Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2015 Summer Zone 1

(a) Write down three hundred thousand and fifty eight as a number.
Answer (a) ...............................................................

(b) Work out.
42 - 8 \times 6
Answer (b) ...............................................................

(c) Write 21 648 correct to the nearest hundred.
Answer (c) ...............................................................

(d) Write 0.05625 correct to 2 decimal places.
Answer (d) ...............................................................

(e) Find \( \frac{3}{7} \) of 182.
Answer (e) ...............................................................

(f) The average temperature in Amsterdam in February is -2\( ^\circ \)C.
In July the average temperature is 21\( ^\circ \)C.
Find the difference between these two temperatures.
Answer (f) ............................................................... \( ^\circ \)C

(g) Write 65\% as a fraction in its lowest terms.
Answer (g) ...............................................................

(h) Divide 133 in the ratio 4 : 3.
Answer (h) .......................... : ..........................

(a) Simplify.
6x - 3y + 2x + y

Answer(a) ....................................................... [2]

(b) Find the value of $2a + b + 3c$ when $a = 3, b = -2$ and $c = 4$.

Answer(b) ....................................................... [2]

(c) $L = 2x + 3y$
Find the value of $x$ when $L = 18.6$ and $y = 2.8$.

Answer(c) $x = $ ....................................................... [2]

(d) Solve the equation.
$5x - 3 = 7$

Answer(d) $x = $ ....................................................... [2]

(e) Complete the mapping diagram for $f : x \rightarrow 2x - 1$.
[2]

PQ and RS are parallel lines.
QR is a straight line and TU is a straight line perpendicular to PQ and RS.
Angle PQR = 26°.

Find the values of a, b, c, and d.



Answer a = ..............................................................
b = ..............................................................
c = ..............................................................
d = ..............................................................

Thirty students and three teachers go by bus on a school trip to the zoo.

(a) The entrance fee is $10 for each student and $15 for each teacher.

Find the total cost of the entrance fees.

Answer(a) $ \text{.................................} [2]

(b) The bus costs $600 to hire.
Lunch costs $5 for each person.

Find the total cost of the trip including the entrance fees.

Answer(b) $ \text{..............................} [2]

(c) The total cost of the trip is divided between the 30 students.

Calculate the cost of the trip for each student.

Answer(c) $ \text{..............................} [2]

A list of numbers is shown below.
5 \ 8 \ 6 \ 2 \ 8 \ 4 \ 5 \ 8
(a) For the list of numbers, find
(i) the mode,
Answer(a)(i) ................................................................. [1]
(ii) the median,
Answer(a)(ii) ................................................................. [1]
(iii) the lower quartile,
Answer(a)(iii) ................................................................. [1]
(iv) the range,
Answer(a)(iv) ................................................................. [1]
(v) the mean.
Answer(a)(v) ................................................................. [1]

(b)
(i) Using the list of numbers, complete the frequency table.

The diagram shows a bookshelf. It is made from a piece of wood 75 cm long, 25 cm wide and 2 cm thick.
(a) Find the volume of this piece of wood.
Answer(a) ........................................................ cm³ [2]
(b) (i) Find the total surface area of this piece of wood.
Answer(b)(i) ........................................................ cm² [3]
(ii) Write your answer to part (b)(i) in square metres.
Answer(b)(ii) ........................................................ m² [1]

Jessie wants to stand 18 books on the bookshelf.

• 5 books are each 3 cm wide
• 6 books are each 4 cm wide
• 4 books are each 2.5 cm wide
• 3 books are each 7 cm wide

23, 16, 9, 2, ...
(a) Find the next two terms in this sequence.
Answer(a) .................................. , .......................... [2]
(b) Find an expression for the nth term of this sequence.
Answer(b) ............................................. [2]

The equation of line $L$ is $2y = 3 - x$.

(a) Find the gradient of line $L$.

Answer(a) ............................................................... [2]

(b) Write down the gradient of a line parallel to $L$.

Answer(b) ............................................................... [1]

(c) Find the equation of the line parallel to $L$ that passes through the point $(0, 6)$. [2]

List the elements in each of the following sets.
(a) (i) $A$
Answer(a)(i) ................................................................. [1]
(ii) $A \cap B$
Answer(a)(ii) ............................................................. [1]
(iii) $A \cup B$
Answer(a)(iii) ............................................................. [1]
(iv) $B'$
Answer(a)(iv) ............................................................. [1]
(v) $A' \cap B$
Answer(a)(v) .......................................................... [1]
(b) Find n(U).
Answer(b) ............................................................... [1]

(a) Triangle $Q$ is a reflection of triangle $P$.
On the grid, draw the line of reflection. Write down the equation of this line.
Answer(a) $\text{..........................}$ [2]

(b) Triangle $S$ is a translation of triangle $P$.
Find the vector for this translation.
Answer(b) $\begin{pmatrix} \text{ } \end{pmatrix}$ [2]

(c) Triangle $R$ is a rotation of triangle $P$.
Find the centre and the angle of rotation.
Answer(c) Centre $=$ $\text{(.................. , ..................)}$
Angle $=$ $\text{..........................}$ [2]

(a) Campbell can text at an average speed of 100 characters per minute.

Find how long it takes her to text a message of 320 characters.
Give your answer in minutes and seconds.

Answer(a) ........................... min ................... s [2]

(b) Diago texts a message of 168 characters in 1 minute 36 seconds.

Find the average speed at which he texts.
Give your answer in characters per minute.

Answer(b) ........................... characters per minute [3]

On the way to work Herr Smit drives over a bridge.
The probability that the bridge is closed is $\frac{1}{80}$.
If the bridge is closed then the probability that Herr Smit is late for work is $\frac{2}{3}$.
If the bridge is open then the probability that he is late for work is $\frac{1}{50}$.
(a) Complete the tree diagram. [3]
(b) Find the probability that the bridge is closed and Herr Smit is not late for work. [2]
(c) In 2014, Herr Smit worked for 250 days.
Estimate the number of days that the bridge was closed and Herr Smit was not late for work. [2]

The diagram shows a sector of a circle, centre $O$, radius $46\text{cm}$. Angle $AOB = 60^{\circ}$.

(a) Explain why $AB = 46\text{cm}$. [2]

(b) Calculate the length of arc $AB$.

Answer(b) .................................................. cm [2]

(c) Calculate the area of sector $AOB$.

Answer(c) .................................................. \text{cm}^2 [2]

(d) Find the area of triangle $AOB$.

Answer(d) .................................................. \text{cm}^2 [3]

(e) Use your answers to part (c) and part (d) to find the area of the shaded segment.

Answer(e) .................................................. \text{cm}^2 [1]

(a) On the diagram, sketch the graph of $y = f(x)$ for $-10 \leq x \leq 3$. [2]
(b) Write down the x co-ordinate of the point where the curve crosses the x-axis.
$\text{Answer(b)} \; x = \text{.................................}$ [1]
(c) Write down the equation of the horizontal asymptote.
$\text{Answer(c)}\; ext{.......................................}$ [1]
(d) On the same diagram, sketch the graph of $y = -2x + 3$. [2]
(e) Find the co-ordinates of the point where the two graphs intersect.
$\text{Answer(e)} (\text{........................} ,\text{........................} )$ [2]
$$f(x) = 3 \times 2^{(0.5x)} - 1$$