MYP year 2 maths practice

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Number systems, recurring decimals and irrational numbers2 questions

Here is a list of numbers: $\sqrt{16}$ , $3$ , $π$ , $\sqrt{6}$ , $3.04$ , $- 5$ .

Write down all the integers in the list. [3]

Decide for each number whether it is a whole number (positive, negative or zero).
Simplify first: for example a square root of a square number is a whole number.
The integers are: $\sqrt{16}$ , $3$ , $- 5$ .
Answer: $\sqrt{16}$ , $3$ , $- 5$

4 steps

Write $\frac{4}{5}$ as a decimal.

[2]

Divide 4 by 5 (or make the denominator a power of 10).
$\frac{4}{5}$ = $0.8$
Answer: $0.8$

3 steps

Fractions, percentages, ratio and proportion2 questions

Work out $\frac{4}{10}$ of 50.

[1]

Divide by 10: $50 \div 10 = 5$ .
Multiply by 4: $5 \times 4 = 20$ .
Answer: $20$

3 steps · 1 to fill in

Amira and Ben share 42 stickers in the ratio $2 : 5$ .

How many stickers does Amira get? [1]
How many more does Ben get than Amira? [1]

Total parts: $2 + 5 = 7$ .
One part: $42 \div 7 = 6$ .
Amira gets $2 \times 6 = 12$ ; Ben gets $5 \times 6 = 30$ .
Difference: 18.
Answers: (a) 12; (b) 18

5 steps · 1 to fill in

Powers, roots and standard form2 questions

Simplify $p^{10} \div p^{4}$ , writing your answer as a single power.

[1]

Same base, so subtract the powers: $p^{10} \div p^{4} = p^{6}$ .
Answer: $p^{6}$

2 steps

Work out $\sqrt{16}$ and $\sqrt[3]{27}$ .

[2]

$\sqrt{16} = 4$ because $4^{2} = 16$ .
$\sqrt[3]{27} = 3$ because $3^{3} = 27$ .
Answer: $4$ and $3$

3 steps · 1 to fill in

Expressions, expanding and factorising2 questions

Expand $4 (3 x - 2)$ .

[1]

Multiply each term in the bracket by 4: $4 \times 3 x = 12 x$ .
$4 \times (- 2) = - 8$
Answer: $12 x - 8$

3 steps · 1 to fill in

Factorise $3 x + 24$ fully.

[1]

The highest common factor of the terms is 3.
Divide each term by 3: $3 (x + 8)$ .
Answer: $3 (x + 8)$

3 steps

Linear equations, inequalities and formulae2 questions

Solve $9 x + 14 = 113$ .

[1]

Subtract 14 from both sides: $9 x = 99$ .
Divide by 9: $x = 11$ .
Answer: $x = 11$

3 steps · 1 to fill in

Solve $8 x + 1 = x + 50$ .

[2]

Collect the x terms on one side and the numbers on the other.
Divide to find $x = 7$ .
Answer: $x = 7$

3 steps · 1 to fill in

Sequences and general rules2 questions

A sequence starts $9, 12, 15, 18$ . 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 3.
Next terms: $18 + 3 = 21$ and $21 + 3 = 24$ .
Answer: $21, 24$ ; add 3 each time

3 steps · 1 to fill in

Find an expression for the $n$ th term of the sequence $18, 20, 22, 24, 26, \dots$ .

[2]

The common difference is 2, so the rule starts $2 n$ .
When $n = 1$ , $2 n = 2$ , so add 16: $2 n + 16$ .
Answer: $2 n + 16$

3 steps

Angles and polygons2 questions

Two angles of a triangle are $47^{\circ}$ and $97^{\circ}$ . Find the third angle.

[1]

The angles in a triangle add up to $180^{\circ}$ .
$180 - 47 - 97 = 36$
Answer: $36^{\circ}$

3 steps · 1 to fill in

Work out the size of each interior angle of a regular heptagon, to 1 decimal place.

[2]

Sum of interior angles: $(7 - 2) \times 180 = 900$ .
Regular, so all 7 are equal: $900 \div 7 = 128.6$ .
Answer: ${128.6}^{\circ}$

3 steps · 1 to fill in

Perimeter, area, surface area and volume2 questions

A circle has radius 9 cm. Work out its circumference, to 1 decimal place.

[1]

$C = 2 π r$ : $2 \times π \times 9$ ≈ 56.5
Answer: 56.5 cm

2 steps

A cuboid is 8 cm long, 4 cm wide and 3 cm high. Work out its volume and its surface area.

