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

(a) Write 356.31
(i) correct to 1 decimal place, ..........................................................[1]
(ii) correct to 2 significant figures, ..........................................................[1]
(iii) correct to the nearest 100, ..........................................................[1]
(iv) in standard form. ..........................................................[1]

(b) (i) Calculate $16.8^2 - \sqrt{9.61}$.
Write down all the figures shown on your calculator, giving your answer as a decimal. ..........................................................[1]
(ii) Myrto estimates that the answer to part (b)(i) is 300.
(a) Find the difference between Myrto's estimate and your answer to part (b)(i). ..........................................................[1]
(b) Write this difference as a percentage of your answer to part (b)(i). .......................................................... % [1]

(a) Write $4 \times 4 \times 4 \times 4 \times 4 \times 4$
(i) as a power of 4, ......................................................... [1]
(ii) as an integer. ......................................................... [1]
(b) Find the value of
(i) $4^4 + 4^2$, ......................................................... [1]
(ii) $4^4 - 4^0$. ......................................................... [1]
(c) Write $\frac{4^{10}}{4^2}$ as a power of 4. ......................................................... [1]

Tingwei buys 2 kg of cheese. The cheese costs $13.50 for one kilogram.
(a) Work out how much Tingwei pays for the 2 kg of cheese.
$ \text{..............................................................} \; [1]
(b) He uses all the cheese to make 200 cheese balls.
Find the mass, \textit{in grams}, of one cheese ball.
\text{..............................................................} \; \text{g} \; [1]
(c) (i) He sells all these cheese balls at a school fair for \$0.25 each.
Work out how much money he received.
$ \text{..............................................................} \; [1]
(ii) The profit goes to the school charity.
Work out how much money goes to the school charity.
$ \text{..............................................................} \; [1]
(d) The school fair makes a total profit of $460.
Write the profit that Tingwei made as a fraction of $460.
Give your answer in its simplest form.
\text{..............................................................} \; [2]

The number of strawberries in each of 20 boxes is listed below.
32 28 27 32 33 28 34 28 29 29
28 28 33 31 33 33 30 29 29 26
(a) Complete the frequency table.
\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Number of} & 26 & 27 & 28 & 29 & 30 & 31 & 32 & 33 & 34 \\ \text{strawberries} & & & & & & & & & \\ \hline \text{Frequency} & 1 & 1 & & & & & & & 1 \\ \hline \end{array} \] [2]
(b) Find
(i) the range, ........................................................................... [1]
(ii) the mode, .......................................................................... [1]
(iii) the median, ........................................................................ [1]
(iv) the mean. .......................................................................... [1]
(c) One of these boxes of strawberries is chosen at random.
Find the probability that it contains
(i) exactly 33 strawberries, .......................................................................... [1]
(ii) fewer than 30 strawberries. ...................................................................... [1]

(a) \( A = 5B - 2C - \frac{1}{2}D \)
(i) Find the value of \( A \) when \( B = 2 \), \( C = 3 \) and \( D = 6 \).
................................................................. [2]
(ii) Find the value of \( B \) when \( A = 12 \), \( C = 1 \) and \( D = 4 \).
................................................................. [3]

(b) Find the value of \( 7p - 4q \) when \( p = -3 \) and \( q = -2 \).
................................................................. [2]

(c) Rearrange \( 2y = 3x - 9 \) to make \( x \) the subject.
\( x = ................................................................. \) [2]

(d) The mass of 1 pomegranate and 2 kiwi fruit is 480g.
The mass of 1 pomegranate and 6 kiwi fruit is 840g.
Find the mass of 1 pomegranate and the mass of 1 kiwi fruit. Show all your working.
1 pomegranate = .......................... g
1 kiwi fruit = .......................... g [4]

30 people were asked where they were going on holiday. The results are to be shown in a pie chart.

[Table_1]

(a) Calculate the sector angle for Spain.
......................................................................................... [2]
(b) Complete the pie chart. Label each sector.
[3]

(a)

AFB and CGD are parallel lines.
EFGH is a straight line and angle $AFH = 105^\circ$.

