MCQ 511 Mark
The factorisation of $\text{x}^2+\text{x}+\frac{1}{4}$ is:
- A
$(\frac{\text{x}}{2}-1)^2$
- B
$(\frac{\text{x}}{2}+1)^2$
- ✓
$(\text{x}+\frac{1}{2})^2$
- D
$(\text{x}-\frac{1}{2})^2$
AnswerCorrect option: C. $(\text{x}+\frac{1}{2})^2$
$\text{x}^2+\text{x}+\frac{1}{4}$
$=\text{x}^2+2(\text{x})(\frac{1}{2})+(\frac{1}{2})^2$
$=(\text{x}+\frac{1}{2})^2$
View full question & answer→MCQ 521 Mark
The factorisation of $36x^2y^2 - 1$ is:
- ✓
$(6xy - 1) (6xy + 1)$
- B
$(6xy - 1)^2$
- C
$(6xy + 1)^2$
- D
$(6 + xy)^2$
AnswerCorrect option: A. $(6xy - 1) (6xy + 1)$
A. $(6xy - 1) (6xy + 1)$
Solution:
$= 36x^2y^2 - 1 = (6xy)^2 - (1)^2$
$= (6xy - 1) (6xy + 1)$
View full question & answer→MCQ 531 Mark
The common factor of $6a^3b^4c^2, 21a^2b$ and $15a^3$ is:
- ✓
$3a^2$
- B
$3a^3$
- C
$6a^3$
- D
$6a^2$
AnswerCorrect option: A. $3a^2$
A. $3a^2$
Solution:
$6 a^3 b^4 c^2=2 \times 3 \times a \times a \times a \times b \times b \times b \times b \times c \times c $
$ 21 a^2 b=3 \times 7 \times a \times a \times a $
$ 15 a^3 64 c 4=3 \times 5 \times a \times a \times a$
View full question & answer→MCQ 541 Mark
If $(\text{x}-\frac{1}{\text{x}})^2=\text{x}^2+\text{a}+\frac{1}{\text{x}^2}$ then a =
Answer$(\text{x}-\frac{1}{\text{x}})^2=\text{x}^2-2+\frac{1}{\text{x}^2}$
$\therefore\text{a}=-2$
View full question & answer→MCQ 551 Mark
Tick $(\checkmark)$ the correct answer:
$(2x - 32x^3) = ?$
- A
$2(x - 4)(x + 4)$
- B
$2x(1 - 2x)^2$
- C
$2x(1 + 2x)^2$
- ✓
$2x(1 - 4x)(1 + 4x)$
AnswerCorrect option: D. $2x(1 - 4x)(1 + 4x)$
D. $2x(1 - 4x)(1 + 4x)$
Solution:
$2x - 32x^3 = 2x(1 - 16x^2)$
$= 2x{(1)^2 - (4x)^2}$
$= 2x(1 - 4x)(1 + 4x)$
View full question & answer→MCQ 561 Mark
The factorisation of $4y^2 - 12y + 9$ is:
- A
$(2y + 3)^2$
- ✓
$(2y - 3)^2$
- C
$(3y + 2)^2$
- D
$(3y - 2)^2$
AnswerCorrect option: B. $(2y - 3)^2$
B. $(2y - 3)^2$
Solution:
$= 4y^2 - 12y + 9$
$= (2y)^2 - 2(2y)(3) + (3)^2$
$= (2y - 3)^2$
View full question & answer→MCQ 571 Mark
Which of the following is one of the factors of $x^4 + 4\ ?$
AnswerCorrect option: B. $(x^2 + 2 + 2x)(x^2 + 2 - 2x)$
B. $(x^2 + 2 + 2x)(x^2 + 2 - 2x)$
View full question & answer→MCQ 581 Mark
The factorisation of $10x^2 - 18x^3 + 14x^4$ is:
- ✓
$2x^2 (7x^2 - 9x + 5)$
- B
$2x (7x^2 - 9x + 5)$
- C
$2\ (7x^2 - 9x + 5)$
- D
$2x^3\ (7x^2 - 9x + 5)$
AnswerCorrect option: A. $2x^2 (7x^2 - 9x + 5)$
A. $2x^2 (7x^2 - 9x + 5)$
Solution:
$10x^2 - 18x^2 + 14x^2 = 2x^2(5 - 9x + 7x^2)$
