Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2017 Summer Zone 1

(a) What type of number is 7?
Give \textbf{two} possible mathematical words to describe it.
\hspace{1cm} \text{.................................................... and .................................................... [2]}

(b) (i) Write down a multiple of 7.
\hspace{1cm} \text{.................................................... [1]}
(ii) Write 7% as a fraction.
\hspace{1cm} \text{.................................................... [1]}
(iii) Work out.
\hspace{1cm} 7 + 7^2 + 7^3
\hspace{1cm} \text{.................................................... [1]}

(c) Write
(i) \frac{1}{7} as a decimal, correct to 2 decimal places,
\hspace{1cm} \text{.................................................... [2]}
(ii) \sqrt{7} as a decimal, correct to 3 significant figures,
\hspace{1cm} \text{.................................................... [2]}
(iii) 7^7 in standard form.
\hspace{1cm} \text{.................................................... [2]}

Rin asked some people how many pets they each have.
The results are shown in the table.

[Table_1]

(a) Find the number of people that Rin asked. ........................................................... [1]

(b) Find how many more people have 1 pet than have 2 pets. ........................................................... [1]

(c) One of the people is chosen at random.
Work out the probability that this person has 1 pet.
Give your answer as a fraction in its simplest form. ........................................................... [2]

(d) Complete the bar chart.
........................................................... [2]

The price of a game of golf at each of two golf clubs is shown below.

(a) (i) Find how much it costs to play 7 games at The Forest golf club.

$\text{.....................................................}$ [1]
(ii) Find how much it costs to play 7 games at The Valley golf club.

$\text{.....................................................}$ [1]
(iii) Find which golf club is cheaper for 7 games, and by how much.

$\text{.....................................................}$ is cheaper by $\text{................................}$ [1]
(b) Jason is given $200 to spend playing golf at The Forest golf club.
Find the greatest number of games he can play.
Show all your working.

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

(a) Here are three angles on a straight line.

Work out the size of angle $x$.
$x = \text{.........................................}$ [1]

(b)
(i) Write down the mathematical name for this triangle.
................................................ [1]
(ii) Find the size of angle $y$.
$y = \text{....................................................}$ [2]
(iii) Write down the number of lines of symmetry this triangle has.
................................................. [1]

(c)
Work out the size of angle $z$.
$z = \text{....................................................}$ [2]

Write each of these as a single power of $x$.
(a) $ x^7 \times x^4 $ .......................................................... [1]
(b) $ \frac{x^{10}}{x^2} $ .......................................................... [1]
(c) $(x^6)^3 $ .......................................................... [1]

(a) Here is a sequence of patterns using squares and crosses. [Image_1: Sequence of patterns]
(i) In the space above, draw Pattern 4. [1]
(ii) Find the number of crosses in Pattern 5. [1]

(b) These are the first three terms of another sequence.
1 2 4
Find two *different* sequences that could have 1, 2 and 4 as their first three terms. In each case, write down the next three terms and the rule for continuing the sequence.
1 , 2 , 4 , .......... , .......... , ..........
Rule ........................................................................................................
1 , 2 , 4 , .......... , .......... , ..........
Rule ........................................................................................................ [6]

A company sells tissues in two different boxes, $A$ and $B$. Each box is a cuboid.

(a) Find the difference between the volumes of the two boxes.

................................................ $\text{cm}^3$ [4]

(b) The total surface area of box $A$ is 1165 $\text{cm}^2$.

Show that the total surface area of box $B$ is approximately 80\% of the total surface area of box $A$.
[5]

(a) Work out the value of $5a - 4b$ when $a = 3$ and $b = 2$.
........................................................... [2]
(b) Factorise completely.
$$3x^2 - 9x$$
........................................................... [2]
(c) Solve.
(i) $4x + 5 = 13$
........................................................... [2]
(ii) $3(x - 4) = 15$
........................................................... [2]
(d) Rearrange this formula to make $A$ the subject.
$$F = 2A + B$$
$A = $ ext{ ................................................... [2]}

(a) Describe fully the single transformation that maps triangle $A$ onto triangle $B$.
............................................................................................................................
............................................................................................................................ [3]

(b) On the grid, translate triangle $A$ by the vector $\begin{pmatrix} 4 \\ 1 \end{pmatrix}$.
Label the image $C$. [2]

(c) On the grid, reflect triangle $B$ in the line $x = 1$.
Label the image $D$. [2]

Tariq sells cars. For each of ten days he records the number of cars sold and the number of hours of sunshine. His results are shown in the table.
[Table_1]

Number of hours of sunshine: 6, 5, 2, 10, 11, 4, 8, 2, 5, 7
Number of cars sold: 3, 6, 11, 2, 0, 7, 2, 12, 7, 5
(a) Complete the scatter diagram to show this information. The first 6 points have been plotted for you.

[2]

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

(c) Calculate
(i) the mean number of hours of sunshine,
..................................... hours [1]
(ii) the mean number of cars sold.
............................................. [1]

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

(e) Use your line of best fit to estimate the number of cars sold on a day when there are 3 hours of sunshine.
.............................................. [1]

(f) This table shows the number of cars Tariq sold each week for one year.
[Table_2]

Number of cars sold: 0 to 20, 21 to 40, 41 to 60, 61 to 80, 81 to 100
Number of weeks: 12, 17, 15, 7, 1
(i) Write down the modal class of the number of cars sold.
..................... to ..................... [1]
(ii) Find the largest possible range and the smallest possible range of the number of cars sold.
Largest range .................................................
Smallest range ................................................. [2]

(a) Tammi travels 7 km at an average speed of 30 km/h.
Find the number of minutes this journey takes.
......................................... minutes [2]

(b) When the speed limit is 50 km/h, Tammi travels at a speed 8% below this limit.
Find the speed at which Tammi travels.
......................................... km/h [2]

(c) In a town, there are 208 roads.
The speed limit on the roads is either 30 km/h or 50 km/h.
The ratio number of 30 km/h roads : number of 50 km/h roads = 11 : 2.
Calculate the number of 30 km/h roads.
......................................... [2]

The diagram shows a rectangular field.

(a) Find how much further it is from $A$ to $B$ when walking along two sides of the field rather than straight across the field.
m [4]
(b) Use trigonometry to calculate angle $x$.
$x =$ [2]

(a) On the diagram, sketch the graph of $y = 2^x - 3$ for values of $x$ from $x = -3$ to $x = 3$. [2]
(b) On the diagram, sketch the graph of $y = \frac{1}{x}$ for values of $x$ from $x = -3$ to $x = 3$. [2]
(c) Find the $x$ co-ordinates of the points of intersection of
$y = 2^x - 3$ and $y = \frac{1}{x}$.
$x = \text{.....................}$ and $x = \text{.....................}$. [2]