Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2021 Winter Zone 2

(a) These are the first three patterns of a sequence made using lines.

(i) In the space above, draw Pattern 4 and Pattern 5. [2]
(ii) Complete the table.
[Table_1]
(iii) Write down the rule for continuing the sequence of lines.
................................................................. [1]

(b) These are the first four terms of a different sequence.
23 17 11 5
Write down the next two terms of this sequence.
..................., ................... [2]

(c) The $n^{th}$ term of another sequence is $n^2 + 5n$.
Find the first three terms of this sequence.
..................., ..................., ................... [2]

(a) Wilfred went to a shop to buy plants for his garden.
Complete the bill.

[Table]

Item                                           Cost ($)
8 shrubs at $9.95 each                        ....................
12 bushes at $.................... each                             207.00
.................... plants at $1.60 each            25.60
Total                                          $....................

(b) The shop bought 960 tomato plants.

(i) In the first week they sold 800 of the tomato plants.
Write $\frac{800}{960}$ as a fraction in its simplest form.
................................................. [1]

(ii) In the second week,
5\% of the remaining 160 plants died
and $\frac{3}{5}$ of the remaining 160 plants were sold.
Work out how many tomato plants \textbf{are left} at the end of the second week.
....................................................... [3]

(c) Olga and Zak each buy some plants.
These plants are all the same price.
Olga pays $67.95 for 15 plants.
Zak buys 12 plants.
Work out how much Zak pays for his plants.
$....................................................

(a)
(i) Write down the coordinates of
(a) point $A$, $\text{( .................. , .................. )}$ [1]
(b) point $B$, $\text{( .................. , .................. )}$ [1]
(c) point $C$. $\text{( .................. , .................. )}$ [1]
(ii) Write down the coordinates of the mid-point of $AC$. $\text{( .................. , .................. )}$ [1]
(iii) Write down the equation of the line $AB$. $\text{............................................}$ [1]

(b)
In the diagram, $PQ$ is parallel to $TS$ and $QS = SR$. $TSR$ is a straight line.
(i) Write down the mathematical name of quadrilateral $PQRT$.
$\text{......................................................}$ [1]
(ii) Find the value of $x$.
$x = \text{......................................................}$ [1]
(iii) Find the value of $y$.
$y = \text{......................................................}$ [2]
(iv) Find the value of $z$.
$z = \text{......................................................}$ [1]

(a) Simplify.
\(5p - 7p + 4p\)
........................................................ [1]

(b) Solve.
\(4x - 1 = 9\)
\(x = ............................................................\) [2]

(c) Factorise fully.
\(15x + 9xy\)
............................................................ [2]

(d) Complete this statement with either > or < .
Show clearly how you decide.
\(11^2 \; ......... \; 5^3\)
[1]

(e) Write down the inequality shown on the number line.

............................................................ [1]

The results of 24 matches played by a football team are recorded below. They can Win (W), Lose (L) or Draw (D).

W   L   W   L   D   W   L   L
L   W   W   L   L   D   L   L
W   L   L   D   W   L   L   W

(a) Complete the table.

[Table_1]

| Result | Frequency | Pie chart angle |
|--------|-----------|-----------------|
| W      |           |                 |
| D      |           |                 |
| L      |           |                 |
| Total  | 24        | 360°            |

(a) Work out the area of quadrilateral $ABCD$.
Give the units of your answer
................................... ........... [3]

(b) Work out the perimeter of quadrilateral $ABCD$.
................................... cm [3]

(c) Use trigonometry to work out the value of $w$.

$w = ..................................................$ [2]

An aircraft flies 40 000 km around the Earth.

(a) Write 40 000 in words.
..................................................................................................................................................... [1]

(b) Change 40 000 km to metres.
Give your answer in standard form.
............................................... m [2]

(c) The flight takes 67 hours.

(i) Change 67 hours to seconds.
Give your answer correct to 2 significant figures.
............................................... s [3]

(ii) Calculate the average speed of the aircraft.
Give your answer in metres per second.
............................................... m/s [1]

This shape is made by joining four identical semi-circles to the sides of a square.
(a) Work out the perimeter of the shape. ......................................... cm [2]
(b) Write down the order of rotational symmetry of the shape. ......................................... [1]
(c) On the diagram, draw all the lines of symmetry. [2]

Shape $A$ is mapped onto shape $B$ by a single transformation.

Describe fully three different types of transformation that will map shape $A$ onto shape $B$.

1 ..........................................................................................................................................................................................................................................................................................................................................................................................

2 ..........................................................................................................................................................................................................................................................................................................................................................................................

3 ..........................................................................................................................................................................................................................................................................................................................................................................................

Tilda recorded the time, in minutes, that each of 100 cars was parked in a hospital car park. Her results are shown in the frequency table.

[Table_1]

(a) Complete the cumulative frequency table. [2]

[Table_2]

(b) On the grid, draw a cumulative frequency curve to show the information. [3]



(c) Use your cumulative frequency curve to find an estimate of

(i) the median, ........................................ min [1]

(ii) the interquartile range. ........................................ min [2]

(d) Tilda thinks that approximately three quarters of the cars were parked in the car park for between 50 and 110 minutes.

Is Tilda correct?
Use information from the curve to justify your answer. [4]

(a) (i) On the diagram, sketch the graph of $y = 7 - x^2$ for $-3 \leq x \leq 3$. [2]
(ii) Find the coordinates of the local maximum. ( \text{ ..................... } , \text{ ..................... }) [1]

(b) (i) On the diagram, sketch the graph of $y = \frac{6}{x^2}$ for values of $x$ from $-3$ to $3$. [2]
(ii) Write down the equation of each asymptote of $y = \frac{6}{x^2}$.
\text{ ..................... and ..................... } [2]

(c) Find the $x$-coordinate of each point of intersection of $y = 7 - x^2$ and $y = \frac{6}{x^2}$. [4]
\text{ ........................................................................................................... }