Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2016 Winter Zone 1

The diagram shows three regular shapes $A$, $B$ and $C$.
(a) Write down the correct mathematical name of each shape.

Shape $A$ ................................................
Shape $B$ ................................................
Shape $C$ ................................................ [4]

(b) Each shape has the same perimeter.
Find the value of $x$ and the value of $y$.

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

A conference centre has 6 rooms. One day all the rooms are used.
[Table_1]
(a) Find the total number of people in the six rooms.
........................................................... [1]
(b) Complete the bar chart for the information above.
[2]
(c) The cost of using each of the rooms for the day is $300. The cost is shared equally between the people using it.
(i) Calculate the total cost of using all six rooms.
$....................................................... [1]
(ii) For Room 4, find the cost per person to use the room.
$....................................................... [1]
(iii) Each person in Room 2 has a lunch that costs $8 per person.
Find the total amount paid by all six people in Room 2.
$....................................................... [2]

(a) \( \sqrt{3} \quad 9 \quad \frac{5}{8} \quad 21 \quad -6 \quad \pi \quad -0.75 \quad 0.33 \quad -18 \quad 3\frac{2}{5} \)
From this list, write down
(i) a positive integer, ................................................ [1]
(ii) a negative integer, ................................................ [1]
(iii) a square number, ................................................ [1]
(iv) a number between 0.5 and 1, ................................................ [1]
(v) an irrational number. ................................................ [1]
(b) Write \( \sqrt{3} \) as a decimal
(i) correct to 4 decimal places, ................................................ [1]
(ii) correct to 4 significant figures. ................................................ [1]
(c) Write 0.33 as a fraction. ................................................ [1]
(d) Write \( 3\frac{2}{5} \) as a decimal. ................................................ [1]
(e) Write \( \frac{5}{8} \) as a percentage. ................................................ % [1]

(a) MONEY
Write down all the letters from this word that have

(i) line symmetry.
.............................................................. [2]

(ii) rotational symmetry.
.............................................................. [2]

(b)
The diagram shows two right-angled triangles.
Triangle $ABC$ is similar to triangle $DEF$.

(i) Work out the lengths $AB$ and $DF$.
$AB = ......................................$ cm
$DF = ......................................$ cm [3]

(ii) Find the ratio area of triangle $ABC :$ area of triangle $DEF$.
..................... : .......................... [2]

Tutku counts the number of petals on each of 100 flowers. Her results are shown in the table.
[Table_1]

Find
(a) the mode, ............................................................... [1]
(b) the median, ............................................................... [1]
(c) the interquartile range, ............................................................... [2]
(d) the mean. ............................................................... [2]

These are the first four terms of a sequence.

326. 319. 312. 305

(a) Find the next two terms in this sequence. $\text{........................ , ........................}$ [2]

(b) Find an expression for the $n\text{th}$ term of this sequence. $\text{...................................................}$ [2]

(c) Pedro says that 249 is a term in this sequence.

Is he correct? Show working to support your answer. [1]

(a) The diagram shows a parallelogram $ABCD$ and a straight line $CDE$.
Find the values of $a$, $b$, $c$ and $d$.

$a = \text{..................................................}$
$b = \text{..................................................}$
$c = \text{..................................................}$
$d = \text{..................................................}$ [4]


(b) The diagram shows a circle, centre $O$, with diameter $EB$.
The line $AC$ is a tangent to the circle at $B$.
$D$ is a point on the circumference and angle $ABD = 62^\circ$.
Find the values of $p$, $q$ and $r$.

$p = \text{..................................................}$
$q = \text{..................................................}$
$r = \text{..................................................}$ [3]

On any evening, the probability that Elise goes to a café is $\frac{2}{5}$.
If Elise goes to a café, the probability that she then goes to the cinema is $\frac{1}{3}$.
If she does not go to a café, the probability that she then goes to the cinema is $\frac{4}{7}$.

(a) Complete the tree diagram.


[3]

(b) Find the probability that, on one evening, Elise goes to a café and goes to the cinema.

.................................................... [2]

(c) Find the probability that, on one evening, Elise goes to the cinema.

.................................................... [3]

Sally leaves home to go to school at 0745. She walks 100 metres to the bus stop and arrives at 0750.
(a) Work out her average walking speed in km/h.
........................................ km/h [3]
(b) The bus leaves the bus stop at 0755.
It travels the 6 km to school at an average speed of 40 km/h.
(i) Calculate the number of minutes that the bus takes to get to school.
........................................ min [3]
(ii) Work out the time that the bus gets to school.
........................................ [1]
(iii) Sally takes 5 minutes to walk from the bus to the classroom. The lesson starts at 08 15. Show that Sally gets to the classroom before the lesson starts.
[1]

(a) Solve.
(i) $5x + 2 = 3x + 6$
................................................... [2]
(ii) $4x - 10 < 10$
................................................... [2]

(b) Show $x > -2$ on the number line.

[1]

(c) Simplify.
(i) $6x^2 \times 2x^6$
................................................... [2]
(ii) \(\frac{15y^8}{5y^2}\)
................................................... [2]

(d) Yassar buys 2 bottles of drink and 3 bars of chocolate for $5.25.
Hassan buys 1 bottle of drink and 2 bars of chocolate for $3.05.

Find the cost of 1 bottle of drink and the cost of 1 bar of chocolate.
Show all your working.

1 bottle of drink = $...................................................
1 bar of chocolate = $................................................... [4]

The diagram shows a rectangular garden, 6 m by 12 m. In the garden there is a circular pond with radius 1.5 m. There is a circular path of width 0.5 m around the pond.
(a) The pond is 0.6 m deep. Work out the volume of water in the pond when it is full. ..................................................m^3 [2]
(b) Work out the area of the path. ..................................................m^2 [2]
(c) The rest of the garden, apart from the pond and the path, is covered by grass. Work out the area covered by grass. ..................................................m^2 [2]

Given the function $f(x) = 6 + x - x^2$:

(a) (i) On the diagram, sketch the graph of $y = f(x)$ for $-3 \leq x \leq 4$. [2]

(ii) Find the co-ordinates of the point where the graph cuts the $y$-axis.

(\text{...............} , \text{...............}) [1]

(iii) Find the co-ordinates of the points where the graph cuts the $x$-axis.

(\text{...............} , \text{...............}) and (\text{...............} , \text{...............}) [2]

(iv) Find the co-ordinates of the local maximum point.

(\text{...............} , \text{...............}) [1]

(b) Given $g(x) = x + 4$:

(i) On the diagram, sketch the graph of $y = g(x)$. [2]

(ii) Find the co-ordinates of the points of intersection of the graph of $f(x)$ and the graph of $g(x)$.

(\text{...............} , \text{...............}) and (\text{...............} , \text{...............}) [2]