Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2022 Summer Zone 2

(a) From this list of numbers, write down
21 22 23 24 25 26 27 28 29
(i) an even number,
........................................... [1]
(ii) a multiple of 6,
........................................... [1]
(iii) a factor of 100,
........................................... [1]
(iv) a prime number.
........................................... [1]
(b) Find the value of
(i) $\sqrt{841}$ ,
........................................... [1]
(ii) $6^3$ .
........................................... [1]
(c) Work out.
\(\frac{13.25 + 35.51}{5.2}\)
Give your answer correct to 2 decimal places.
........................................... [2]

Quadrilateral $ABCD$ is drawn on a 1 cm square grid.


(a) Write down the mathematical name of quadrilateral $ABCD$.
................................................... [1]

(b) Write down the coordinates of point $B$.
( ...................... , ...................... ) [1]

(c) Work out the area and the perimeter of quadrilateral $ABCD$.

Area ............................................. cm$^2$
Perimeter ............................................. cm [2]

(d) On the diagram, draw the lines of symmetry of quadrilateral $ABCD$. [2]

(a) These are the first four terms of a sequence.

4 \hspace{10pt} 8 \hspace{10pt} 12 \hspace{10pt} 16

(i) Write down the next two terms of this sequence.
\text{.................... , ....................} \hspace{10pt} [1]

(ii) Write down the rule for continuing this sequence.
\text{...............................................} \hspace{10pt} [1]

(iii) Find the $n$th term of this sequence.
\text{...............................................} \hspace{10pt} [1]

(b) Look at the patterns of numbers in this table.

\[\begin{array}{|c|c|} \hline \text{Row 1} & 20^2 - 19^2 = 39 \\ \hline \text{Row 2} & 19^2 - 18^2 = 37 \\ \hline \text{Row 3} & 18^2 - 17^2 = 35 \\ \hline \text{Row 4} & 17^2 - 16^2 = 33 \\ \hline \text{Row 5} & \\ \hline \text{Row 8} & \\ \hline \end{array}\]

(i) Complete Row 5 of the table. \hspace{10pt} [1]

(ii) Complete Row 8 of the table. \hspace{10pt} [2]

(iii) Find the $n$th term of this sequence.
39 \hspace{10pt} 37 \hspace{10pt} 35 \hspace{10pt} 33
\text{...............................................} \hspace{10pt} [2]

In the diagram, $AQB$ and $PBC$ are straight lines and $PQ = PB$.
(a) What type of triangle is $BPQ$? ............................................................... [1]
(b) Find the value of $x$. $$x = ext{........................................................}$$ [3]
(c) Find the value of $y$. $$y = ext{........................................................}$$ [1]
(d) $AB$ and $BC$ are two sides of a regular polygon.
Work out the number of sides of this polygon. ............................................................... [2]

(a) The table shows the melting point, in °C, of some metals.

[Table_1]

| Metal | Melting point (°C) |
|------------|--------------------|
| Zinc | 420 |
| Gold | 1063 |
| Silver | 893 |
| Copper | 1084 |
| Aluminium | 660 |

(i) Write these five temperatures in order of size starting with the smallest.
...................... , ...................... , ...................... , ...................... , ......................
smallest [1]

(ii) Write 1063 correct to the nearest 10.
.............................................. [1]

(iii) Write 1084 in words.
........................................................................................................................................................................ [1]

(b) Brass can be made by combining copper and zinc in this ratio.
copper : zinc = 13 : 7
Work out the mass of copper and the mass of zinc used to make 60 kg of brass.

copper ........................................ kg
zinc ........................................... kg [2]

(a) (i) A train travels from Amsterdam to Brussels in 2 hours 15 minutes. It leaves Amsterdam at 11 10.
Work out the time the train arrives in Brussels. ................................................. [1]

(ii) On its return journey, the train leaves Brussels at 14 50. It arrives in Amsterdam at 17 15.
Work out the length of time this journey took. Give your answer in hours and minutes. ................ h ................. min [1]

(b) One day, the adult train fare from Amsterdam to Brussels is 75 euros.

