Practice Paper 1 (Edexcel IGCSE Maths)

A particle is moving along a straight line. At time t seconds, the displacement, x metres,

of the particle from a fixed point O on the line is given by

x = t3 - 6t2 + 15t t . 0

At time t seconds, the acceleration of the particle is a m/s2

Find an expression for a in terms of t.

a = .....................................................................

A particle is moving along a straight line. At time t seconds, the displacement, x metres,

of the particle from a fixed point O on the line is given by

x = t3 - 6t2 + 15t t . 0

At time t seconds, the acceleration of the particle is a m/s2

Find the least speed of the particle.

.....................................................................m/s

Given that 6 q 53k + 4 = 750

find the exact value of k.

k = ....................................................................

The equation of a curve is given by

8

2

y

x

5

x

=

−

x

Complete the table of values for y, giving your values of y to 2 decimal places where

necessary.

The equation of a curve is given by

8

2

y

x

5

x

=

−

x

On the grid, plot the points from your completed table and join them to form a

smooth curve.

The equation of a curve is given by

8

2

y

x

5

x

=

−

x

By drawing a suitable straight line on the grid, find an estimate, to 1 decimal

place, for the range of values of x in 0.8 - x - 6 for which 4x3 - 21x2 - 12x + 32 0

Question 10 continued

y

8 –

x

Turn over for a spare grid if you need to redraw your graph.

Question 10 continued

Question 10 continued

Only use this grid if you need to redraw your graph.

y

8 –

x

y

x

Figure 3

Figure 3 shows a triangle, A, drawn on a grid.

Triangle A is transformed to triangle B under the transformation with matrix P where

$\mathbf{P} = \begin{pmatrix} 2 & -1 \\ \tfrac{3}{2} & \tfrac{1}{2} \end{pmatrix}$

On the grid in Figure 3, draw and label triangle B.

y

x

Figure 4

Figure 4 shows triangle A drawn on a grid.

Triangle B is transformed to triangle C under the transformation with matrix Q where

$\mathbf{Q} = \begin{pmatrix} 3 & -4 \\ 1 & -2 \end{pmatrix}$

y

x

Figure 3

Figure 3 shows a triangle, A, drawn on a grid.

Triangle A is transformed to triangle B under the transformation with matrix P where

$\mathbf{P} = \begin{pmatrix} 2 & -1 \\ \tfrac{3}{2} & \tfrac{1}{2} \end{pmatrix}$

On the grid in Figure 4, draw and label triangle C.

Triangle C is the image of triangle A under a single transformation.

y

x

Figure 3

Figure 3 shows a triangle, A, drawn on a grid.

Triangle A is transformed to triangle B under the transformation with matrix P where

$\mathbf{P} = \begin{pmatrix} 2 & -1 \\ \tfrac{3}{2} & \tfrac{1}{2} \end{pmatrix}$

Describe fully this transformation.

Turn over for a spare copy of Figure 3 and Figure 4 if you need to redraw your triangles.

Only use these grids if you need to redraw your triangles.

y

x

Figure 3

y

x

Figure 4

The lengths of cod caught by fishermen in a small fishing boat last month were measured.

The incomplete table and histogram below give information about the length of each cod caught last month.

Complete the table and the histogram.

Cod that have a length less than 35 cm are returned to the sea.

Calculate an estimate, to one decimal place, of the percentage of cod caught that were returned to the sea from the boat last month.

Without using a calculator and showing all your working, express

$\sqrt{605} - \sqrt{80}$

in the form $\sqrt{n}$ where $n$ is an integer.

Vincent plays a game in which he can score 0, 1, 2, 3 or 4 each time he plays the game.

The score he gets in a game is independent of the score he got in the previous games.

The table gives information about the probability of getting each score in a game.

Vincent plays the game 150 times.

Calculate the number of times he would expect to score 1

Vincent plays the game another two times and records his two scores.

He adds these two scores together to get his Total.

Vincent plays a game in which he can score 0, 1, 2, 3 or 4 each time he plays the game.

The score he gets in a game is independent of the score he got in the previous games.

The table gives information about the probability of getting each score in a game.

Vincent plays the game 150 times.

Calculate the probability that Vincent’s Total is greater than 6

Given that for these two games Vincent has a Total greater than 6 points,

Vincent plays a game in which he can score 0, 1, 2, 3 or 4 each time he plays the game.

The score he gets in a game is independent of the score he got in the previous games.

The table gives information about the probability of getting each score in a game.

Vincent plays the game 150 times.

calculate the probability that he got a score of 4 in the first of these two games.

Question 7 continued

The function f is defined for all values of x by f : x 6 x2 - 2

Write down the range of f.

12

The function g is given by g : x 6

x

3

4

where

≠

−

3

x

4

The function f is defined for all values of x by f : x 6 x2 - 2

Calculate fg

The table below gives information about the lengths of time, in minutes, that 75 cars were parked in a car park on Sunday.

Calculate an estimate for the mean length of time, in minutes to one decimal place, that the cars were parked in the car park on Sunday.

The incomplete table and incomplete histogram give information about the lengths of time, in minutes, that 132 cars were parked in the car park on Monday.

Complete the histogram and the table.

A = {a, b, c, d}

Write down all the subsets of A that contain the element b.