Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2022 Summer Zone 1

(a) Write the number 20 202 in words.
..................................................................................................................

(b) Work out.
$$\frac{6.27 + 2.48}{1.75}$$
...........................................

(c) Write down all the factors of 42.
..........................................

(d) Write down a prime number between 15 and 20.
........................................

(e) Write 7832.948
(i) correct to 2 decimal places,
......................................................
(ii) correct to 4 significant figures,
......................................................
(iii) correct to the nearest 100.
......................................................

(f) Insert the symbols (), +, −, × so that the following statement is correct.
5   3   4   1   =   9

(g) Jeffrey invests $550 for 3 years at a rate of 3.2% per year simple interest.
Work out the interest he receives.
$ ........................................

Wim measures the amount of rain, in mm, each day for 31 days. The bar chart shows his results.

(a) Write down the mode. ........................................... mm [1]
(b) Write down the number of days that had no rain. ........................................... [1]
(c) Work out the mean amount of rain per day. ........................................... mm [2]
(d) Wim picks one of these days at random.
Find the probability that, on that day, the amount of rain was 3 mm or more. ........................................... [1]

The diagram shows a circle, centre $O$, radius 4.2 cm.
$A$, $B$ and $C$ are points on the circle.
The line $DE$ touches the circle at $C$.
(a) Write down the mathematical name for each of these straight lines.
$AC$ is a .................................................................
$DE$ is a .................................................................
$AB$ is a ................................................................. [3]
(b) Work out
(i) the circumference of the circle, ......................................... cm [2]
(ii) the area of the circle. ......................................... cm$^2$ [2]
(c) Angle $AOB = 110^\circ$.
Calculate the area of sector $AOB$. ......................................... cm$^2$ [2]

The diagram shows point A and point C plotted on a 1 cm² grid.
(a) Plot point B (5, 7) and point D (-1, 7) and draw the quadrilateral ABCD. [2]
(b) (i) Find the length of AC.
\( AC = \text{.................................} \text{ cm} \) [1]
(ii) Use Pythagoras’ Theorem to find the length of AB.
\( AB = \text{.................................} \text{ cm} \) [2]
(c) Write down the mathematical name for quadrilateral ABCD.
\( \text{.................................} \) [1]
(d) Reflect quadrilateral ABCD in the line \( y = 4 \). [2]

(a) Solve.
(i) $6x = 96$

$x = \text{.........................................}$ [1]

(ii) $7x - 6 = -13$

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

(b) Simplify.
(i) $5r - 2r - r$

$\text{.........................................}$ [1]

(ii) $4a - 3b - 7a + 2b$

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

(c) $T = 4m + 2n$

Find
(i) the value of $T$ when $m = 1.8$ and $n = -0.3$,

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

(ii) the value of $n$ when $T = 26$ and $m = 3.4$.

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

30 members of a sports club were asked what their favourite game was. They could choose from tennis (T), squash (S) or badminton (B). These are the results.
B T S S T S B B T S
S S S T T T S S B T
B T S S T T B S S T
(a) Complete the frequency table.
[Table_1] Game | Frequency
Tennis (T) |
Squash (S) |
Badminton (B) | [2]
(b) Find how many more members chose tennis than badminton.
................................................ [1]
(c) One of the 30 members is chosen at random. Write down the probability that this member chose squash.
................................................ [1]
(d) Shadana begins to draw a pie chart to show the results.
(i) Show that the sector angle for tennis is 132°. [2]
(ii) Complete the pie chart for Shadana. [3]

Gheza wants to know if the number of weeks that a song is Number One in the charts is related to the length of the song, in minutes.
The table shows the results for one year.

[Table_1]

(a) Complete the scatter diagram.
The first 6 points have been plotted for you.



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

(c) Find
(i) the mean number of weeks at Number One,
.......................................................................... [1]

(ii) the mean length of a song.
.......................................................................... min [1]

(d) On the scatter diagram, draw a line of best fit. [2]

(a) The $n^{th}$ term of a sequence is $2n^2 + 3$.
Write down the first three terms of this sequence.
.......................... , .......................... , ......................... [2]

(b) These are the first four terms of a different sequence.
$$5 \quad -3 \quad -11 \quad -19$$
(i) Find the next two terms of the sequence.
.......................... , ......................... [2]
(ii) Find the $n^{th}$ term of the sequence.
.................................................... [2]
(iii) Sanjay says that $-101$ is a term of the sequence.
Show that he is not correct. [2]

(a) Describe fully the \textit{single} transformation that maps shape $A$ onto shape $B$.
................................................................................................................................................................................
................................................................................................................................................................................ [3]
(b) Describe fully the \textit{single} transformation that maps shape $A$ onto shape $C$.
................................................................................................................................................................................
................................................................................................................................................................................ [2]
(c) Rotate shape $A$ 90^\circ clockwise about $(0, 0)$. [2]

The diagram shows a sketch of the graph of $$y = 0.5x^3 + 0.65x^2 - 2x + 2 \quad \text{for} \quad -4 \leq x \leq 3.$$
(a) Find the coordinates of the point where the graph crosses the $y$-axis.
\( \quad ( \text{..............} , \text{..............} ) \quad [1] \)
(b) Find the coordinates of the point where the graph crosses the $x$-axis.
\( \quad ( \text{..............} , \text{..............} ) \quad [1] \)
(c) Find the coordinates of the local maximum.
\( \quad ( \text{..............} , \text{..............} ) \quad [2] \)
(d) Find the coordinates of the local minimum.
\( \quad ( \text{..............} , \text{..............} ) \quad [2] \)
(e) On the diagram, sketch the graph of $y = 8$. \quad [1]
(f) Solve this equation.
\[ 0.5x^3 + 0.65x^2 - 2x + 2 = 8. \]
\( x = \quad \text{..........................................} \quad [1] \)

The diagram shows a regular hexagon with centre $O$ and $OA = OB = 14 \text{ cm}$.

(a) Work out the size of angle $x$ and the size of angle $y$.
$$x = \text{..........................}$$
$$y = \text{..........................}$$ [2]

(b) Write down the length of $AB$.
$$AB = \text{.......................... cm}$$ [1]

(c) Work out the area of triangle $AOB$.
$$ \text{.......................... cm}^2$$ [3]

The regular hexagon is the cross-section of a prism. The length of the prism is 5 cm.
(d) Work out the volume of the prism.
$$ \text{.......................... cm}^3$$ [2]

Ruben’s house is 1.3 km from the supermarket.

(a) He walks to the supermarket at a speed of 5 km/h.

Work out how long it takes him.
Give your answer in minutes and seconds.

....................... min ....................... s [3]

(b) On another day, Ruben cycles to the supermarket in a time of 5 minutes 12 seconds.

(i) Show that 12 seconds = 0.2 minutes.

[1]

(ii) Work out Ruben’s average speed when cycling to the supermarket.
Give your answer in km/h.

.................................. km/h [2]