Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2018 Summer Zone 1

(a) Work out.
(i) $16.4 - 23.8$ ......................................................... [1]
(ii) $5.2 - 3 \times 4.1$ ......................................................... [1]
(b) (i) Work out $\sqrt{14.2}$ ......................................................... [1]
(ii) Write 64\% as a fraction in its lowest terms. ......................................................... [2]
(c) Write the following in order of size, starting with the smallest.
$\frac{5}{9}$ 0.55 55.5\%
$\hspace{1cm} \text{smallest}$ .................. $<$ .................. $<$ .................. [1]
(d) (i) Write 2076 in words. ......................................................................................................................... [1]
(ii) Write two million, five hundred and fifty thousand and two as a number. ......................................................... [1]

(a) A pack of 200 cards is 80mm thick. Find the thickness of 1 card.
.......................................................... mm [1]

(b) Write 358.297
(i) correct to 1 decimal place,
.......................................................... [1]
(ii) correct to 3 significant figures,
.......................................................... [1]
(iii) correct to the nearest 10.
.......................................................... [1]

(c) Work out 59\% of $348.
$ .......................................................... [2]

(d) Divide 630 in the ratio 8 : 13.
.......................... : .......................... [2]

[Table_1]
(a) For lunch, Clint has 1 bread roll, 1 lettuce leaf, 1 tomato, 2 slices of chicken and 1 apple.
Work out the total number of calories in Clint’s lunch.
................................................................. [2]

(b) Work out your answer to part (a) as a percentage of 2500.
................................................................. % [1]

(c) A bagel costs $0.65 .
Find the greatest number of these bagels that Clint can buy with $10. How much change does he receive?
........................................ bagels
change = $ ..................................................... [3]

(a) Find the lowest common multiple (LCM) of 7 and 8. .................................................. [2]
(b) Find the highest common factor (HCF) of 18 and 48. .................................................. [2]
(c) Jovana invested some money at a rate of 3% per year simple interest. At the end of 4 years the interest is $78. Work out the amount that she invested. $ .................................................. [3]
(d) Isabelle invests $800 at a rate of 3.2% per year compound interest. Work out the value of the investment at the end of 2 years. $ .................................................. [3]
(e) Change 8 kilometres per hour to metres per minute. .................... metres per minute [2]

Merel counts the number of three-letter words on every page of a book. Her results are shown in the table.

[Table_1]

P, R \text{ and } S \text{ lie on a circle, centre } O.
MPN \text{ is a tangent to the circle at } P \text{ and angle } RPN = 48^{\circ}.
(a) Find the size of
(i) \text{ angle } OPR,
\quad \text{Angle } OPR = \text{........................................} [1]
(ii) \text{ angle } ORP,
\quad \text{Angle } ORP = \text{................................................} [1]
(iii) \text{ angle } POR,
\quad \text{Angle } POR = \text{................................................} [1]
(iv) \text{ angle } SOR,
\quad \text{Angle } SOR = \text{.................................................} [1]
(v) \text{ angle } SRP,
\quad \text{Angle } SRP = \text{.................................................} [1]
(vi) \text{ angle } OSR.
\quad \text{Angle } OSR = \text{.................................................} [2]

(b) \enspace OP = 3\text{ cm}.
Find
(i) \text{ the circumference of the circle,}
\quad \text{.................................................} \text{ cm} [2]
(ii) \text{ the length of the minor arc } SR,
\quad \text{.................................................} \text{ cm} [2]
(iii) \text{ the area of the circle,}
\quad \text{.................................................} \text{ cm}^{2} [2]
(iv) \text{ the area of the minor sector } SOR.
\quad \text{.................................................} \text{ cm}^{2} [2]

(a) Complete the mathematical name of each of these angles.

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

(a) On any day, the probability that the sun will shine is 0.64. If the sun is shining, the probability that Mees goes to the beach is 0.82. If the sun is not shining, the probability that Mees goes to the beach is 0.15.

(i) Complete the tree diagram.

sun is shining ..................... 0.64 ..................... goes to the beach
.................................................. does not go to the beach

sun is not shining ..................... ..................... goes to the beach
.................................................. does not go to the beach

[3]

(a) (ii) Find the probability that the sun is shining and Mees does not go to the beach.
.................................................. [2]

(b) On any day in June, the probability that it does not rain is 0.7. There are 30 days in June.

Find the number of days that it is expected to rain in June.
.................................................. [2]

A scientist measures the temperature at seven different heights above sea level.
The table shows her results.

[Table_1]

Height above sea level ($h$ metres): 0, 500, 1000, 1500, 2500, 3000, 5000
Temperature (${\degree}C$): 15, 11, 8.5, 5, -1, -5, -17

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


(b) What type of correlation is shown in the scatter diagram? ............................................................ [1]

(c) Find
(i) the mean height, .................................................. m [1]
(ii) the mean temperature. ....................................... ${\degree}C$ [1]

(d) (i) Plot the mean point on the scatter diagram. [1]
(ii) On the scatter diagram, draw a line of best fit. [2]
(iii) Use your line of best fit to estimate the temperature at a height of 4000m. ....................................... ${\degree}C$ [1]

(a) (i) Solve.
$$2x - 3 < 15$$
.......................................................... [2]
(ii) Show your answer to part (a)(i) on this number line.
[Image_1: Number line from -2 to 10]
.......................................................... [1]
(b) Solve.
$$3x + 5 = 4x - 3$$
$$x = ext{..........................................................}$$ [2]
(c) Expand the brackets and simplify.
$$(2x - 1)(x + 3)$$
.......................................................... [2]
(d) Simplify fully.
(i) $$r^2 × r^3$$
.......................................................... [1]
(ii) $$\frac{p^8}{p^2}$$
.......................................................... [1]

Given the function \( f(x) = -2x^2 + 12x - 10 \):

(a) On the diagram, sketch the graph of \( y = f(x) \) for \( 0 \leq x \leq 6 \). [2]

(b) Find the co-ordinates of the points where the graph crosses the x-axis.

( ............... , ............... ) and ( ............... , ............... ) [2]

(c) Find the co-ordinates of the local maximum.

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

(d) (i) On the same diagram, draw the line \( y = x - 2 \). [2]

(ii) Solve.
\(-2x^2 + 12x - 10 = x - 2\)

\( x = ....................... \) or \( x = ....................... \) [2]