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

(a) A bar of chocolate costs $0.80.
Jenny buys 5 of these bars of chocolate.
(i) How much does Jenny pay for these 5 bars of chocolate?
$ ..................................................... [1]
(ii) Find how much change she receives from $5.
$ ..................................................... [1]
(iii) One day there is a special offer on these bars of chocolate.
Chris wants 15 bars of chocolate.
Find how much he pays using the special offer.
$ ..................................................... [2]
(iv) Chris shares these 15 bars between himself and his brother in the ratio 3 : 2.
Find how many bars his brother receives.
..................................................... [2]

(b) Asli buys 3 slices of pizza and 1 salad for $2.10.
Arend buys 2 slices of pizza and 2 salads for $2.20.
Find the cost of 1 slice of pizza and the cost of 1 salad.
Show all your working.
1 slice of pizza = $ .....................................................
1 salad = $ ..................................................... [4]

(a) (i) Write the number three million two thousand and one in figures. ........................................................ [1]
(ii) Work out $10 - 2 \times 6$. ........................................................ [1]
(iii) Find the value of $\sqrt{125.44}$. ........................................................ [1]

(b) Complete the list of factors of 20.
1 , .......... , .......... , .......... , .......... , 20 [2]

(c) (i) Calculate $6.1 \times 3.4^2$, giving your answer as a decimal.
Write down your full calculator display. ........................................................ [1]
(ii) Give your answer to part (c)(i) correct to 2 decimal places. ........................................................ [1]
(iii) Give your answer to part (c)(i) correct to 2 significant figures. ........................................................ [1]

(a) Simplify.
$5a + 9b - 2a + 2b$
.................................................. [2]

(b) $R = 6M + 2N$
(i) Find $R$ when $M = -3$ and $N = 5$.
.................................................. [2]
(ii) Find $M$ when $R = 26$ and $N = 4$.
.................................................. [2]

(c) Solve.
$3x = 6x + 15$
.................................................. [2]

(d) Factorise completely.
$3a^2 - 12ab$
.................................................. [2]

(e) Simplify.
$4x^2y \times 2x^3y^2$
.................................................. [2]

Eight friends were asked these questions:
• How many minutes did you spend revising for the mathematics test?
• What was your test score?

The results are shown in the table.

[Table_1]

Number of minutes | 60 | 75 | 100 | 150 | 180 | 220 | 270 | 300
Score | 62 | 47 | 58 | 65 | 62 | 81 | 90 | 75

(a) Complete the scatter diagram. The first four points have been plotted for you.


(b) Find
(i) the mean number of minutes spent revising, $\text{.....................}$ [1]
(ii) the mean mark scored on the mathematics test. $\text{.....................}$ [1]

(c) (i) Plot the mean point on the scatter graph. [1]
(ii) Draw a line of best fit by eye on the scatter graph. [2]
(iii) Use your line of best fit to find an estimate of the mark scored on the mathematics test by a student who spent 200 minutes revising. $\text{.....................}$ [1]

30 students were asked which drink they liked best. The results are shown in the table.

[Table_1: Drink and Number of students]

(a) Complete the bar chart.
[Image_1: Incomplete bar chart]
[2]

(b) Find the probability that one of these 30 students, chosen at random, likes
(i) ice tea best, .................................................. [1]
(ii) orange juice or green tea best, .................................................. [1]
(iii) coffee best. .................................................. [1]

(c) Complete the pie chart to show the results in the table.
[Image_2: Incomplete pie chart]
[3]

The distance from Breda to Amsterdam is 105 km.
(a) A train from Breda to Amsterdam takes 35 minutes to complete the journey.
Calculate the average speed of the train in km/h.
.................................. km/h [2]
(b) Another train from Breda to Amsterdam travels at an average speed of 84 km/h.
Find the time taken for this train to travel from Breda to Amsterdam.
Give your answer in hours and minutes.
.......... hours .......... minutes [2]

Suyeon asks each of 23 students in her class to count the number of steps in their house. The results are listed below.

23 12 16 23 18 46 32 35 15 21 16 42 41 18 34 26 41 47 23 48 23 33 37

(a) Complete the ordered stem and leaf diagram to show this information.

______________
| 1 | 2
| 2 |
| 3 |
| 4 |
Key: ............ | ............ represents ......................... [3]

(b) Find
(i) the mode,
......................................................... [1]
(ii) the median,
......................................................... [1]
(iii) the interquartile range,
......................................................... [2]
(iv) the mean.
......................................................... [1]

(a) Write $\frac{43}{200}$ as a decimal.
.................................................. [1]

(b) Write the following fractions in order, starting with the smallest.
$\frac{13}{50} \quad \frac{11}{40} \quad \frac{1}{4} \quad \frac{43}{200}$
.................. , .................. , .................. , ..................
smallest [1]

(c) $\frac{13}{50} = \frac{x}{100}$
Find the value of $x$.
$x =$ .................................................. [1]

(d) Write $\frac{11}{40}$ as a percentage.
...................................... % [1]

(e) Calculate, giving each answer as a fraction.
(i) $\frac{13}{50} + \frac{43}{200}$
..................................................[1]
(ii) $\frac{11}{40} \div \frac{13}{50}$
..................................................[1]
(iii) $1 \frac{1}{4} \times \frac{43}{200}$
..................................................[1]

These are the first four terms of a sequence.
64 81 98 115
(a) Write down the next two terms in this sequence.
...................... , ...................... [2]
(b) Find an expression for the $n^{th}$ term of this sequence.
................................................. [2]

Alperen asks 30 students if they like fish $(F)$ or cheese $(C)$.
19 like fish, 24 like cheese and 2 like neither fish nor cheese.
(a) Complete the Venn diagram.

[2]

(b) Write down the number of students who like fish or cheese but not both.
......................................................... [1]

(c) Shade the region $F \cap C'$.
[1]

(d) One student is chosen at random.

Find the probability that this student likes cheese only.
......................................................... [1]

On the grid, draw the image of
(a) shape ⌐ after a reflection in the $y$-axis, [1]
(b) shape ⌐ after a rotation of $90^\circ$ clockwise about the origin, [2]
(c) shape ⌐ after a translation of $\begin{pmatrix} -6 \\ -5 \end{pmatrix}$. [2]

Tamay has 15 identical silver coins.
Each coin is a cylinder of radius 1.5 cm and height 0.5 cm.

(a) Find the total surface area of one coin.
......................................... $\text{cm}^2$ [3]

(b) (i) Find the total volume of all 15 coins.
......................................... $\text{cm}^3$ [2]

(ii) The 15 coins are melted down to make one large cylinder of height 3 cm.
Calculate the radius of this cylinder.
Give your answer correct to 1 decimal place.
......................................... $\text{cm}$ [3]

On the diagram, sketch the graph of $y = f(x)$ for $-3.5 \leq x \leq 3$. [2]
Write down the co-ordinates of the point where the graph crosses the $y$-axis. $(\text{.............. , .............})$ [1]
Write down the co-ordinates of the points where the graph crosses the $x$-axis. $(\text{.............. , .............})$ and $(\text{.............. , .............})$ and $(\text{.............. , .............})$ [2]
Write down the co-ordinates of the local minimum. $(\text{.............. , .............})$ [2]
On the same diagram, sketch and label clearly the graph of
(i) $y = f(x) + 2$, [1]
(ii) $y = f(x - 1)$. [1]