \frac {a-1}{1+a} $


$\frac{1}{3}(-2p+6q-9r)-\frac{1}{6}(-4p -18q +24r) = $

maths use of brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $-\frac{4}{3}p$

  2. 5q

  3. -7r

  4. 5q-7r

Show answer
Correct Option: D
Explanation:

$\frac{1}{3}(-2p+6q-9r)-\frac{1}{6}(-4p -18q +24r) = \frac{1}{3}(-2p+6q-9r)-\frac{1}{3}(-2p -9q +12r) $
$=\frac{1}{3} [\left (-2p+6q-9r)-(-2p -9q +12r) \right]$
$=\frac{1}{3} (-2p + 6q - 9r + 2p + 9q -12r)$
$=\frac{1}{3} (15q - 21r)$
$=(5q - 7r)$

$ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left ( y + a -\frac{1}{4}(a+y) \right )\right ]$

maths use of brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $(a+y)^{2}$

  2. $\frac{3a}{16}$

  3. $\frac{9}{16}(a+y)^{2}$

  4. 1

Show answer
Correct Option: C
Explanation:

$ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left ( y + a -\frac{1}{4}(a+y) \right )\right ]$
= $ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left (\frac{3}{4}(a+y) \right) \right ]$
= $ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{4}(a+y)\right ]$
= $ \frac{3}{4}(a+y) \left [ \frac{3}{4}(a+y)\right ]$
= $ \frac{9}{16}(a+y)^2$

$-84\times 29+365=$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $2436$

  2. $2801$

  3. $-2801$

  4. $-2071$

  5. None of these

Show answer
Correct Option: D
Explanation:

Given Exp. $=-84\times (30-1)+365$
$=-(84\times 30)+84+365$
$=-2520+449$
$=-2071$

In a class, there are 18 boys who are over 160 em tall. If these constitute three-fourths of the boys and the total number of boys is two-third of the total number of students in the class, what is the number of girls in the class?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. 6

  2. 12

  3. 18

  4. 24

Show answer
Correct Option: B
Explanation:

Total number of boys $\displaystyle=18\div\frac{3}{4}=24$

Total number of students $\displaystyle=24\times\frac{3}{2}=36$

$\therefore$ Number of girls $=36-24=12$

$35+15\times 1.5=$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $85$

  2. $51.5$

  3. $57.5$

  4. $5.25$

  5. None of these

Show answer
Correct Option: C
Explanation:

Given Exp.$=35+15\times \cfrac{3}{2}=35+\cfrac{45}{2}=35+22.5=57.5$

$(800\div 64)\times (1296\div 36)=$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $420$

  2. $460$

  3. $500$

  4. $540$

  5. None of these

Show answer
Correct Option: E
Explanation:

Given Exp. $=\cfrac { 800 }{ 64 } \times \cfrac { 1296 }{ 36 } =450$

$9+\cfrac { 3 }{ 4 } +7+\cfrac { 2 }{ 17 } -\left( 9+\cfrac { 1 }{ 15 }  \right) =$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $7+\cfrac { 719 }{ 1020 } $

  2. $9+\cfrac { 817 }{ 1020 } $

  3. $9+\cfrac { 719 }{ 1020 } $

  4. $7+\cfrac { 817 }{ 1020 } $

  5. None of these

Show answer
Correct Option: D
Explanation:

Given the sum $=9+\cfrac { 3 }{ 4 } +7+\cfrac { 2 }{ 17 } -\left( 9+\cfrac { 1 }{ 15 }  \right) $
$=(9+7-9)+\left( \cfrac { 3 }{ 4 } +\cfrac { 2 }{ 17 } -\cfrac { 1 }{ 15 }  \right) $
$=7+\cfrac { 765+120-68 }{ 1020 } $
$=7+\cfrac { 817 }{ 1020 } $

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