View full question & answer→MCQ 591 Mark
The factorisation of $am^2 + bm^2 + bn^2 + an^2$ is:
- A
$(a + b) (m^2 - n^2)$
- ✓
$(a + b) (m^2 + n^2)$
- C
$(a - b) (m^2 + n^2)$
- D
$(a - b) (m^2 - n^2)$
AnswerCorrect option: B. $(a + b) (m^2 + n^2)$
B. $(a + b) (m^2 + n^2)$
Solution:
$= am^2 + bm^2 + bn^2 + an^2$
$= m^2(a + b) + n^2(b + a)$
$= (a + b) (m^2 + n^2)$
View full question & answer→MCQ 601 Mark
The value of $(0.68)^2 - (0.32)^2$ is:
AnswerCorrect option: D. $0.36$
D. $0.36.$
Solution:
Value $= (0.68 + 0.32) (0.68 - 0.32) = 0.36.$
View full question & answer→MCQ 611 Mark
Nia has solved $(x + 4)^2 = x^2 + 16$ correct if required.
AnswerCorrect option: B. $(x + 4)^2 = x^2 + 16 + 8x$
B. $(x + 4)^2 = x^2 + 16 + 8x$
Solution:
Expand $(x + 4)^2$ using the indentity, $(a + b)^2 = a^2 + b^2 + 2ab$
$\Rightarrow (x + 4)^2 = x^2 + 4^2 + 2 × x × 4 = x^2 +16 + 8x$
View full question & answer→MCQ 621 Mark
The factorisation of $x^2 - 9$ is:
- A
$(x – 3)^2$
- B
$(x + 3)^2$
- ✓
$(x + 3) (x – 3)$
- D
AnswerCorrect option: C. $(x + 3) (x – 3)$
C. $(x + 3) (x - 3)$
Solution:
$x^2 - 9 = (x)^2 - (3)^2 $
$= (x - 3) (x + 3)$
View full question & answer→MCQ 631 Mark
If the factors of $a^2 + b^2 + 2(ab + bc + ca)$ are $(a + b + m)$ and $(a + b + nc),$ then the value of $m + n$ is:
View full question & answer→MCQ 641 Mark
The factorisation of $6x^2 - 5x - 6$ is:
- ✓
$(2x - 3) (3x + 2)$
- B
$(2x + 3) (3x + 2)$
- C
$(2x - 3) (3x - 2)$
- D
$(2x + 3) (3x - 2)$
AnswerCorrect option: A. $(2x - 3) (3x + 2)$
A. $(2x - 3) (3x + 2)$
Solution:
$= 6x^2 - 5x - 6$
$= 6x^2 - 9x + 4x - 6$
$= 3x(2x - 3) + 2(2x - 3)$
$= (2x – 3) (3x + 2)$
View full question & answer→MCQ 651 Mark
Tick $(\checkmark)$ the correct answer:
$ab - mn + an - bm = ?$
- A
$(a - b)(m - n)$
- ✓
$(a - m)(b + n)$
- C
$(a - n)(m + b)$
- D
$(m - a)(n - b)$
AnswerCorrect option: B. $(a - m)(b + n)$
$ab - mn + an - bm$
$= ab + an - bm - mn$
$= a(b + n) - m(b + n)$
$= (a - m)(b + n)$
View full question & answer→MCQ 661 Mark
The value of $\frac{0.564\times0.564\times-0.436\times0.436}{0.564-0.436}$ is:
AnswerValue $=\frac{(0.564+0.436)(0.564-0.436)}{0.564-0.436}=1$
View full question & answer→MCQ 671 Mark
The factors of $4y^2 - 12y + 9$ is:
- A
$(2y + 3)^2$
- ✓
$(2y - 3)^2$
- C
$(2y - 3) (2y + 3)$
- D
AnswerCorrect option: B. $(2y - 3)^2$
B. $(2y - 3)^2$
Solution:
$=4 y^2-12 y+9 $
$ =4 y^2=(2 y)^2 \& 9=3^2 \& 12 y=2.3 .2 y $