(i) The fare for a child is $\frac{3}{5}$ of the adult fare.
Work out the child fare for the journey. ........................................ euros [1]

(ii) On another day the adult fare of 75 euros is increased by 12\%.
Work out the adult fare on this day. ........................................ euros [2]

(c) The train from Amsterdam to Brussels travels 180 km in 2 hours 15 minutes.
Work out the average speed of the train in kilometres per hour. ........................................ km/h [2]

The graph shows the cost, \( y \) dollars, of printing \( x \) cards.
(a) (i) Find the cost of printing 45 cards.
$ .............................................. [1]
(ii) Find the largest number of cards that can be printed for $28.
................................................ [1]
(b) (i) Find the equation of the line in the form \( y = mx + c \).
\( y = .............................................. \) [3]
(ii) Any number of cards can be printed. Steffi needs 100 cards.
Use your equation from part (b)(i) to find how much these will cost.
$ .............................................. [2]

(a) On the diagram, sketch the graph of $y = x^2 + 3x$ for $-4 \leq x \leq 3$. [2]
(b) On the diagram, sketch the graph of $y = 2x + 6$ for $-4 \leq x \leq 3$. [2]
(c) Find the coordinates of each point of intersection of $y = x^2 + 3x$ and $y = 2x + 6$.
(\text{..................., ...................}) \text{ and } (\text{..................., ...................}) [2]

(a) Complete each of these statements using $<$ or $>$.
$$11 \ ext{.........} \ 7$$
$$-11 \ ext{.........} \ -7$$

(b) Simplify.
(i) $x + 3x + 5x$ ........................................................ [1]
(ii) $6p - 2t - 4p + 3t$ ........................................................ [2]

(c) Factorise fully.
$12x + 3xy$ ........................................................ [2]

(d) Solve.
(i) $\frac{x}{5} = 5$
$x = \text{.............................................}$ [1]
(ii) $7x + 3 = 3x + 5$
$x = \text{.............................................}$ [2]

(e) $y = 6x^2$
(i) Find the value of $y$ when $x = 5$.
$y = \text{.............................................}$ [1]
(ii) Find the value of $x$ when $y = 294$.
$x = \text{.............................................}$ [2]
(iii) Rearrange the formula $y = 6x^2$ to make $x$ the subject.
$x = \text{.............................................}$ [2]

A garage sells used cars. The table shows the selling price, in $, and the distance travelled, in km, of eight used cars. All cars are of the same make and model.
[Table_1]

(a) Complete the scatter diagram. The first four points have been plotted for you.

[2]

(b) What type of correlation is shown in the scatter diagram?
................................................ [1]

(c) The mean distance travelled is 24000 km and the mean selling price is $4500.
On the scatter diagram, draw a line of best fit.
[2]

(d) Another used car of this make and model had travelled a distance of 30000 km. Use your line of best fit to estimate the selling price of this car.
$ ................................................ [1]

The diagram shows three right-angled triangles $ABC$, $BCD$ and $CDE$. $AC = 54$ mm, $CD = 45$ mm, $CE = 35$ mm and angle $BAC = 68^{\circ}$.
(a) Use trigonometry to show that $BC = 134$ mm, correct to the nearest mm. [2]
(b) Use trigonometry to find angle $BCD$.
Angle $BCD = \text{.............................................}$ [2]
(c) Use Pythagoras’ Theorem to find $DE$.
$DE = \text{.............................................}$ mm [2]

The table shows the frequency distribution for the masses, in kg, of 100 students.

[Table]

(a) Complete the cumulative frequency table.

[Table]

(b) On the grid below, draw the cumulative frequency curve for this data.



(c) Use your cumulative frequency curve to find an estimate of
(i) the median, ...............................................................kg [1]
(ii) the interquartile range. .........................................kg [2]

(d) Use your cumulative frequency curve to find an estimate for the number of students with a mass of less than 68kg. ............................................................. [1]

(a) A cube has edges of length 3 cm.

(i) Find the volume of the cube. ......................................... cm$^3$ [2]

(ii) Find the total surface area of the cube. ......................................... cm$^2$ [2]

(b) Some cubes, each with edges of length 3 cm, are placed in a box. The box is a cuboid with dimensions 30 cm by 20 cm by 15 cm. Work out the greatest number of these cubes that can be placed in the box. ......................................... [3]