Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2019 Summer Zone 1

(a) Write in words the number 6015.
............................................................................................................................ [1]
(b) Find the value of
(i) $4^3$, ............................................................ [1]
(ii) $\frac{2(3+9)}{3 \times 16}$, ............................................................ [1]
(iii) $3 \times 5^2$, ............................................................ [1]
(iv) $40 - 10 \times 2$. ............................................................ [1]
(c) Find
(i) $\sqrt{81}$, ............................................................ [1]
(ii) a prime number between 20 and 30, ............................................................ [1]
(iii) 60 as a product of prime factors. ............................................................ [2]

This shape is drawn on a 1 $\text{cm}^2$ grid.
(a) (i) Work out the area and the perimeter of the shape. Give the units of each answer.
Area = \text{.......................} ..............
Perimeter = \text{.......................} .............. [4]
(ii) The shape is enlarged by a scale factor of 3.
Find the perimeter of the enlarged shape. Give your answer in metres.
...................................................... m [3]
(b) Write down the order of rotational symmetry of the shape.
...................................................... [1]
(c) On the diagram, draw all the lines of symmetry. [2]
(d) Work out the sum of all the interior angles of the shape.
...................................................... [3]
(e) Write down the co-ordinates of point $A$ and point $B$.
$A$ ( ..................... , .................... )
$B$ ( ..................... , .................... ) [2]

(a) A packet of cereal costs $2.80.
Work out the largest number of these packets that can be bought with $20.
How much change would you get?
................. packets and $ .................... change [3]
(b) A packet originally contained 450 g of cereal.
The mass of cereal in the packet is increased by 15%.
Work out how much extra cereal is added to the packet.
....................................... g [2]
(c) 51 out of 300 people said they would buy the heavier packet of cereal.
Work out 51 as a percentage of 300.
....................................... % [1]

This formula can be used to change a temperature in degrees Celsius, $C$, to a temperature in degrees Fahrenheit, $F$:

$$F = 2C + 30$$

(a) Find the value of $F$ when
(i) $C = 0$, .................................................. [1]
(ii) $C = 120$. .................................................. [1]

(b) Find the value of $C$ when $F = 350$. .................................................. [2]

(c) Find the value of $C$ when $F = C$. .................................................. [2]

(d) Rearrange the formula to make $C$ the subject.

$$F = 2C + 30$$

$C = $ .................................................. [2]

Henri records the number of people in each car passing through his village. The results are shown in the table.

[Table_1]
Number of people | Number of cars
1 | 35
2 | 25
3 | 20
4 | 10
5 | 10

(a) Complete the bar chart to show this information.
[2]

(b) Find the total number of cars that Henri recorded.
....................................................... [1]

(c) Using the results in the table, work out
(i) the mode,
....................................................... [1]
(ii) the median,
....................................................... [1]
(iii) the mean.
....................................................... [2]

(d) One of the cars is chosen at random.
Work out the probability that it contains
(i) 4 people,
....................................................... [1]
(ii) 1 or 2 people.
Give your answer as a fraction in its simplest form.
....................................................... [2]

(a) These are the first four terms of a sequence.
11 18 25 32
(i) Write down the rule for continuing this sequence.
.............................................................................................................................................. [1]
(ii) Find an expression for the $n^{th}$ term of this sequence.
............................................................... [2]

(b) Here are the first four terms of another sequence.
23 18 13 8
Find the next two terms of this sequence.
.......................... , .......................... [2]

(a) On the grid, draw the image of the shape after a translation by vector \( \begin{pmatrix} 4 \\ -2 \end{pmatrix} \).
[2]
(b) On the grid, draw the image of the shape after a rotation of 90\textdegree{} anticlockwise about the point \( O \).
[2]

(a) Simplify.
$$4a + 2a - 3a$$
.................................................. [1]

(b) Solve.
(i) $$17 - x = 4$$
$$x = \text{..................................................}$$ [1]

(ii) $$\frac{x}{5} = 4$$
$$x = \text{..................................................}$$ [1]

(iii) $$2(3x + 1) = 44$$
$$x = \text{..................................................}$$ [3]

(c) Factorise fully.
$$12x - 30$$
.................................................. [2]

(d) Simplify fully.
(i) $$\frac{x^4 \times x^3}{x^7}$$
.......................................................... [2]

(ii) $$\frac{15y^6}{3y^2}$$
.......................................................... [2]

Crystal carries out a survey of cars, vans and lorries that drive past her house.
(a) She sees a total of 500 of these types of vehicle. The ratio $\text{cars : vans : lorries} = 14 : 4 : 7$.
Work out how many of each type of vehicle she sees.

Cars ..............................
Vans ..............................
Lorries .............................. [3]
(b) One car travels 2.5 km in 5 minutes.
Work out the speed of this car in kilometres per hour.
.............................. km/h [2]
(c) Crystal measures the speed of each of the 500 vehicles. Her results are shown in the table.

[Table_1]
\begin{array}{|c|c|} \hline \text{Speed (s km/h)} & \text{Frequency} \\ \hline 0 < s \leq 10 & 0 \\ 10 < s \leq 20 & 20 \\ 20 < s \leq 30 & 230 \\ 30 < s \leq 40 & 170 \\ 40 < s \leq 50 & 60 \\ 50 < s \leq 60 & 20 \\ \hline \end{array}
(i) Complete the cumulative frequency table.

[Table_2]
\begin{array}{|c|c|} \hline \text{Speed (s km/h)} & \text{Cumulative Frequency} \\ \hline s \leq 10 & 0 \\ s \leq 20 & \\ s \leq 30 & \\ s \leq 40 & \\ s \leq 50 & \\ s \leq 60 & 500 \\ \hline \end{array} [1]
(ii) On the grid, draw a cumulative frequency curve for this information.

[3]
(iii) Use your cumulative frequency curve to estimate the number of cars travelling faster than 35 km/h.
............................................ [2]

A cylinder has radius $7 \text{ cm}$ and height $h \text{ cm}$.
(a) Show that the area of the circular end of the cylinder is $154 \text{ cm}^2$, correct to the nearest whole number. [2]

(b) The volume of the cylinder is $2 \text{ litres}$.
Work out the value of $h$.

$h = \text{..........................................}$ [2]

(c) A cube has side length $x \text{ cm}$. It has the same volume as the cylinder.
Find the value of $x$.

$x = \text{.............................................}$ [3]

A vertical post, 1.75 m tall, stands on horizontal ground. One day, the post casts a shadow of length 3.28 m.



(a) Find the value of \( x \).

\( x = \text{.................................................} \) [2]

(b) Find the value of \( y \), the angle of elevation of the Sun.

\( y = \text{...................................................} \) [2]

The diagram shows the graph of $y = x + 2$ for $-3 \leq x \leq 5$.

(a) Find the co-ordinates of the $y$-intercept. $\text{( ................. , ................. )}$ [1]

(b) On the diagram, sketch the graph of $y = x^2 - x - 1$ for $-3 \leq x \leq 5$. [2]

(c) Solve this equation.

$$x^2 - x - 1 = x + 2$$

$x = \text{..................}$ or $x = \text{..................}$ [2]