Cambridge IGCSE Mathematics - International - 0607 - Core Paper 3 2021 Summer Zone 1

(a) Work out.
(i) $\sqrt{36}$ ................................................... [1]
(ii) $7^3$ ................................................... [1]

(b) (i) $4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4^n$
Write down the value of $n$.
$n = \text{...................................................}$ [1]
(ii) Write down the value of $4^0$.
................................................... [1]

(c) Work out. $$\frac{1}{2^2 + \sqrt{17}}$$ Give your answer correct to 3 decimal places.
................................................... [2]

(d) (i) Write $0.000\,082$ in standard form.
................................................... [1]
(ii) Work out.
$(7.3 \times 10^9) \times (1.8 \times 10^{-4})$
Give your answer in standard form.
................................................... [2]

Points $A, B$ and $C$ are plotted on a $1 \text{ cm}^2$ grid.

(a) Write down the coordinates of
(i) point $B,$
$( \text{..................} , \text{..................} )$ [1]
(ii) point $A.$
$( \text{..................} , \text{..................} )$ [1]

(b) On the grid, plot the point $(-3, -1)$ and label it $D.$ [1]

(c) Join $A, B, C$ and $D$ to form a quadrilateral.
Write down the mathematical name of quadrilateral $ABCD.$
................................................... [1]

(d) Work out the area of quadrilateral $ABCD.$
......................................... $\text{ cm}^2$ [2]

(e) On the grid, draw the reflection of quadrilateral $ABCD$ in the $x$-axis. [2]

Ralf records the number of people in each car entering the school car park. The results are shown in the table.

[Table_1]

(a) Work out the total number of cars that Ralf records.
................................................... [1]

(b) Work out the total number of people in these cars.
................................................... [2]

(c) On the grid, draw and label a bar chart to show the information in the table.

(a) Ana is 28 years 3 months old.

Change 28 years 3 months into months.

.............................. months [2]

(b) Ana has three children.
The ages of the children are

7 years 11 months
5 years 4 months
2 years 6 months.

For these three ages, work out

(i) the range,

..................... years ...................... months [1]

(ii) the mean.

..................... years ...................... months [3]

(c) Jon has a watch that records the number of calories he uses when he goes for a walk.
He uses 0.05 calories for each step he takes.
He takes 1250 steps for every kilometre he walks.
One day he uses 300 calories on a walk.

Work out how far he has walked.

...................................... km [2]

(a) Complete this sequence of patterns by drawing Pattern 1 and Pattern 5.

Pattern 1    Pattern 2    Pattern 3    Pattern 4    Pattern 5
x        x           x
x        x           x        x
x       x        x       x
x     x      x      x      x x
x x x x x
[2]

(b) These are the first four terms of a sequence.
4 7 10 13
For this sequence, write down
(i) the next term,
.................................................. [1]
(ii) the rule for continuing the sequence.
.................................................................................... [1]

(c) The $n^{\text{th}}$ term of another sequence is $3n^2$.
Work out the first two terms of this sequence.
.................... and .................... [2]

(d) These are the first five terms of a different sequence.
7 15 23 31 39
Find the $n^{\text{th}}$ term of this sequence.
.................................................. [2]

(a) Simplify.
$$3y + 4y - y$$
................................................ [1]

(b) Solve.
(i) $$x + 6 = 20$$
$$x = ext{................................................}$$ [1]
(ii) $$\frac{x}{4} = 8$$
$$x = ext{................................................}$$ [1]
(iii) $$2(x - 3) = 14$$
$$x = ext{................................................}$$ [2]

(c) On the number line, show the inequality $$x \geq 4$$.

[1]

(d) Factorise.
$$5x + 20$$
................................................ [1]

(e) Multiply out the brackets and simplify.
$$(6x + 5)(x - 3)$$
................................................ [2]

(a) [Image_1: Triangle ABC with angles 48°, 84°, and angle B is 84°] What type of triangle is $ABC$?
Show how you decide.
[2]
(b) Work out the size of one exterior angle of a regular pentagon.
.................................................... [2]
(c) [Image_2: Diagram showing shape with angles 57°, 34° at B and C respectively, 126° at A and x° at D, with $ADE$ as a straight line]
In the diagram, $ADE$ is a straight line.
(i) Find the value of $x$.
$x = ....................................................$ [2]
(ii) Show that $ABCD$ is not a trapezium.
[2]

Here are three unbiased spinners made from regular polygons.

[Image_1: Spinner A with numbers 5, 3, 6, 5, 4; Spinner B with numbers 1, 6, 2, 4, 5, 3; Spinner C with numbers 1, 2, 3, 4, 5, 6]

(a) (i) For Spinner A work out the probability of getting 6. ........................................................ [1]

(ii) Spinner A is spun twice. Work out the probability of getting 6 each time. ........................................................ [2]

(b) Show that, of the three spinners, Spinner C has the greatest probability of getting 6 on one spin. [4]

(a) Amir has car insurance, home insurance and health insurance. In one year he spends a total of $5775 on insurance in the ratio car : home : health = 2 : 3 : 6.
Work out how much he spends on each type of insurance.

Car $.................................................
Home $.................................................
Health $................................................. [3]

(b) A company offers Samal health insurance for $850 when it is not bought online. The company offers a 15% reduction when this insurance is bought online.
Work out how much this insurance will cost Samal if she buys it online.

$................................................. [2]

(c) Terry’s car insurance increases from $900 to $1100.
Work out the percentage increase.

................................................. % [3]

(a) The line with equation $y = mx + 1$ passes through the point (3, 19).
Work out the value of $m$.

$m = \text{..........................................}$ [3]

(b) 
In the diagram, the line meets the $x$-axis at $A (-4, 0)$ and the $y$-axis at $B (0, 8)$.
(i) Find the coordinates of the mid-point of $AB$.
( $\text{......................}$ , $\text{......................}$ ) [2]
(ii) Find the equation of the line $AB$.
................................................ [3]

In this question, all lengths are in metres.



The diagram shows a shed in the shape of a prism.

(a) Use Pythagoras’ Theorem to show that $h = 1.5$.

[2]

(b) Use trigonometry to find the value of $x$.

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

(c) (i) The end of the shed is shaded.
Calculate this area.

$\text{..........................................} \text{ m}^2$ [2]

(ii) Work out the volume of the shed.
Give the units of your answer.

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

(a) (i) On the diagram, sketch the graph of $y = x^3 + 3x^2$ for $-3 \le x \le 2$. [2]
(ii) Find the coordinates of the local minimum.
($\text{....................... , .......................}$) [1]
(iii) Find the coordinates of the local maximum.
($\text{....................... , .......................}$) [1]
(b) On the diagram, sketch the graph of $y = 3x^2 - 5$ for $-3 \le x \le 2$. [2]
(c) Find the coordinates of the point of intersection of the graphs of $y = x^3 + 3x^2$ and $y = 3x^2 - 5$.
($\text{....................... , .......................}$) [2]