MYP year 3 maths practice

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Number systems, recurring decimals and irrational numbers2 questions

Here is a list of numbers: $- 3$ , $\sqrt{49}$ , $3.04$ , $\frac{4}{5}$ , $π$ , $\sqrt{6}$ .

Write down all the rational numbers in the list. [3]

Decide for each number whether it is a fraction of two integers.
Simplify first: for example a square root of a square number is a whole number.
The rational numbers are: $- 3$ , $\sqrt{49}$ , $3.04$ , $\frac{4}{5}$ .
Answer: $- 3$ , $\sqrt{49}$ , $3.04$ , $\frac{4}{5}$

4 steps

Write $\frac{3}{4}$ as a decimal.

[2]

Divide 3 by 4 (or make the denominator a power of 10).
$\frac{3}{4}$ = $0.75$
Answer: $0.75$

3 steps

Fractions, percentages, ratio and proportion2 questions

Work out 60% of 360.

[1]

60% means 60 out of 100, so multiply by $\frac{60}{100}$ .
$\frac{60}{100} \times 360 = 216$
Answer: $216$

3 steps · 1 to fill in

Gita and Hugo share 231 minutes of screen time in the ratio $4 : 3$ .

How many minutes of screen time does Gita get? [1]
How many more does Gita get than Hugo? [1]

Total parts: $4 + 3 = 7$ .
One part: $231 \div 7 = 33$ .
Gita gets $4 \times 33 = 132$ ; Hugo gets $3 \times 33 = 99$ .
Difference: 33.
Answers: (a) 132; (b) 33

5 steps · 1 to fill in

Powers, roots and standard form2 questions

Simplify $a^{11} \div a^{6}$ , writing your answer as a single power.

[1]

Same base, so subtract the powers: $a^{11} \div a^{6} = a^{5}$ .
Answer: $a^{5}$

2 steps

Write $0.0511$ in standard form.

[1]

Move the decimal point so the number is between 1 and 10: 5.11.
The point moved 2 places right, so the power is -2: $5.11 \times 10^{- 2}$ .
Answer: $5.11 \times 10^{- 2}$

3 steps

Expressions, expanding and factorising2 questions

Expand $9 (8 x - 2)$ .

[1]

Multiply each term in the bracket by 9: $9 \times 8 x = 72 x$ .
$9 \times (- 2) = - 18$
Answer: $72 x - 18$

3 steps · 1 to fill in

Factorise $42 x - 7$ fully.

[1]

The highest common factor of the terms is 7.
Divide each term by 7: $7 (6 x - 1)$ .
Answer: $7 (6 x - 1)$

3 steps

Linear equations, inequalities and formulae2 questions

Solve $5 x + 9 = 34$ .

[1]

Subtract 9 from both sides: $5 x = 25$ .
Divide by 5: $x = 5$ .
Answer: $x = 5$

3 steps · 1 to fill in

Solve $2 (6 x + 2) = 7 x - 6$ .

[2]

Expand the bracket first. Collect the x terms on one side and the numbers on the other.
Divide to find $x = - 2$ .
Answer: $x = - 2$

3 steps · 1 to fill in

Sequences and general rules2 questions

A sequence starts $19, 18, 17, 16$ . Continue it for two more terms and describe, in words, how to get from one term to the next.

[2]

The difference between terms is -1.
Next terms: $16 - 1 = 15$ and $15 - 1 = 14$ .
Answer: $15, 14$ ; subtract 1 each time

3 steps · 1 to fill in

Find an expression for the $n$ th term of the sequence $19, 15, 11, 7, 3, \dots$ .

[2]

The common difference is -4, so the rule starts $- 4 n$ .
When $n = 1$ , $- 4 n = - 4$ , so add 23: $- 4 n + 23$ .
Answer: $- 4 n + 23$

3 steps

Angles and polygons2 questions

Four angles meet at a point. Three of them are $99^{\circ}$ , $106^{\circ}$ and $65^{\circ}$ . Find the fourth angle.

[1]

Angles around a point add up to $360^{\circ}$ .
$360 - 99 - 106 - 65 = 90$
Answer: $90^{\circ}$

3 steps · 1 to fill in

Work out the size of each interior angle of a regular hexagon.

[2]

Sum of interior angles: $(6 - 2) \times 180 = 720$ .
Regular, so all 6 are equal: $720 \div 6 = 120$ .
Answer: $120^{\circ}$

3 steps · 1 to fill in

Perimeter, area, surface area and volume2 questions

A circle has radius 7 cm. Work out its area, to 1 decimal place.

[1]

$A = π r^{2}$ : $π \times 7^{2}$ ≈ 153.9
Answer: 153.9 cm²

2 steps

A cylinder has radius 12 cm and height 12 cm. Work out its volume, to 3 significant figures.

