Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2020 Winter Zone 2

Ben was born on 25th March, 1936.
(a) Write the number 1936 in words. [1]
(b) Work out how old Ben is on the 25th March, 2020. [1]
(c) Work out the year of Ben’s 99th birthday. [1]
(d) Find $\sqrt{1936}$. [1]
(e) Write down 1936
(i) correct to the nearest 10, [1]
(ii) correct to 2 significant figures, [1]
(iii) in standard form. [1]
(f) Write down a multiple of 1936. [1]

The number of seconds that it took each of 15 students to run 200 metres is shown below.
32 35 29 41 41
39 51 57 45 62
42 53 38 43 60
(a) Work out the mean.
.................................................. s [1]
(b) Complete the stem-and-leaf diagram to show this information.
__________________________________________________________________
__________________________________________________________________
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Key ........ | ....... represents ....................... [3]
(c) Find
(i) the range,
.................................................. s [1]
(ii) the mode,
.................................................. s [1]
(iii) the median,
.................................................. s [1]
(iv) the interquartile range.
.................................................. s [2]

A supermarket sells saving stamps for $0.10 each. These stamps are stuck onto pages in a special stamp book.
(a) Each page of the stamp book has 35 stamps.
Work out how much is paid for the stamps to fill one page.
$ ................................. [1]

(b) It costs $49 to fill the book with stamps.
Find the number of pages in the book.
............................................ [2]

(c) Each full book of stamps can be used in the supermarket to pay for food costing $52.
(i) Work out how much is saved by paying for food with a full book of stamps.
$ .............................................. [1]
(ii) Work out the answer to part (i) as a percentage of $49.
.............................................. % [2]

(d) Fred buys fruit and coffee for $49.
The ratio cost of fruit : cost of coffee = 3 : 4.
Find the cost of the coffee.
$ .............................................. [2]

(a) Petra has a birthday party. The party starts at 19 30 and ends at 23 45.
(i) Find how long the party lasts.
..................... hours ..................... minutes [1]
(ii) The cost of hiring a band for the party is a total of $150. The cost of hiring a hall is $50 per hour. Petra hires the hall for 6 hours.
Find the total cost of hiring the hall and the band.
$ .............................................. [2]

(b) Petra received $650 for her birthday.
(i) She invests half of this in a bank at a rate of 3.1% per year compound interest.
Work out the value of her investment at the end of 3 years.
$ .............................................. [3]
(ii) Petra invests the other half of her birthday money in a different bank at a rate of 3.5% per year simple interest.
Work out the value of this investment at the end of 3 years.
$ .............................................. [3]

The diagram shows a circle, centre O. The straight line ABC touches the circle at B. DOEC is a straight line, D and E lie on the circumference and angle OBD = 31^\circ.
(a) Using the letters in the diagram, write down
(i) the diameter, .................................................... [1]
(ii) a radius, .................................................... [1]
(iii) a chord, .................................................... [1]
(iv) the tangent. .................................................... [1]
(b) Find
(i) angle OBC, \(\text{Angle } OBC = \text{....................................................} \) [1]
(ii) angle ABD, \(\text{Angle } ABD = \text{....................................................} \) [1]
(iii) angle BOD, \(\text{Angle } BOD = \text{....................................................} \) [2]
(iv) angle BCO. \(\text{Angle } BCO = \text{....................................................} \) [2]

(a) The diagram shows a shape drawn on a 1 cm$^2$ grid. (i) Use Pythagoras’ theorem to calculate the value of $x$. $x =$ ext{................................................} [2]
(ii) Work out the perimeter of the shape. ext{.........................................} cm [1]
(b) Shade one small square so that the diagram has line symmetry. [1]
(c) Shade one small square so that the diagram has rotational symmetry of order 2. [1]
(d) $ABC$ and $DEF$ are similar triangles. Find the value of $x$. $x =$ ext{................................................} [2]

One day, Mr Amir made a note of the number of employees who were on time for work and the number who were late for work.
He asked each employee if they ate breakfast or not.
The information is shown in the table.

| | Number who ate breakfast | Number who did not eat breakfast | Total |
|---|-------------------------|-------------------------------|------|
| Number who were on time for work | 12 | a | 17 |
| Number who were late for work | 2 | c | b |
| Total | 14 | 6 | 20 |

(a) Work out the value of each of a, b and c.

a = ...........................................
b = ...........................................
c = ........................................... [3]

(b) An employee is chosen at random.

Find the probability that this employee

(i) was on time,
................................................. [1]

(ii) did not eat breakfast,
................................................. [1]

(iii) ate breakfast and was late for work.
................................................. [1]

U = \{F, R, A, C, T, I, O, N\}
X = \{R, A, T, I, O\}
Y = \{F, A, C, T\}

(a) Write down the elements in $X \cap Y$. .......................................................... [1]

(b) Complete the Venn diagram. [2]

(c) Find $n(X \cup Y)^{\prime}$. .......................................................... [1]

(d) On the Venn diagram below, shade the region $X^{\prime} \cup Y$. [1]

(a) f(x) = 2x^2 - 1
(i) Find f(4).
................................................... [1]
(ii) Find x when f(x) = 17.
x = .................. or x = .................. [3]

(b) Solve.
(i) 7x - 14 = 14
x = ................................................. [2]
(ii) 5x - 3 = 3x + 7
x = ................................................. [2]

(c) Expand.
3x(x - 4)
............................................................ [2]

(d) Simplify fully.
$$\frac{18r^8}{6r^2}$$
............................................................ [2]

(e)
(i) $3^6 \times 3^m = 3^{18}$
Find the value of m.
m = ................................................. [1]
(ii) $\frac{8^n}{8^3} = 8^2$
Find the value of n.
n = .................................................. [1]

(f) Solve the simultaneous equations.
You must show all your working.
$$\begin{align*} 2x + 4y &= 22 \\ 2x - 3y &= 15 \end{align*}$$
x = ................................................. [2]
y = ................................................. [2]

(a) (i) On the diagram, sketch the graph of $y = 8 \times (1.4)^{-x} + 2$ for $-1 \leq x \leq 12$. [2]
(ii) Find the coordinates of the point where the graph crosses the $y$-axis.
( ....................... , ........................ ) [1]
(iii) Write down the equation of the horizontal asymptote.
....................................................... [1]
(b) On the same diagram, sketch the graph of $y = x + 3$. [2]
(c) Find the coordinates of the point of intersection of the graphs of
$y = 8 \times (1.4)^{-x} + 2$ and $y = x + 3$.
( ....................... , ........................ ) [2]

Describe fully the single transformation that maps
(a) shape $A$ onto shape $B$,
...................................................................................................................
................................................................................................................... [3]

(b) shape $A$ onto shape $C$,
...................................................................................................................
................................................................................................................... [2]

(c) shape $A$ onto shape $D$,
...................................................................................................................
................................................................................................................... [2]

(d) shape $A$ onto shape $E$.
...................................................................................................................
................................................................................................................... [3]