$ =4 y^2-12 y+9=(2 y)^2-2 \times 3 \times(2 y)+(3)^2 $
$ =(2 y-3)^2 \text { By algebraic identities: }(a-b)^2=a^2+b^2-2 a b$
View full question & answer→MCQ 681 Mark
Tick $(\checkmark)$ the correct answer:
$x^2 + 4x - 21 = ?$
- A
$(x - 7)(x + 3)$
- ✓
$(x + 7)(x - 3)$
- C
$(x - 7)(x - 3)$
- D
$(x + 7)(x + 3)$
AnswerCorrect option: B. $(x + 7)(x - 3)$
B. $(x + 7)(x - 3)$
Solution:
$x^2 + 4x - 21$
$= x^2+ 7x - 3x - 21$
$= x(x + 7) - 2(x + 7)$
$= (x - 3)(x + 7)$
View full question & answer→MCQ 691 Mark
What is the coefficient of $'a'$ when $9a^2 + 18a$ is divided by $(a + 2)\ ?$
- A
$18$
- ✓
$9$
- C
$\frac{1}{2}$
- D
$2$
View full question & answer→MCQ 701 Mark
The quotient of $28x^2 + 14x$ is:
AnswerB. $2x$
Solution:
$\frac{28\text{x}^21}{14\text{x}}=\frac{2\times2\times7\times\text{x}\times\text{x}}{2\times7\times\text{x}}=2\text{x}$
View full question & answer→MCQ 711 Mark
The factorisation of $6x - 42$ is:
- ✓
$6(x - 7)$
- B
$3(x - 7)$
- C
$2(x - 7)$
- D
$6(x + 7)$
AnswerCorrect option: A. $6(x - 7)$
$6x – 42 = 6(x - 7)$
View full question & answer→MCQ 721 Mark
The factorisation of $x^2yz + xy^2z + xyz^2$ is:
- ✓
$xyz(x + y + z)$
- B
$x^2yz(x + y + z)$
- C
$xy^2z(x + y + z)$
- D
$xyz^2(x + y + z)$
AnswerCorrect option: A. $xyz(x + y + z)$
A. $xyz(x + y + z)$
Solution:
$x^2yz + xy^2z + xyz^2 = xyz (x + y + z)$
View full question & answer→MCQ 731 Mark
The common factor of $24x^3y^4, 36x^4z^4$ and $48x^3y^2z$ is:
- ✓
$12x^3$
- B
$24x^3$
- C
$36x^3$
- D
$48x^3$
AnswerCorrect option: A. $12x^3$
A. $12x^3$
Solution:
$24x^3y^4 = 2 \times 2 \times 2 \times 3 \times x \times x \times x \times y \times y \times y \times y$
$36x^4z^4 = 2 \times 2 \times 3 \times 3 \times x \times x \times x \times x \times z \times z \times z \times z$
$48x^3y^2z = 2 \times 2 \times 2 \times 2 \times 3 \times x \times x \times x \times y \times y \times z$
View full question & answer→MCQ 741 Mark
The common factor of $a^3b^3$ and $ab^2$ is:
- A
$a^2b^2$
- B
$a^2b$
- C
$ab$
- ✓
$ab^2$
AnswerCorrect option: D. $ab^2$
D. $ab^2$
Solution:
$a^3b^3 = a \times a \times a \times b \times b \times b$
$ab^2 = a \times b \times b$
The common factors are:$ a \times b \times b = ab^2$
View full question & answer→MCQ 751 Mark
The factorisation of $(\frac{{\text{x}^2}}{{\text{y}}^2}-2+\frac{{\text{y}^2}}{{\text{x}^2}})\text{x}\not=0$ is:
- A
$(\frac{\text{x}}{\text{y}}+\frac{\text{y}}{\text{x}})^2$
- ✓
$(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
