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

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

  1. 4

  2. 3

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

  1. $\displaystyle (a-b)^{2}$
  2. $\displaystyle (|a|-|b|)^{2}$
  3. $\displaystyle |a^{2}-b^{2}|$
  4. $\displaystyle a^{2}+b^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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

  1. $x^3+14$
  2. $x^3-14$
  3. $-x^3+14$
  4. $x^3+16$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
$=$ $((x^3-2)\div2^2)\times 4+16$
$=$ $\dfrac{x^3-2}{4}\times 4+16$
$=$ $x^3+14$

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

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

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

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

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

  1. $-9x-12$
  2. $-9x-4x^2$
  3. $-9x-5$
  4. $-4x-5$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
$=$ $4-x^2\div x +(4\times-(\dfrac{2x^3}{x^2}))-3^2$
$=$ $4-x+(4\times -2x)-9$
$=$ $4-x-8x-9$
$=$ $-9x-5$

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

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

  1. $x^3+199x^2-x+1$
  2. $2x^3+199x^2-x+1$
  3. $2x^3-199x^2-x+1$
  4. $2x^3+199x^2-x-1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
$=$ $[((100+x)x^4)\div x^2]\times 2 - (x+x^2-1)$
$=$ $\dfrac{(100+x)(x^4)}{x^2}\times 2-x-x^2+1$
$=$ $200x^2+2x^3-x-x^2+1$
$=$ $2x^3+199x^2-x+1$

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

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

  1. $x^3+2x^2-x-2$
  2. $x^3-2x^2-x-2$
  3. $-x^3+2x^2-x-2$
  4. $x^3+2x^2+x-+$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
$=$ $\frac{x-1(x^2+x-2)(x+1)(x-1)}{(x-1(x-1)}$
$=$ $x^3+x^2-2x+x^2+x-2$
$=$ $x^3+2x^2-x-2$

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

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

  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. $8x^2+2y^2-4xy^2-8x+22y+10$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
$=$ $12-[5y+2xy^2-4x^2+4x+6y-y^2+1]\times 2$
$=$ $12- [2xy^2-4x^2+4x+11y-y^2+1]\times 2$
$=$ $12-[4xy^2-8x^2+8x+22y-2y^2+2]$
$=$ $12-4xy^2+8x^2-8x-22y+2y^2-2$
$=$ $8x^2+2y^2-4xy^2-8x-22y+10$

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

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

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

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

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

  1. $10y^4+11y^2+y$
  2. $-10y^4+11y^2-y$
  3. $-10y^4+11y^2+y$
  4. $-10y^4-11y^2+y$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
$=$ $2y-y+y^2+5y[-2y^3+2y]$
$=$ $y+y^2-10y^4+10y^2$
$=$ $-10y^4+11y^2+y$