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

(a) Complete the statement.
6 weeks = ..........................................days [1]

(b) Write in figures the number fifteen thousand and twenty seven.
.................................................. [1]

(c) Write
(i) 144.1 correct to the nearest 10,
.................................................. [1]
(ii) 5.5349 correct to 2 decimal places,
.................................................. [1]
(iii) 50617 correct to 2 significant figures.
.................................................. [1]

(d) Write 0.7
(i) as a fraction,
.................................................. [1]
(ii) as a percentage.
..........................................% [1]

(e) Find the value of $0.7^3$.
.......................................... [1]

Tam recorded the number of hours of homework he did each night for 25 nights. His results, in hours, are shown below.
4 1 4 3 2 3 4 2 1
1 3 2 1 2 1 1 3 5
4 1 3 3 1 3 4
(a) Complete the frequency table.
[Table]
| Number of hours | Number of nights |
|-----------------|------------------|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
[2]
(b) Which number of hours is the mode?
............................................. hours [1]
(c) Draw a bar chart to show this information.

[2]
(d) On one of the nights, Tam did mathematics homework, English homework and history homework. The pie chart shows the time he spent on each subject.

(i) Work out the fraction of the total time he spent on mathematics homework. Give your answer in its simplest form.
.............................................. [2]
(ii) Tam spent 3 hours altogether on his homework that night.
Work out the time, in minutes, Tam spent on English homework.
.............................................. min [3]

(a) Write down the co-ordinates of
(i) $T$, ( ................. , ................. ) [1]
(ii) $R$. ( ................. , ................. ) [1]
(b) On the grid, draw the line of symmetry of the quadrilateral. [1]
(c) Measure the size of angle $p$.
.......................................................[1]

In each part, give the mathematical name for the shape described.
(a) A quadrilateral with each pair of opposite sides parallel. .................................................. [1]
(b) A triangle with exactly two sides equal in length. .................................................. [1]
(c) A polygon with 6 sides. .................................................. [1]
(d) A quadrilateral with all sides of equal length but not all angles equal. .................................................. [1]
(e) A solid shape with six faces. Four of the faces are identical rectangles and the other two faces are identical squares. .................................................. [1]

(a) A box contains 40 orange counters and 32 blue counters only.
(i) Write the ratio orange counters : blue counters in its simplest form.
........................... : ........................... [2]
(ii) Some of the orange counters are removed. The ratio orange counters : blue counters is now 1 : 2. Work out how many orange counters have been removed.
.................................................. [2]

(b) Another box contains 6 white counters, 3 black counters and 2 red counters only.
(i) One of the 11 counters is chosen from the box at random. Write down the colour of the counter that is least likely to be chosen.
................................................ [1]
(ii) One of the 11 counters is chosen from the box at random. Work out the probability that this counter is white.
................................................ [1]
(iii) One white counter is removed from the box of 11 counters. A counter is now chosen from the box at random. Work out the probability that this counter is white.
................................................ [1]

(c) A different box contains 180 counters. The counters are either yellow or green in the ratio yellow counters : green counters = 5 : 1.
Work out the number of counters of each colour.
yellow ...................................................
green .................................................... [2]

John and Asif take part in a 30 km cycle race.

(a) John starts his race at 10 15. He takes 1$\frac{1}{2}$ hours to complete the race.

(i) At what time does John complete the race?
...................................................... [1]

(ii) Work out John’s average speed, in km/h, for the 30 km race.
.................................... km/h [1]

(b) Asif completes the 30 km race at a speed of 16 km/h.

Work out the time, in hours and minutes, Asif takes to complete the race.
....................... h ........................ min [3]

(a) Find the missing terms in each of these sequences.

(i) ............ , 9, 17, 25, ............

(ii) ............ , 8, 16, ............ , 64

(iii) 35, 25, 16, 8, ............ , ............

(iv) .................. , 2x−4, 3x−9, 4x−14, ..................

(b) The nth term of another sequence is $n^2+n$.
Find the first three terms of this sequence.

...................... , ........................ , ........................

(c) Find the nth term of this sequence.

1, 5, 9, 13, ...

.................................................

(a) (i) Rearrange this formula to make $d$ the subject.
$$C = \pi d$$
$d = \text{..............................}$ [1]

(ii) A circle has a circumference of 2 metres.
Work out the diameter of this circle.
Give your answer in centimetres, correct to the nearest whole number.
$\text{.............................. cm}$ [3]

(b) A CD is a ring with inner radius 0.8 cm and outer radius 6 cm.
Find the area of the CD, shown shaded.
$\text{.............................. cm}^2$ [4]

(a) Factorise completely.
12x + 16
.........................................................[2]
(b) Multiply out the brackets.
2x(3x - 5)
.........................................................[2]
(c) Solve.
8(2x + 3) = 48
x = .........................................................[3]

A square has side 8 cm.
A small square is drawn inside this larger square so that the corners of the small square touch the sides of the larger square.



(a) (i) Calculate the area of the shaded triangle.
.................................................. cm^2 [2]

(ii) Using your answer to part (a)(i), calculate the area of the small square.
.................................................. cm^2 [2]

(b) Calculate the perimeter of the small square.
.................................................. cm [3]

The cumulative frequency curve shows the heights, in cm, of 200 girls.
(a) Find the median height. ........................................ cm [1]
(b) Work out the inter-quartile range of the heights. ........................................ cm [2]
(c) Find the number of girls with a height of 160cm or less. ........................................ [1]

(a) The diagram shows a ladder, 5 m long, leaning against a vertical wall.
The bottom of the ladder is on horizontal ground, 3.5 m from the wall.
Use trigonometry to find the value of $x$.

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

(b) A different ladder leans against the same wall.
This ladder makes an angle of $49^\circ$ with the ground and touches the wall 4 m above the ground.
Use trigonometry to find the length of this ladder.
Include a labelled sketch in your working.
.................................................... m [4]

A painting is valued at $2400. The value of the painting increases by 5% each year.
Find the value of the painting at the end of 3 years.
$ ................................................ [4]

A curve has equation $y = x^2 + x - 6$.
(a) Find the co-ordinates of the points where this curve crosses
(i) the $y$-axis,
( ................ , ................ ) [1]
(ii) the $x$-axis.
( ................ , ................ ) and ( ................ , ................ ) [2]
(b) Find the co-ordinates of the local minimum.
( ................ , ................ ) [2]
(c) Find the equation of the line of symmetry of the curve.
.................................................... [2]