2 Marks Questions

Question 12 Marks

What should be the value of a if the value of $2 x^2+x-a$ equals $5,$ when $x = 0?$

Answer

$2 x^2+x-a$
$=2(0)^2+(0)-a \ldots(\text { when } x=0)$
$=-a$
According to the question,
$-a=5$
$a=-5$

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Question 22 Marks

If $p=-10$, find the value of $p^2-2 p-100$

Answer

$=p^2-2 p-100$
$=(-10)^2-2(-10)-100$
$=100+20-100$
$=120-100$
$=20$

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Question 32 Marks

If $z = 10$, find the value of $=z^3-3(z-10)$

Answer

$=z^3-3(z-10)$
$=z^3-3 z+30$
$=(10)^3-3(10)+30$
$=1000-30+30$
$=1000+30-30$
$=1030-30$
$=1000$

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Question 42 Marks

Simplify the expression $2a – 2b – 4 – 5 + a$ and find their value if $a = –1, b = –2.$

Answer

$=2a – 2b – 4 – 5 + a$
$= 2a – 2b – 4 – 5 + a$
$= 2a + a – 2b – 4 – 5 [$rearranging terms$]$
$= 3a – 2b –9$
$= 3(-1) – 2(-2)–9$
$= -3 + 4 - 9$
$= -12 + 4= -8$

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Question 52 Marks

Simplify the expression $10 – 3b – 4 – 5b$ and find their value if $b = –2.$

Answer

$=10 – 3b – 4 – 5b$
$=10 – 3b – 4 – 5b$
$= –3b – 5b + 10 – 4 [$rearranging terms$]$
$= –8b + 6$
$= – 8(–2) + 6$
$= 16 + 6= 22$

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Question 62 Marks

Simplify the expression $3a + 5 – 8a + 1$ and find its value, if $a = –1$

Answer

$3a + 5 – 8a + 1$
$= 3(-1) + 5 - 8(-1) + 1$
$= -3 + 5 + 8+ 1$
$= -3 + 14$
$= 1$

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Question 72 Marks

Simplify the expression $2 – 8x + 4x + 4$ and find its value if $x = 3.$

Answer

$=2 – 8x + 4x + 4$
$= 4x – 8x + 2 + 4 [$rearranging terms$]$
$= –4x + 6 = – 4(3) + 6$
$= –12 + 6= -6$

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Question 82 Marks

Simplify $3x – 5 – x + 9$ and find the value if $x = 3.$

Answer

The given expression is:
$3x - 5 - x + 9$
$= 3x - x - 5 + 9$
$= 2x - 5 + 9$
$= 2x + 4$
Put $x = 3,$ we get
$2x + 4 = 2(3) + 4$
$= 6 + 4$
$= 10$

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Question 92 Marks

Simplify the expression $4(2x – 1) + 3x + 11$ and find the value if $x$ is equal to $2.$

Answer

$= 4(2x – 1) + 3x + 11$
$= 8x – 4 + 3x + 11$
$= 8x + 3x + 11 – 4 [$rearranging terms$]$
$= 11x + 7$
$= 11 (2) + 7$
$= 22 + 7$
$= 29$

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Question 102 Marks

Simplify $6x + 5(x – 2)$ and find the value if $x$ is equal to $2.$

Answer

The given expression is: $6x + 5(x - 2)$
Opening the brackets, we get
$6x + 5x - 10 = 11x - 10$
Put $x = 2,$ we get
$11x - 10 = 11(2) - 10$
$= 22 - 10 = 12$

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Question 112 Marks

Simplify the expression $3 (x + 2) + 5x – 7$ and find the value If $x$ is equal to $2.$

Answer

$= 3 (x + 2) + 5x – 7$
$= 3 (2 + 2) + 5(2) - 7$
$= 3(4) + 10 - 7$
$= 12 + 10 - 7$
$= 22 - 7$
$= 15$

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Question 122 Marks

Simplify the expression $x + 7 + 4 (x – 5)$ and find the value if $x$ is equal to $2.$

Answer

$= x + 7 + 4 (x – 5)$
$= x + 7 + 4x – 20$
$= x + 4x + 7 – 20 [$rearranging terms$]$
$= 5x – 13$
$= 5(2) – 13$
$= 10 – 13$
$= –3$

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Question 132 Marks

$p=-2$, find the value of $-2 p^3-3 p^2+4 p+7$

Answer

$=-2 p^3-3 p^2+4 p+7$
$=-2 p^3-3 p^2+4 p+7$
$=-2(-2)^3-3(-2)^2+4(-2)+7$
$=-2(-8)-3(4)-8+7=16-12-8+7$
$=16+7-12-8=23-20=3$

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Question 142 Marks

Simplify the expression $2\left(a^2+a b\right)+3-a b$ and find its value when $a = 5$ and $b = –3$

Answer

$=2 a^2+2 a b+3-a b$
$=2 a^2+2 a b-a b+3 \ldots[\text { rearranging terms }]$
$=2 a^2+a b+3$
when $a=5, b=-3$ then
$=2(5)^2+(5)(-3)+3$
$=50-15+3$
$=50+3-15$
$=53-15$
$=38$

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Question 152 Marks

Substituting $a=3$ and $b=2$ in $a^3-b^3$ what will be the final answer?

Answer

Given Expression is: $a^3-b^3$
Substitute $a=3, b=2$, we get
$a^3-b^3=3^3-2^3$
$=3 \times 3 \times 3-2 \times 2 \times 2$
$=9 \times 3-4 \times 2$
$=27-8$
$=19$

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Question 162 Marks

Substitute $a=3$ and $b=2$ in $a^2+2 a b+b^2$

Answer

The given expression is: $a^2+2 a b+b^2$
Put $a=3, b=2$, we get
$a^2+2 a b+b^2=3^2+2 \times 3 \times 2+2^2$
$=9+2 \times 6+4$
$=9+12+4$
$=25$

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Question 172 Marks

Substitute $a = 3$ and $b = 2$ in $7a – 4b$

Answer

The given expression is: $7a – 4b$
Substitute $a = 3, b = 2,$ we get
$7a – 4b = 7 \times 3 – 4 \times 2$
$= 21 – 8$
$= 13.$

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Question 182 Marks

Subtract $24ab – 10b – 18a$ from $30ab + 12b + 14a$

Answer

Here, we have
$30ab + 12b + 14a – (24ab – 10b – 18a)$
$= 30ab + 12b + 14a – 24ab + 10b + 18a$
$= 30ab – 24ab + 12b + 10b + 14a + 18a$
$= 6ab + 22b + 32a$

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Question 192 Marks

Collect like terms and simplify the expression: $12 m^2-9 m+5 m-4 m^2-7 m+10$

Answer

By rearranging the terms in the given expression, we get
$12 m^2-4 m^2+5 m-9 m-7 m+10$
$=(12-4) m^2+(5-9-7) m+10$
$=8 m^2+(-4-7) m+10$
$=8 m^2+(-11) m+10$
$=8 m^2-11 m+10$

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Maths 2 Marks Questions

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