Practice Paper 1 (Edexcel IGCSE Maths)

$x$ is an integer.

Prove that $35+(3x+1)^{2}--2x(4x--3)$ is a square number.

Three tins, $A$, $B$and $C$ , each contain buttons.

Tin $A$ contains $x$buttons. Tin $B$ contains 4 times the number of buttons that tin $A$ contains. Tin $C$ contains 7 fewer buttons than tin $A$.

The total number of buttons in the three tins is 137

Work out the number of buttons in tin $C$.

Make $f$ the subject of $m=\sqrt{\frac{1}{3}ef}$

The 3rd term of an arithmetic series, $A$, is 19 The sum of the first 10 terms of $A$ is 290

Find the 10th term of $A$.

Solve the simultaneous equations

$3x+y=-4$

$3x-4y=6$

Solve $x^{2}+2x>6x+5$

Represent your solution set to part (a) on the number line below.

For the curve with equation $y=x^{3}-7x^{2}-5x$: find $\frac{dy}{dx}$

find the $x$-coordinates of the two turning points on the curve.

By considering the shape of the curve determine which of your answers to (b) is the $x$-coordinate of a maximum point.

The functions $f$ and $g$are such that

$f(x)=x^{2}-2xg(x)=x+3$

The function $h$ is such that $\mathrm{h} ( x ) = \text{fg} ( x ) \text{for} x greater-than \text{or} \text{slanted} \text{equal} \text{to} - 2$

Express the inverse function $h^{-1}(x)$ in the form $h^{-1}(x)$ = .........

$h^{-1}(x)$ = ................

The lines $y=x---2$ and $x+y=10$ are drawn on the grid.

On the grid, mark with a cross (x) each of the points with integer coordinates that are in the region defined by

$y>x-2\,x+y<10\,x>3$

The diagram shows part of the curve with equation $y=f(x)$. The coordinates of the maximum point of the curve are (3, 5).

Write down the coordinates of the maximum point of the curve with equation

(i) $y = \mathrm{f} ( x + 3 )$

(ii) $y=-f(x)$

(iii) $y=f(-x)$

The curve with equation $y=f(x)$ is transformed to give the curve with equation $y=f(x)-4$

Describe the transformation.

Tick all the statements that are true for any rhombus.

square The diagonals are lines of symmetry

size 26px square The diagonals bisect each other

size 26px square The diagonals are perpendicular

size 26px square The diagonals are equal in length

Toy building bricks are available in two sizes, small and large.

The small and large bricks are mathematically similar.

A small brick has volume 8cm³ and width 2.1cm.

A large brick has volume 15.625 cm³.

Calculate the width of a large brick.

..................................................... cm

The diagram shows the positions of three ships, $A,B$ and $C$.

Ship $B$ is due north of ship $A$. The bearing of ship $C$from ship $A$ is 120°

Calculate the bearing of ship $C$ from ship $B$. Give your answer correct to the nearest degree.

In the diagram,

• E, F and D are points on the circumference of the circle
• G, D and H lie on a tangent to the circle
• angle EFD = 55°
• angle FDE = 43°.

Explain why angle HDF is 82°.

Triangle $ABC$ is similar to triangle $PQR$.

Find $PQ$.

$PQ=$ ......................................... cm

Here are two solids.

Which solid has the greater volume?

You must show your working.

Katie invests £200 in a savings account for 2 years.

The account pays compound interest at an annual rate of

3.3% for the first year 1.5% for the second year

Work out the total amount of money in Katie's account at the end of 2 years.

Katie travels to work by train. The cost of her weekly train ticket increases by 12.5% to £225

Katie's weekly pay increases by 5% to £535.50

Compare the increase in the amount of money Katie has to pay for her weekly train ticket with the increase in her weekly pay.