Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2019 Winter Zone 2

(a) Write \( \frac{2}{5} \) as a decimal.
.................................................. \[1\]

(b) Write \( \frac{9}{16} \) as a percentage.
.................................................. % \[1\]

(c) Work out \( 68.52 - 3.41 \times 7.9 \).
.................................................. \[2\]

(d) Write down a factor of 17.
.................................................. \[1\]

(e) Write \( \frac{28}{49} \) in its simplest form.
.................................................. \[1\]

(f) Write down the next two terms in this sequence.
\[81, \ 74, \ 67, \ 60, \ldots\]
.................., .................. \[2\]

(g) \$380 is invested at a rate of 3\% per year simple interest.
Work out the interest at the end of 4 years.
\$ .................................................. \[2\]

(h) Cupcakes cost \$1.30 each.
Find the largest number of these cupcakes that can be bought with \$10.
.................................................. \[2\]

Benji has 15 bags of potatoes.
The number of potatoes in each bag is shown below.
38 36 42 36 36
41 40 38 37 39
39 40 37 38 36

(a) Complete the frequency table.

[Image_1: Table]
\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \text{Number of potatoes} & 36 & 37 & 38 & 39 & 40 & 41 & 42 \\ \hline \text{Frequency} & 4 & & & & & & \\ \hline \end{array}
[2]

(b) For the number of potatoes, find

(i) the range,
................................................
[1]

(ii) the mode,
................................................
[1]

(iii) the median,
................................................
[1]

(iv) the mean.
................................................
[1]

(c) Complete the bar chart.
[Image_2: Incomplete Bar Chart]
[2]

(a) Write sixty thousand and twenty in figures.

(b) Complete the mapping diagram for the function \( f(x) = 3x - 4 \).


(c) Write down a prime number between 35 and 45.

(d) \( \frac{8}{15} = \frac{a}{75} \)
Find the value of \( a \).

(e) Write 6789 correct to the nearest 10.

(f) Write 189.436 correct to 2 decimal places.

(g) Write 3462
(i) correct to 3 significant figures,
(ii) in standard form.

The diagram shows two points, $A$ and $B$, plotted on a $1\,\text{cm}^2$ grid.



(a) Write down the co-ordinates of point $A$ and the co-ordinates of point $B$.

\( A \ (\ ....................... \ ,\ ....................... \ ) \)
\( B \ (\ ....................... \ ,\ ....................... \ ) \) [2]

(b) Calculate the length of $AB$.

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

(c) Find the co-ordinates of the midpoint of $AB$.

\( (\ ....................... \ ,\ ....................... \ ) \) [1]

(d) Find the gradient of $AB$.

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

(e) Write down the equation of the line parallel to $AB$ passing through $(0, 3)$.

\( y = \ ..................................................... \) [2]

Two cylindrical candles are mathematically similar. The small candle has radius 2 cm and height 5 cm. The large candle has radius 7 cm.

(a) Find the height of the large candle.
.................................................. cm [2]
(b) The small candle burns for 4 hours and the large candle burns for 60 hours.
Write the ratio $4 : 60$ in its simplest form.
......................... : ...................... [1]
(c) The price of the large candle is $28.
In a sale, this price is reduced by 15%.
Find the sale price.
$............................................................ [2]

(a) For each diagram, draw all the lines of symmetry.

[3]

(b) Simi makes a flower using some mathematical shapes.
The centre is a circle with radius 2 cm.
Each of the five petals is an isosceles triangle with base 2.3 cm and perpendicular height 4 cm.
The stem is a rectangle with length 6 cm and width 1 cm.

Find the total area shaded.

............................................ cm$^2$ [4]

The table shows the age, in months, and length, in centimetres, of seven babies.

[Table_1: Table showing age and length of babies]

(a) Complete the scatter diagram to show this information.
The first three points have been plotted for you.

[Image_1: Scatter diagram]

(b) Find.
(i) the mean age, .......................................... months [1]
(ii) the mean length. .......................................... cm [1]

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

(d) Use your line of best fit to find an estimate for the length of a baby aged 7 months. .......................................... cm [1]

(a)



The diagram shows a vertical tower, $PQ$, standing on horizontal ground. Matthijs stands at point $A$. He is 1.8 m tall.
The base of the tower, $P$, is 36 m from point $A$.
Find the height of the tower.
.....................................................m [3]

(b)



$AB$ and $AC$ are tangents to a circle with centre, $O$, and radius 4 cm. Angle $BAC = 38^\circ$.

(i) Write down the size of angle $OBA$.
Angle $OBA =$ ..................................................... [1]

(ii) Find the size of angle $BOC$.
Angle $BOC =$ ..................................................... [1]

(c) Use trigonometry to find the length of $OA$.
$OA =$ ..................................................... cm [3]

20 people were asked if they liked banana milk shake, $B$, or chocolate milk shake, $C$.
[Image_1: Venn diagram with B, C, 4, 3, 9, and U]
(a) Complete the Venn diagram. [1]
(b) Write down $n(B \cap C)$. .................................................. [1]
(c) One of these 20 people is chosen at random.
Find the probability that this person likes
(i) banana milk shake, .................................................. [1]
(ii) chocolate milk shake but not banana milk shake. .................................................. [1]
(d) On the Venn diagram, shade $C' \cap B$. [1]

Given \(f(x) = x^3 - 5x^2 + 2x + 8\):
(a) On the diagram, sketch the graph of \(y = f(x)\) for \(-2 \leq x \leq 5\). [3]
(b) Write down the co-ordinates of the point where the curve crosses the \(y\)-axis.
( \(.....................\ , \ .....................\) ) [1]
(c) Write down the co-ordinates of the three points where the curve crosses the \(x\)-axis.
( \( ................, ...............\ ), \( ................, ...............\ ), \( ................, ...............\) ) [2]
(d) Find the co-ordinates of the local maximum.
( \( .....................\ , \ .....................\) ) [2]
(e) Find the number of times that the line \(y = 9\) crosses the curve \(y = f(x)\).
........................................................ [1]

(a) Solve.
(i) $3y = 6$
$y = \text{...............................}$ [1]
(ii) $6y - 5 = 13$
$y = \text{...............................}$ [2]
(iii) $3 - y > 6$
$\text{.......................................}$ [2]

(b) Expand and simplify.
$(5y - 7)(3y - 4)$
$\text{.......................................}$ [2]

(c) $P = 2T - 6$
(i) Find the value of $P$ when $T = 8$.
$P = \text{.......................................}$ [1]
(ii) Rearrange the formula to make $T$ the subject.
$T = \text{.......................................}$ [2]

(d) Simplify.
$\frac{2y}{3} + \frac{y}{5}$
$\text{.......................................}$ [2]

Angie goes to school on 5 days each week.
On a school day, the probability that Angie gets up before 7 am is $\frac{9}{10}$.
On a non-school day, the probability that Angie gets up before 7 am is $\frac{1}{20}$.
(a) Complete the tree diagram.

[3]
(b) One day of the week is chosen at random.
Find the probability that the day is a non-school day and that Angie gets up before 7 am.
..................................................... [2]