Find

(i) angle $EFB$,
Angle $EFB =$ .............................. [1]

(ii) angle $CGF$.
Angle $CGF =$ .............................. [1]

(b)

$AOB$ and $COD$ are diameters of a circle, centre $O$.
The lines $AD$ and $CB$ are parallel and angle $CAB = 70^\circ$.

Find the values of $p$, $q$, $r$ and $s$.

$p =$ ..............................
$q =$ ..............................
$r =$ ..............................
$s =$ .............................. [4]

The diagram shows four straight cycle tracks $HB$, $HC$, $BC$ and $CS$.
$BC = CS$ and $HC = 2.5\text{ km}$.
Angle $HBC = 90^\circ$ and angle $BHC = 40^\circ$.

(a) Abimela cycles from home, $H$, to school, $S$, each day along cycle track $HC$ and $CS$.
(i) Use trigonometry to find the distance $BC$.
$\text{..........................................................}$ km [2]

(ii) Find the distance Abimela cycles to school.
$\text{..........................................................}$ km [1]

(b) One day track $HC$ is blocked and she has to cycle along tracks $HB$, $BC$ and $CS$.
Find the distance $HB$.
$\text{..........................................................}$ km [2]

(c) Find the \textit{extra} distance that Abimela now has to cycle to school.
$\text{..........................................................}$ km [1]

(a) On the grid, plot the points $A(2, 3)$ and $B(5, 7)$.
Draw the line $AB$. [2]

(b) Write down the co-ordinates of the midpoint of $AB$.
$( ext{..................} , ext{..................})$ [1]

(c) Find the gradient of $AB$.
...................................................... [2]

(d) Find the equation of the line parallel to $AB$ that passes through the point $(0, 4)$.
.............................................................. [2]

The diagram shows 12 solid cylinders packed into a box. Each cylinder has radius 1 cm and length 15 cm.
(a) (i) Find the volume of one cylinder. ............................................................. cm³ [1]
(ii) Work out the volume of 12 cylinders. ............................................................. cm³ [1]
(b) The box measures 15 cm by 12 cm by 4 cm.
Find the volume of the box. ............................................................. cm³ [1]
(c) Find the volume of the box not taken up by the cylinders. ............................................................. cm³ [1]
(d) Write your answer to part (c) as a percentage of the total volume of the box. ............................................................. % [1]

The diagram shows a pentagon, $P$.
(a) Draw the image of $P$ after a reflection in the $y$-axis. Label this image $Q$. [1]
(b) Draw the image of $P$ after a translation by the vector $\begin{pmatrix} 2 \\ -6 \end{pmatrix}$. Label this image $R$. [2]
(c) Draw the image of $P$ after an enlargement, scale factor 3, centre $(0, 0)$. Label this image $S$. [2]
(d) Find the ratio
length of horizontal side of $S$ : length of horizontal side of $P$.
.......................... :...................... [1]
(e) Choose a word from the list to complete the statement.

Congruent     Regular     Similar

$P$ and $S$ are $\text{.....................}$ shapes. [1]

The masses of 200 meerkats are recorded in the frequency table.

[Table_1]

(a) Write down the modal group.
..................... < x \leq ..................... [1]

(b) (i) Show that the midpoint of the first group is 250. [1]

(ii) Find an estimate of the mean mass of these 200 meerkats.
................................................... g [2]

(c) Complete the cumulative frequency table.

[Table_2]

[2]

(d) Complete the cumulative frequency curve.

[Graph_1]

[3]

(e) Use your graph to find
(i) the median,
.................................................. g [1]

(ii) the inter-quartile range,
................................................. g [2]

(iii) the number of meerkats with a mass of more than 850 g.
................................................... [2]

(a) On the diagram, sketch the graph of $y = f(x)$ from $x = -3$ to $x = 3$. [4]

(b) Write down the equation of the vertical asymptote for this graph.
$\text{..............................................................}$ [1]
(c) Find the co-ordinates of the local minimum point.
$(\text{.....................} , \text{.....................})$ [1]
(d) Write down the number of solutions of $y = f(x)$ when $y = 6$.
$\text{..............................................................}$ [1]