Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

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

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

  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. $-4x^5+12x^4-3x^3+x^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.
$=$ $4x^3[(3x-x^2)-1]+(x^2)[x+1]$
$=$ $4x^3[3x-x^2-1]+x^3+x^2$
$=$ $12x^4-4x^5-4x^3+x^3+x^2$
$=$ $-4x^5+12x^4-3x^3+x^2$

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

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

  1. $15x^{12}-12x-4$
  2. $15x^4-12x-4$
  3. $15x^4+12x-4$
  4. $5x^4-12x-4$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
$=$ $5x[2x(x^2+x^3)-x^3]-4x^2\div x^2-12x$
$=$ $5x[2x^3+2x^4-x^3]-\dfrac{4x^2}{x^2}-12x$
$=$ $5x[x^3+2x^4]-4-12x$
$=$ $5x^4+10x^4-12x-4$
$=$ $15x^4-12x-4$

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

Use the BODMAS rule to simplify the expression: 

  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. $-x^4+4x^3-x^2+xy^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.
$=$ $xy^2+x^3+[-x^3+x^2]2x+x^3-x^2$
$=$ $xy^2+x^3-x^4+2x^3+x^3-x^2$
$=$ $xy^2+4x^3-x^4-x^2$
$=$ $-x^4+4x^3-x^2+xy^2$

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

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

  1. $x^3+7x^2+8x+1$
  2. $x^3-7x^2+8x-1$
  3. $x^3+7x^2+8x-1$
  4. $x^3+7x^2-8x-1$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
$=$ $x^2\times(x-1)+[(2x+2)\times 4x]-1$
$=$ $x^3-x^2+8x^2+8x-1$
$=$ $x^3+7x^2+8x-1$

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

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

  1. $x^2+23x+46$
  2. $-x^2+23x+46$
  3. $-x^2-23x+46$
  4. $-x^2+23x-46$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
$=$ $24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$
$=$ $24x+24-x^2+24-x-2$
$=$ $-x^2+46+23x$
$=$ $-x^2+23x+46$

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

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

  1. $2x^5-3x^2-18x$
  2. $2x^5+3x^2-18x$
  3. $2x^5+3x^2+18x$
  4. $-2x^5-3x^2-18x$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
$=$ $3x(x-2)+x(x^2\times 2x)-12x$
$=$ $3x^2-6x+x^3\times2x^2-12x$
$=$ $3x^2-6x+2x^5-12x$
$=$ $2x^5+3x^2-18x$

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

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

  1. $2$
  2. $2\sqrt{a-1}$
  3. $-2$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

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 $\displaystyle 2x=3y$.


  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. $\displaystyle m=\frac{100\left ( x-y \right )}{x+y};m=20$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $

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

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

  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. $\displaystyle b=2\sqrt{\frac{a+1}{a-1}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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} $


Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals estimation and rounding off estimations, bounds and rounding off

Divide $0.3297$ by $0.07$, correct to $2$ significant digits.

  1. $4.4$
  2. $4.7$
  3. $4.9$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$0.3297 \div 0.07 = 4.71$

as the digit in ten's place is not greater than 5, it cannot be replaced.
$\therefore 0.3297 \div 0.07 = 4.7$