[2]

$V = π r^{2} h = π \times 12^{2} \times 12 \approx 5430$
Answer: 5430 cm³

2 steps

Pythagoras' theorem2 questions

The two sides next to the right angle of a triangle measure 9 cm and 3 cm. How long is the longest side, to 1 decimal place?

[1]

$c^{2} = 9^{2} + 3^{2} = 90$
$c = \sqrt{90} \approx 9.5$
Answer: 9.5 cm

3 steps

A right-angled triangle has hypotenuse 11 cm and one shorter side 6 cm. Work out the length of the third side, to 1 decimal place.

[2]

The hypotenuse is the longest side, so subtract: $11^{2} - 6^{2} = 85$ .
$\sqrt{85} \approx 9.2$
Answer: 9.2 cm

3 steps

Transformations, congruence and similarity2 questions

Move the point $P (- 2, - 4)$ by the translation vector $(\begin{matrix} - 2 \\ - 1 \end{matrix})$ . Where does it end up?

[1]

Add -2 to x and -1 to y.
Answer: $(- 4, - 5)$

2 steps

Triangle T has corners at $(1, 3)$ , $(1, 4)$ , $(2, 2)$ . Turn T through $90^{\circ}$ anticlockwise about the origin and give the corners of the new triangle.

[2]

A quarter turn anticlockwise about the origin sends $(x, y)$ to $(- y, x)$ .
Answer: $(- 3, 1)$ , $(- 4, 1)$ , $(- 2, 2)$

2 steps

Collecting data, sampling and bias2 questions

A class survey asked 31 students one question. The frequencies are: apple 9, banana 8, orange 4, grapes ?.

Find the missing frequency. [1]
What fraction of the students chose grapes? Simplify it. [1]

The frequencies add up to the number of students: $31 - 21 = 10$ .
Answers: (a) 10; (b) $\frac{10}{31}$

2 steps

In a survey of 24 people, 8 chose art. In a pie chart of the results, what angle is the sector for art?

[2]

Each person gets $360 \div 24$ .
$\frac{8}{24} \times 360 = 120^{\circ}$
Answer: $120^{\circ}$

3 steps · 1 to fill in

Averages and spread2 questions

Here are some data: $36, 20, 12, 31, 20$ . Find the mean, median, mode and range.

Mean [1]
Median [1]
Mode [1]
Range [1]

Mean: add them up and divide by 5: $119 \div 5 = 23.8$ .
Median: put them in order (12, 20, 20, 31, 36) and take the middle.
Range = largest − smallest.
Answers: (a) $23.8$ ; (b) $20$ ; (c) $20$ ; (d) $24$

4 steps

The mean of 8 numbers is 12. 7 of them are $8, 17, 6, 20, 10, 13, 5$ . Find the missing number.

[2]

Total of all 8 numbers: $12 \times 8 = 96$ .
Subtract the ones you know: $96 - 79 = 17$ .
Answer: $17$

3 steps · 1 to fill in

Probability of single and combined events2 questions

There are 5 yellow, 1 purple, 5 white counters in a bag. Without looking, Zoe pulls one out.

Find the chance that Zoe's counter is yellow. [1]
Find the chance that it is NOT yellow. [1]

There are 11 counters altogether and 5 are yellow.
P(not A) = 1 − P(A).
Answers: (a) $\frac{5}{11}$ ; (b) $\frac{6}{11}$

3 steps

The probability that a spinner lands on blue is $0.2$ . It is spun 200 times. How many times would you expect it to land on blue?

[1]

Expected frequency = probability × number of trials: $0.2 \times 200 = 40$ .
Answer: 40

2 steps

Sets and Venn diagrams2 questions

$A$ is the set of multiples of 3 and $B$ the set of multiples of 7, using the whole numbers from 1 to 17.

List the elements of $A \cap B$ . [2]
How many elements are in $A \cup B$ ? [2]

$A = {3, 6, 9, 12, 15}$ , $B = {7, 14}$
Intersection: in both. Union: in either (count each number once).
Answers: (a) $\emptyset$ ; (b) 7

3 steps

In a class of 26 students, 7 study French, 10 study Spanish and 3 do both.

How many students study French only? [1]
How many students do neither? [2]

Fill in the middle of the Venn diagram first: 3.
Then study French only: $7 - 3 = 4$ ; study Spanish only: $10 - 3 = 7$ .
Neither: $26 - 4 - 7 - 3 = 12$ .
Answers: (a) 4; (b) 12

4 steps · 1 to fill in

Algorithms and flowcharts2 questions

Follow these instructions. Start with 6. Multiply by 2, then subtract 2. Repeat with the answer until you have done this 3 times.

What number do you finish with? [2]

The numbers are 10, 18, 34.
Answer: 34

2 steps

A flowchart says: start with 23. If the number is even, halve it; if it is odd, multiply it by 3 and add 1. Stop when you reach 1. How many steps does it take?

[2]

Write each number down as you go and count the steps until you reach 1.
Answer: 15 steps

2 steps

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