Question 1

Solve the simultaneous equations

$\begin{array}{ll}& 2x+5y=11
\ & 3x-2y=-12\ 
\end{array}$

Accepted Answer

$x=-2, y=3$

Answer

$x=4, y=-3$

Answer

$x=1, y=5$

Answer

$x=2, y=4$

Question 2

Solve the simultaneous equations

$2x-7y=12$
$5x-y=-3$

Accepted Answer

$x=-1, y=-2$

Answer

$x=1, y=-4$

Answer

$x=-2, y=1$

Answer

$x=2, y=3$

Question 3

Solve the simlutaneous equations

$3x+8y=12$
$2x+12y=13$

Accepted Answer

$x=2, y= \frac{ 3 }{ 4 }$

Answer

$x= \frac{1}{2}, y= 3$

Answer

$x= \frac{2}{3}, y= -1$

Answer

$x= -\frac{1}{3}, y= 2$

Question 4

Two families go to the cinema. The first family buys one adult ticket and three child tickets and pays £39. The second family buys two adult tickets and four child tickets and pays £62.
Form and solve a pair of simultaneous equations to work out the cost of an adult ticket and the cost of a child ticket.

Accepted Answer

Adult ticket costs $£15$,
Child ticket costs $£8$

Answer

Adult ticket costs $£18$,
Child ticket costs $£12$

Answer

Adult ticket costs $£11$,
Child ticket costs $£6$

Answer

Adult ticket costs $£20$,
Child ticket costs $£15$

Question 5

The mass of $20$ apples and $30$ satsumas is $4050	ext g.$ The mass of $12$ apples and 15 satsumas is $2205	ext g$.
Work out the mass of one apple and the mass of one satsuma.

Accepted Answer

Mass of apple $= 	ext { 90g}$
Mass of satsuma $= 	ext { 75g}$

Answer

Mass of apple $= 	ext { 100g}$
Mass of satsuma $= 	ext { 60g}$

Answer

Mass of apple $= 	ext { 80g}$
Mass of satsuma $= 	ext { 70g}$

Answer

Mass of apple $= 	ext { 120g}$
Mass of satsuma $= 	ext { 90g}$

Question 6

Expand $(2x-y)3xy$

Accepted Answer

$6x^2y-3xy^2$

Answer

$3x^2y-6xy^2$

Answer

$6xy-3xy$

Answer

$6x^2y+xy-3xy^2$

Question 7

Expand and simplify $(x+2)(y+1)$

Accepted Answer

$xy+x+2y+2$

Answer

$xy+2$

Answer

$xy+2y+3x$

Answer

$x^2+2y+3$

Question 8

Expand and simplify $(2m+3n)(3m-2n)$

Accepted Answer

$6m^2+5mn-6n^2$

Answer

$6m+5mn-6n$

Answer

$6m^2-6n^2$

Answer

$6m^2-6n^2$

Question 9

Expand and simplify $(4x+1)^2$

Accepted Answer

$16x^2+8x+1$

Answer

$12x^2+4x+2$

Answer

$8x^2+1$

Answer

$16x^2+10x$

Question 10

Work out an expression for the area of the triangle in expanded form.

Accepted Answer

$2x^2+x-1$

Answer

$4x^2+6x-3$

Answer

$3x^2-2x+4$

Answer

$x^2+2x-2$

Question 11

Expand and simplify $(x-1)(2-x)(x+4)$

Accepted Answer

$-x^3-x^2+10x-8$

Answer

$-3x^3+2x^2+4x-12$

Answer

$2x^4+3x^2+10x-12$

Answer

$5x^2+12x-6$

Question 12

A cube has side length ($x + 1$)cm. Work out an expression for the volume of the cube in the form $ax^3+bx^2+cx+d$.

Accepted Answer

$x^3+3x^2+3x+1$ cm$^3$

Answer

$3x^3+x^2+9x+5$ cm$^3$

Answer

$2x^3+5x^2+3x+2$ cm$^3$

Answer

$5x^3+7x^2+x+1$ cm$^3$

Question 13

Factorise fully $16x+12xy$

Accepted Answer

$4x(4+3y)$

Answer

$2x(8+6y)$

Answer

$4x(4x+3xy)$

Answer

$6x(2+3y)$

Question 14

Factorise fully $8p-4p^2q+6pq$

Accepted Answer

$2p(4-2pq+3q)$

Answer

$4p(2-pq+2)$

Answer

$3p(2p-3pq+2)$

Answer

$2pq(4-2p+3)$

Question 15

What is the missing length on the diagram?

The area is given as $x^2+3x$ and the height as $x$.

Accepted Answer

$x+3$

Answer

$x^2+9$

Answer

$x+1$

Answer

$x^2+3$

Question 16

Factorise $x^2+9p-10$

Accepted Answer

$(x+10)(x-1)$

Answer

$(2x+5)(x-2)$

Answer

$2(x+2)(x-5)$

Answer

$(x+5)(x-2)$

Question 17

Factorise $y^2-14y+49$

Accepted Answer

$(y-7)^2$

Answer

$(y+11)(y-4)$

Answer

$(y+4)(y-3)$

Answer

$(y-7)(y+3)$

Question 18

A rectangle has area $x^2+6x-27$. Work out expressions for the lengths of the two sides of the rectangle.

Accepted Answer

$x+9$ and $x+3$

Answer

$x+1$ and $x+7$

Answer

$x+5$ and $x+4$

Answer

$2x+4$ and $x+2$

Question 19

Factorise $y^2-81$

Accepted Answer

$(y-9)(y+9)$

Answer

$(y+7)(y+12)$

Answer

$(2y+13)(y+6)$

Answer

$(y+9)(y+9)$

Question 20

Factorise $p^2-9q^2$

Accepted Answer

$(p-3q)(p+3q)$

Answer

$(p+3q)(p+3q)$

Answer

$(p-2q)(p+3q)$

Answer

$(p^2-q)(p+3q)$

Question 21

The area of a parallelogram is $x^2-121$.

What is the expression for the BASE of the parallelogram in terms of $x$?

Accepted Answer

$x +11$

Answer

$x + 15$

Answer

$x + 3$

Answer

$x - 34$

Question 22

The area of a parallelogram is $x^2-121$.

What is the expression for the HEIGHT of the parallelogram in terms of $x$?

Accepted Answer

$x - 11$

Answer

$x - 15$

Answer

$x +11$

Answer

$x + 15$

Question 23

Factorise $6x^2+5x-4$

Accepted Answer

$(2x-1)(3x+4)$

Answer

$(x-3)(6x+4)$

Answer

$(x-5)(x+6)$

Answer

$(4x-2)(x+3)$

Question 24

Factorise $12x^2+20x+3$

Accepted Answer

$(2x+3)(6x+1)$

Answer

$(2x+2)(3x+1)$

Answer

$(12x+4)(x+3)$

Answer

$(5x+2)(4x+6)$

Question 25

A square has area $9x^2+30x+25$. Work out the perimeter of the square in terms of $x$.

Accepted Answer

$12x+20$

Answer

$6x^2+4$

Answer

$16x+22$

Answer

$24x+8$

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