Question 1

Solve $x^2-7x-8$

Accepted Answer

$x=8$ or $x=-1$

Answer

$x=6$ or $x=-2$

Answer

$x=3$ or $x=-4$

Answer

$x=4$ or $x=2$

Question 2

Solve $x^2+5x=0$

Accepted Answer

$x= 0$  or $x=-5$

Answer

$x=4$ or $x=-6$

Answer

$x=2$ or $x=-3$

Answer

$x=5$ or $x=-1$

Question 3

Solve $x^2-1=0$

Accepted Answer

$x=1$ or $x=-1$

Answer

$x=3$ or $x=-2$

Answer

$x=-1$ or $x=0$

Answer

$x=3$ or $x=-2$

Question 4

Solve $x^2-12x=-35$

Accepted Answer

$x=7$ or $x=5$

Answer

$x=6$ or $x=8$

Answer

$x=9$ or $x=3$

Answer

$x=11$ or $x=2$

Question 5

Solve $x^2+3x=10$

Accepted Answer

$x=-5$ or $x=2$

Answer

$x=-8$ or $x=4$

Answer

$x=5$ or $x=-6$

Answer

$x=-10$ or $x=1$

Question 6

Solve $x^2=144$

Accepted Answer

$x=12$ or $x=-12$

Answer

$x=8$ or $x=-4$

Answer

$x=-9$ or $x=8$

Answer

$x=10$ or $x=-15$

Question 7

Solve $6x^2+13x-5=0$

Accepted Answer

$x= \frac{1}{3}$ or $x=- \frac{ 5 }{ 2 }$

Answer

$x= \frac{1}{4}$ or $x=- \frac{ 7 }{ 3 }$

Answer

$x= \frac{2}{3}$ or $x=- \frac{ 9 }{ 5 }$

Answer

$x= \frac{1}{5}$ or $x=\frac{ 7 }{ 5 }$

Question 8

Solve $7x^2-19x-6=0$

Accepted Answer

$x= -\frac{2}{7}$ or $x=3$

Answer

$x= -\frac{5}{6}$ or $x=4$

Answer

$x= -\frac{5}{8}$ or $x= \frac{1}{4}$

Answer

$x= -\frac{4}{9}$ or $x=5$

Question 9

Here is a rectangle. The area of the rectangle is 5cm$^2$.

Work out the length of the shortest side of the rectangle.

Accepted Answer

1cm

Answer

4cm

Answer

3cm

Answer

5cm

Question 10

Solve $3x^2-7x-10=0$, giving your answer to 3 significant figures if appropriate.

Accepted Answer

$x= \frac{ 10}{ 3}$ or $x=-1$

Answer

$x=- \frac{ 7}{ 2}$ or $x=3$

Answer

$x= \frac{ 5}{ 2}$ or $x=-3$

Answer

$x=- \frac{ 3}{ 2}$ or $x=5$

Question 11

Solve $5x^2+4x-20=0$, giving your answer to 3 significant figures if appropriate.

Accepted Answer

$x=1.64$ or $x=-2.44$

Answer

$x=1.01$ or $x=-3$

Answer

$x=4$ or $x=-6$

Answer

$x=1.96$ or $x=-3.37$

Question 12

Solve $25+10x-2x^2=0$, giving your answer to 3 significant figures if appropriate.

Accepted Answer

$x=6.83$ or $x=-1.83$

Answer

$x=9.95$ or $x=-3.17$

Answer

$x=6$ or $x=-1$

Answer

$x=8.43$ or $x=-2.05$

Question 13

Solve $x^2-10x+7=0$, giving your answers in the form $a\pm{b} \sqrt{c},$where $a, b$ and $c$ are integers.

Accepted Answer

$5 \pm{3}\sqrt{2}$

Answer

$6 \pm{2}\sqrt{3}$

Answer

$3 \pm{3}\sqrt{2}$

Answer

$9 \pm{5}\sqrt{3}$

Question 14

Solve $x^2+2x-11=0$, giving your answers in the form $a\pm{b} \sqrt{c},$where $a, b$ and $c$ are integers.

Accepted Answer

$-1 \pm{2}\sqrt{3}$

Answer

$-3 \pm{3}\sqrt{5}$

Answer

$3 \pm{4}\sqrt{7}$

Answer

$-2 \pm{3}\sqrt{2}$

Question 15

Solve $2x^2+22=16x$, giving your answers in the form $a\pm{b} \sqrt{c},$where $a, b$ and $c$ are integers.

Accepted Answer

$4 \pm{}\sqrt{5}$

Answer

$8 \pm{2}\sqrt{7}$

Answer

$-5 \pm{2}\sqrt{3}$

Answer

$-8 \pm{5}\sqrt{11}$

Question 16

Here is a trapezium. The lengths of the parallel sides are $(x+2)	ext{ cm}$ and $(x+4)	ext{ cm}.$  The height is $(x-1)	ext{ cm}.$ The area of the trapezium is $	ext{10 cm}^2.$ 

Work out the height of the trapezium to $2$ decimal places.

Accepted Answer

$	ext{1.74 cm}$

Answer

$	ext{2.76 cm}$

Answer

$	ext{3.14 cm}$

Answer

$	ext{3.86 cm}$

Question 17

What is $x^2+6x+5$ in the form $(x+p)^2+q$?

Accepted Answer

$(x+3)^2-4$

Answer

$(x+2)^2-3$

Answer

$(x+3)(x-3)$

Answer

$(x+3)^2+14$

Question 18

What is $x^2-4x+10$ in the form $(x+p)^2+q$?

Accepted Answer

$(x-2)^2+6$

Answer

$(x-3)(x+4)$

Answer

$(x-3)^2+2$

Answer

$(x+2)^2-6$

Question 19

What is $x^2-10x$ in the form $(x+p)^2+q$?

Accepted Answer

$(x-5)^2-25$

Answer

$(x-5)^2-10$

Answer

$(x+100)^2-100$

Answer

$(x+5)^2+10$

Question 20

What is $x^2+x+1$ in the form $(x+p)^2+q$?

Accepted Answer

$(x+ \frac{1}{2})^2+ \frac{ 3 }{ 4 }$

Answer

$(x+ \frac{3}{2})^2+\frac{ 3 }{ 2 }$

Answer

$(x+ \frac{1}{2})^2-\frac{ 1 }{ 2 }$

Answer

$(x+ \frac{1}{2})^2-\frac{ 4 }{ 3 }$

Question 21

Solve the equation $x^2-2x-11=0$.

Give your answer in the form $a \pm{b} \surd 3$, where $a$ and $b$ are integers.

Accepted Answer

$1 \pm{2} \surd 3$

Answer

$3 \pm{3} \surd 3$

Answer

$-2 \pm{3} \surd 2$

Answer

$-5 \pm{7} \surd 2$

Question 22

What is $2x^2+8x+7$ in the form $a(x+p)^2+q$?

Accepted Answer

$2(x+2)^2-1$

Answer

$5(x+1)^2+5$

Answer

$4(x+2)^2+1$

Answer

$2(x+4)^2-16$

Question 23

What is $12+10x-x^2$ in the form $a(x+p)^2+q$?

Accepted Answer

$37-(x-5)^2$

Answer

$15-(x-3)^2$

Answer

$6(x-4)^2-3$

Answer

$3(x-8)^2+13$

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