- C
$(\frac{\text{x}}{\text{y}}-1)^2$
- D
$(\frac{\text{x}}{\text{y}}+1)^2$
AnswerCorrect option: B. $(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
$=\frac{\text{x}^2}{\text{y}^2}-2+\frac{\text{y}^2}{\text{x}^2}$
$=(\frac{\text{x}}{\text{y}})^2-2(\frac{\text{x}}{\text{y}})(\frac{\text{y}}{\text{x}})+(\frac{\text{y}}{\text{x}})^2$
$=(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
View full question & answer→MCQ 761 Mark
Tick $(\checkmark)$ the correct answer:
$4z^2 - 8z + 3 = \ ?$
- ✓
$(2z - 1)(2z - 3)$
- B
$(2z + 1)(3 - 2z)$
- C
$(2z + 3)(3z - 1)$
- D
$(z - 1)(4z - 3)$
AnswerCorrect option: A. $(2z - 1)(2z - 3)$
A. $(2z - 1)(2z - 3)$
Solution:
$4 z^2-8 z+3 $
$ =4 z^2-6 z-2 z+3 $
$ \{4 \times 3=12,12=(-6) \times(-2),-8=-6-2\} $
$ =2 z(2 z-3)-1(2 z-3) $
$ =(2 z-1)(2 z-3)$
View full question & answer→MCQ 771 Mark
Divide as directed: $5 (2x + 1) (3x + 5) ÷ (2x + 1)$
- A
$(3x + 5)$
- B
$5$
- ✓
$5 (3x + 5)$
- D
AnswerCorrect option: C. $5 (3x + 5)$
$5 (3x + 5)$
View full question & answer→MCQ 781 Mark
The quotient of $12a^8b^8 + (-a^6b^6)$ is:
- A
$3a^2b^2$
- B
$3a^2b$
- C
$3ab^2$
- ✓
$-3a^2b^2$
AnswerCorrect option: D. $-3a^2b^2$
D. $-3a^2b^2$
Solution:
$=-\frac{12\text{a}^8\text{b}^8}{4\text{a}^6\text{b}^8}$
$=-\frac{2\times2\times3\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}}{2\times2\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}}$
$=-3\text{a}^2\text{b}^2$
View full question & answer→MCQ 791 Mark
Tick $(\checkmark)$ the correct answer:
$(12m^2 - 27) =\ ?$
- A
$(2m - 3)(3m - 9)$
- B
$3(2m - 9)(3m - 1)$
- ✓
$3(2m - 3)(2m + 3)$
- D
AnswerCorrect option: C. $3(2m - 3)(2m + 3)$
c. $3(2m - 3)(2m + 3)$
Solution:
$12m^2- 27$
$= 3(4m^2- 9)$
$= 3(2m - 3)(2m + 3)$
View full question & answer→MCQ 801 Mark
The factors of $x^2 + 2x^2 + 9$ is:
AnswerCorrect option: B. $(x^2 - 2x +3)(x^2 + 2x +3)$
B. $(x^2 - 2x +3)(x^2 + 2x +3)$
View full question & answer→MCQ 811 Mark
Which of the following is quotient obtained on dividing $-18xyz^2$ by $-3xz?$
- ✓
$6yz$
- B
$-6yz$
- C
$6xy^2$
- D
$6xy$
View full question & answer→MCQ 821 Mark
Correct the error in $(2x)^2 + 5(2x) + 7 = 2x^2 + 7x + 7$
- A
$(2x)^2 + 5(2x) + 7 = 4x + 7x + 7$
- ✓
$(2x)^2 + 5(2x) + 7 = 4x^2 + 10x + 7$
- C
$(2x)^2 + 5(2x) + 7 = 4x^2 + 7x + 7$
- D
$(2x)^2 + 5(2x) + 7 = 4x + 10x + 7$
AnswerCorrect option: B. $(2x)^2 + 5(2x) + 7 = 4x^2 + 10x + 7$
B. $(2x)^2 + 5(2x) + 7 = 4x^2 + 10x + 7$
