Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2018 Winter Zone 2

(a) Here is a list of numbers.

8 \hspace{0.5cm} 10 \hspace{0.5cm} 14 \hspace{0.5cm} 17 \hspace{0.5cm} 20 \hspace{0.5cm} 25

From this list, write down

(i) an odd number,
............................... [1]

(ii) a multiple of 7,
............................... [1]

(iii) a square number.
............................... [1]

(b) Here are the first four numbers in a sequence.

8 \hspace{0.5cm} 11 \hspace{0.5cm} 14 \hspace{0.5cm} 17

Write down the next two terms in this sequence.
......................... , ........................ [2]

(c) Write 3658 correct to the nearest 100.
.......................................... [1]

(d) Write 68.437

(i) correct to 2 decimal places,
............................... [1]

(ii) correct to 3 significant figures.
............................... [1]

(e) $s = 2m + 3n$

Find the value of $s$ when $m = 4.8$ and $n = 1.6$.

$s = ..........................................$ [2]

(f) Change 2.3 kilometres into metres.
......................................... m [1]

A school shop sells the following.
[Table_1]

(a) Gigue buys 3 pencils and 1 sharpener.
Work out how much he spends.

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

(b) The cost of a ruler is increased by 20\%.
Work out the new cost of a ruler.

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

(c) In a sale, the cost of a sharpener is reduced to 19 cents.
Work out the percentage reduction.

......................................\% [2]

Some students were asked to choose their favourite colour of candy. All their choices are shown in the table.

[Table_1: Favourite colour (Red, Blue, Yellow, Green, Orange), Number of students (6, 5, 2, 2, 3)]

(a) Find the number of students that were asked.
.................................................. [1]

(b) One of these students is chosen at random.
Find the probability that their favourite colour of candy is blue.
.................................................. [1]

(c) Complete the bar chart.

[Image_1: Bar chart with Favourite colour (Red, Blue, Yellow, Green, Orange) and Number of students (0 to 7)] [2]

There are 36 cars altogether in a car park.
There are 11 black cars, 10 red cars and the rest of the cars are blue.

(a) Work out the number of blue cars.
............................................................... [1]

(b) Write down the fraction of cars in the car park that are black.
............................................................... [1]

(c) The information is to be shown in a pie chart.
Work out the sector angle for red cars.
............................................................... [2]

(a) [Image_1: VR IEN D]
From the letters above, write down all the letters that have
(i) line symmetry, .......................................................... [2]
(ii) rotational symmetry, .......................................................... [2]
(iii) both line symmetry and rotational symmetry, ..................................................... [1]
(iv) neither line symmetry nor rotational symmetry. ..................................................... [1]
(b) On a poster, the letter I is a rectangle of width 2 cm and height 11 cm.
(i) Work out the perimeter of the letter I. .......................................................... cm [1]
(ii) Work out the area of the letter I. .......................................................... cm² [1]

A bag contains 15 marshmallows. 8 of these are white and 7 are pink. Terry picks a marshmallow at random from the bag and eats it. He then picks a second marshmallow at random from the bag and eats it.
(a) Complete the probability tree diagram.

[3]
(b) Find the probability that both marshmallows were white.
.............................................................................[2]

(a) Describe fully the single transformation that maps triangle A onto triangle B.
....................................................................................................................................................
.................................................................................................................................................... [2]
(b) Describe fully the single transformation that maps triangle A onto triangle C.
....................................................................................................................................................
.................................................................................................................................................... [2]
(c) On the grid, draw the image of triangle A after a rotation of 180° about the origin. Label this image D.
[2]
(d) Describe fully the single transformation that maps triangle C onto triangle D.
....................................................................................................................................................
.................................................................................................................................................... [2]

The diagram shows a rectangle joined to a semicircle. There is a path along the perimeter of this shape.

(a) Show that the length of the path is 757m, correct to the nearest metre. [3]

(b) Maggie runs around the path at a speed of 220 metres per minute.
Work out how long it takes Maggie to run around the path.
Give your answer in minutes.
.........................................min [1]

(c) Jack takes 10 minutes to walk around the path.
Work out his average speed in km/h.
.........................................km/h [3]

(d) Work out the total area enclosed by the path.
.........................................m$^2$ [3]

(e) The area inside the path is covered with grass.
Grass cost $0.29 for one square metre.
Work out the total cost for the grass.
$......................................... [1]

The diagram shows a 1cm$^2$ grid.

(a) On the grid, plot the points $R(2, 2)$, $S(8, 2)$ and $T(8, 8)$. Join these points to form a right-angled triangle. [2]
(b) Find
(i) the length of $RS$, .................................................. cm [1]
(ii) the area of the triangle, .................................................. cm$^2$ [1]
(iii) the gradient of $RT$. .................................................. [2]
(c) Find the co-ordinates of the midpoint of $RT$. ( ........................ , ........................ ) [1]
(d) Write down the equation of the line $ST$. .................................................. [1]

(a)
The diagram shows a circle, centre $O$.
$AB$ and $CD$ are parallel chords and the line $EDF$ is a tangent to the circle at $D$.
Angle $ODC = 10^{\circ}$ and angle $OCB = 15^{\circ}$.
Find the size of
(i) angle $ODE$, Angle $ODE = \text{................................................} \,[1]$
(ii) angle $CDF$, Angle $CDF = \text{................................................} \,[1]$
(iii) angle $COD$, Angle $COD = \text{................................................} \,[2]$
(iv) angle $CBA$. Angle $CBA = \text{................................................} \,[1]$

(b)
The diagram shows a pentagon.
Find the value of $x$.
$x = \text{................................................} \,[3]$

The Venn diagram shows the number of students in a class wearing a T-shirt, $T$, or a cardigan, $C$.

(a) There are 20 students in total in the class. Complete the Venn diagram. [1]
(b) Find the probability that one of these students, chosen at random, wears
(i) both a T-shirt and a cardigan, ...................................... [1]
(ii) a T-shirt but not a cardigan. ...................................... [1]
(c) Find $n(T)$. ........................................................... [1]
(d) On the Venn diagram, shade $C \cap T'$. [1]

(a) $T = 5R - S$
Find the value of $T$ when $R = 3$ and $S = 4$.

$T = \text{..........................}$ [2]

(b) Simplify fully.

(i) $3a - 6b + 2a - b$
........................................... [2]

(ii) \( \frac{10x}{5x} \)
............................................ [1]

(c) Solve.

(i) \( \frac{x}{2} = 5 \)
$x = \text{...........................................}$ [1]

(ii) $7x + 2 = 51$
$x = \text{...........................................}$ [2]

(d) Expand the brackets and simplify.
$4(x+2) + 2(2x+1)$
........................................... [2]

(e) Write down the inequality shown by this number line.

........................................... [1]

(f) Solve these simultaneous equations.
You must show all your working.
$$2x-y=9$$
$$3x+y=16$$

$x = \text{..........................}$
$y = \text{..........................}$ [2]

The diagram shows the graph of $y = f(x)$ where $f(x) = -2x^2 + 5x + 6$ for $-2 \leq x \leq 4$.
(a) Use your calculator to find the zeros of $f(x)$.
...................... and ...................... [2]
(b) Use your calculator to find the co-ordinates of the local maximum.
( ...................... , ...................... ) [2]
(c) Write down the equation of the line of symmetry.
................................................. [1]