Volume [1]
Surface area [2]

Volume = length × width × height = $8 \times 4 \times 3 = 96$ .
Surface area: three pairs of rectangles, $2 (32 + 24 + 12) = 136$ .
Answers: (a) 96 cm³; (b) 136 cm²

3 steps · 1 to fill in

Pythagoras' theorem2 questions

The two sides next to the right angle of a triangle measure 12 cm and 16 cm. How long is the longest side?

[1]

$c^{2} = 12^{2} + 16^{2} = 400$
$c = \sqrt{400} = 20$
Answer: 20 cm

3 steps · 1 to fill in

A right-angled triangle has hypotenuse 15 cm and one shorter side 9 cm. Work out the other side.

[2]

$b^{2} = 15^{2} - 9^{2} = 144$
$b = 12$
Answer: 12 cm

3 steps · 1 to fill in

Transformations, congruence and similarity2 questions

Reflect the point $P (1, 1)$ in the y-axis. Where does it end up?

[1]

Reflecting in the y-axis keeps y and changes the sign of x.
Answer: $(- 1, 1)$

2 steps

Triangle T has corners at $(3, 2)$ , $(1, 2)$ , $(1, 4)$ . Enlarge T by a scale factor of 3 about the origin and give the corners of the new triangle.

[2]

Multiply every coordinate by 3.
Answer: $(9, 6)$ , $(3, 6)$ , $(3, 12)$

2 steps

Collecting data, sampling and bias2 questions

A class survey asked 21 students one question. The frequencies are: football 7, swimming 2, dance ?, chess 6.

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

The frequencies add up to the number of students: $21 - 15 = 6$ .
Answers: (a) 6; (b) $\frac{1}{3}$

2 steps

In a survey of 45 people, 17 chose cats. In a pie chart of the results, what angle is the sector for cats?

[2]

Each person gets $360 \div 45$ .
$\frac{17}{45} \times 360 = 136^{\circ}$
Answer: $136^{\circ}$

3 steps · 1 to fill in

Averages and spread2 questions

Here are some data: $4, 14, 3, 3, 5$ . Find the mean, median, mode and range.

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

Mean: add them up and divide by 5: $29 \div 5 = 5.8$ .
Median: put them in order (3, 3, 4, 5, 14) and take the middle.
Range = largest − smallest.
Answers: (a) $5.8$ ; (b) $4$ ; (c) $3$ ; (d) $11$

4 steps

The mean of 6 numbers is 14. 5 of them are $18, 13, 19, 20, 11$ . Find the missing number.

[2]

Total of all 6 numbers: $14 \times 6 = 84$ .
Subtract the ones you know: $84 - 81 = 3$ .
Answer: $3$

3 steps · 1 to fill in

Probability of single and combined events2 questions

There are 8 red, 4 blue, 9 green counters in a bag. Without looking, Zoe pulls one out.

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

There are 21 counters altogether and 4 are blue.
P(not A) = 1 − P(A).
Answers: (a) $\frac{4}{21}$ ; (b) $\frac{17}{21}$

3 steps

The probability that a spinner lands on blue is $0.3$ . It is spun 20 times. How many times would you expect it to land on blue?

[1]

Expected frequency = probability × number of trials: $0.3 \times 20 = 6$ .
Answer: 6

2 steps

Sets and Venn diagrams2 questions

$A$ is the set of multiples of 2 and $B$ the set of multiples of 7, using the whole numbers from 1 to 21.

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

$A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}$ , $B = {7, 14, 21}$
Intersection: in both. Union: in either (count each number once).
Answers: (a) ${14}$ ; (b) 12

3 steps

In a class of 26 students, 13 like cats, 20 like dogs and 8 do both.

How many students like cats only? [1]
How many students do neither? [2]

Fill in the middle of the Venn diagram first: 8.
Then like cats only: $13 - 8 = 5$ ; like dogs only: $20 - 8 = 12$ .
Neither: $26 - 5 - 12 - 8 = 1$ .
Answers: (a) 5; (b) 1

4 steps · 1 to fill in

Algorithms and flowcharts2 questions

Follow these instructions. Start with 8. Multiply by 2, then subtract 3. Repeat with the answer until you have done this 4 times.

What number do you finish with? [2]

The numbers are 13, 23, 43, 83.
Answer: 83

2 steps

A flowchart says: start with 20. 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: 7 steps

2 steps

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