Solution:
Consider the Left Hand Side of the given equation,
$(2x)^2 + 5(2x) + 7$
$\Rightarrow (2x \times 2x) + 5 \times (2x) + 7$
$\Rightarrow 4x^2 +10x +7$
View full question & answer→MCQ 831 Mark
Divide as directed: $26xy (x + 5) (y - 4) ÷ 13x (y - 4)$
- ✓
$2y(x + 5)$
- B
$(x + 5)$
- C
$2y$
- D
AnswerCorrect option: A. $2y(x + 5)$
$2y(x + 5)$
View full question & answer→MCQ 841 Mark
Tick $(\checkmark)$ the correct answer:
$x^2 + 6x + 8 = ?$
- A
$(x + 3)(x + 5)$
- B
$(x + 3)(x + 4)$
- ✓
$(x + 2)(x + 4)$
- D
$(x + 1)(x + 8)$
AnswerCorrect option: C. $(x + 2)(x + 4)$
C. $(x + 2)(x + 4)$
Solution:
$x^2 + 6x + 8$
$= x^2+ 4x + 2x + 8$
${8 = 4 × 2, 6 = 4 + 2}$
$= x(x + 4) + 2(x + 4)$
$= (x + 2)(x + 4)$
View full question & answer→MCQ 851 Mark
The factors of $x^2 + xy + 8x + 8y$ are:
- A
$(2x + y) (x + 8)$
- B
$(x + 2y) (x + 8)$
- ✓
$(x + y) (x + 8)$
- D
$(x + y) (2x + 8)$
AnswerCorrect option: C. $(x + y) (x + 8)$
C. $(x + y) (x + 8)$
Solution:
$= x^2 + xy + 8x + 8y$
$= x(x + y) + 8(x + y)$
$=(x + y) (x + 8)$
View full question & answer→MCQ 861 Mark
The factorisation of $6xy - 4y + 6 - 9x$ is:
- ✓
$(3x - 2)(2y - 3)$
- B
$(3x + 2)(2y - 3)$
- C
$(3x - 2)(2y + 3)$
- D
$(3x + 2)(2y + 3)$
AnswerCorrect option: A. $(3x - 2)(2y - 3)$
$= 6xy - 4y + 6 - 9x$
$= 2y(3x - 2) - 3(- 2 + 3x)$
$= (3x - 2)(2y - 3)$
View full question & answer→MCQ 871 Mark
Tick $(\checkmark)$ the correct answer:
$ab - a - b + 1 = ?$
- ✓
$(a - 1)(b - 1)$
- B
$(1 - a)(1 - b)$
- C
$(a - 1)(1 - b)$
- D
$(1 - a)(b - 1)$
AnswerCorrect option: A. $(a - 1)(b - 1)$
$ab - a - b + 1$
$= a(b - 1) - 1(b - 1)$
$= (a - 1)(b - 1)$
View full question & answer→MCQ 881 Mark
When we factorise $x^2 + 5x + 6,$ then we get:
AnswerCorrect option: C. $(x + 2) (x + 3)$
C. $(x + 2) (x + 3)$
Solution:
The factors of a form:
$= (x + a) (x + b) = x^2 + (a + b) x + ab$
$= x^2 + 5x + 6$
$= a + b = 5$ and $ab = 6$
$= x^2 + 5x + 6 = (x + 2) (x + 3)$
View full question & answer→MCQ 891 Mark
The common factor of $2x, 3x^3, 4$ is:
AnswerA. $1$
Solution:
$3x^3 = 3 \times x \times x \times x$
$4 = 2 \times 2$
View full question & answer→MCQ 901 Mark
The common factor $12y$ and $30$ is:
Answer$12y = 2 \times 2 \times 3 \times y$
$30 = 2 \times 3 \times 5$
View full question & answer→MCQ 911 Mark
The factorisation of $12a^2b + 15ab^2$ is:
- ✓
$3ab (4a + 5b)$
- B
$3a^2b (4a + 5b)$
- C
$3ab^2 (4a + 5b)$
- D
$3a^2b^2 (4a + 5b)$
AnswerCorrect option: A. $3ab (4a + 5b)$
A. $3ab (4a + 5b)$
Solution:
$12a^2b + 15ab^2 = 3ab(4a + 5b)$
View full question & answer→MCQ 921 Mark
The factorisation of $x^2 + x + xy + y + zx + z$ is:
- ✓
$(x + y + z) (x + 1)$
- B
$(x + y + z) (x + y)$
- C
$(x + y + z) (y + z)$
- D
$(x + y + z) (z + x)$
AnswerCorrect option: A. $(x + y + z) (x + 1)$
A. $(x + y + z) (x + 1)$
Solution:
$= x^2 + x + xy + y + zx + z$
$= x(x + 1) + y(x + 1) + z(x + 1)$
$= (x + 1) (x + y + z)$
View full question & answer→MCQ 931 Mark
Factorize by grouping $15pq + 15 + 9q +25p$
- A
$(pq + 1) (3q + 5p)$
- B
$(3pq + 5p) (5 + 3q)$
- C
$(3q + 3) (5p + 5)$
- ✓
$(3q + 5) (5p + 3)$
AnswerCorrect option: D. $(3q + 5) (5p + 3)$
To factorize this expression, rearrange the terms in tills expression $= 15pq +25p + 9q + 15$
Take Sp as the common factor of the first two terms and $3$ as the common factor of the other two terms.
$= 5p(3q + 5) + 3(3q + 5)$
$= (3q + 5) (5p + 3)$
View full question & answer→MCQ 941 Mark
The value of $0.76 \times 0.76 \times 0.76 + 0.24 \times 0.24 \times \frac{0.24}{0.76} \times 0.76 - 0.76 \times 0.24 + 0.24 + 0.24$ is:
View full question & answer→MCQ 951 Mark
The factors of $xyz$ are:
Answer$x, y$ and $z$ are all the factors of $xyz.$
View full question & answer→MCQ 961 Mark
The factors of $4y^2- 12y + 9$ is:
- ✓
$(2y - 3)^2$
- B
$(2y + 3)^2$
- C
$(2y - 3) (2y + 3)$
- D
AnswerCorrect option: A. $(2y - 3)^2$
A. $(2y - 3)^2$
Solution:
$= 4y^2- 12y + 9$
$= 4y^2 = (2y)^2 \&\ 9 = 3^2 \&\ 12y = 2.3.2y$
$= 4y^2- 12y + 9 = (2y)^2 - 2 \times 3 \times (2y) + (3)^2$
$= (2y - 3)^2$ By algebraic identities: $(a - b)^2 = a^2+b^2 - 2ab.$
View full question & answer→MCQ 971 Mark
What is the $HCF$ of $2x^2y\ \&\ 3xy^2?$
- A
$6xy$
- B
$6x^2y^2$
- ✓
$xy$
- D
$x^2y^2$
View full question & answer→MCQ 981 Mark
The real factors of $x^2 + 4$ are:
View full question & answer→MCQ 991 Mark
The value of $99^2$ is:
AnswerCorrect option: B. $(90)^2 - 2(90)(9) + (9)^2$
B. $(90)^2 + 2(90) (9) + (9)^2$
Solution:
$= 99^2 = (90 + 9)^2$
$= (90)^2 + 2(90) (9) + (9)^2$
View full question & answer→MCQ 1001 Mark
Tick $(\checkmark)$ the correct answer:
$40 + 3x - x^2 = ?$
- A
$(x + 5)(x - 8)$
- B
$(5 - x)(8 + x)$
- ✓
$(5 + x)(8 - x)$
- D
$(5 - x)(8 - x)$
AnswerCorrect option: C. $(5 + x)(8 - x)$
C. $(5 + x)(8 - x)$
Solution:
$40 + 3x - x^2$
$= 40 + 8x - 5x - x^2$
${40 = 8x(-5), 3 = 8 - 5}$
$= 8(5 + x) - x(5 + x)$
$= (8 - x)(x + 5)$
View full question & answer→