MYP year 1 maths practice

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Number systems, recurring decimals and irrational numbers2 questions

Here is a list of numbers: $0.75$ , $- 9$ , $\frac{1}{7}$ , $14$ .

Write down all the integers in the list. [2]

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: $- 9$ , $14$ .
Answer: $- 9$ , $14$

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 $\frac{3}{8}$ of 24.

[1]

Divide by 8: $24 \div 8 = 3$ .
Multiply by 3: $3 \times 3 = 9$ .
Answer: $9$

3 steps · 1 to fill in

Elif and Femi share 44 stickers in the ratio $1 : 3$ .

How many stickers does Elif get? [1]
How many more does Femi get than Elif? [1]

Total parts: $1 + 3 = 4$ .
One part: $44 \div 4 = 11$ .
Elif gets $1 \times 11 = 11$ ; Femi gets $3 \times 11 = 33$ .
Difference: 22.
Answers: (a) 11; (b) 22

5 steps · 1 to fill in

Powers, roots and standard form2 questions

Work out $6^{2}$ and $4^{3}$ .

[1]

$6^{2} = 6 \times 6 = 36$
$4^{3} = 4 \times 4 \times 4 = 64$
Answer: $36$ and $64$

3 steps · 1 to fill in

Work out $\sqrt{36}$ and $\sqrt[3]{27}$ .

[2]

$\sqrt{36} = 6$ because $6^{2} = 36$ .
$\sqrt[3]{27} = 3$ because $3^{3} = 27$ .
Answer: $6$ and $3$

3 steps · 1 to fill in

Expressions, expanding and factorising2 questions

Simplify $3 x + 7 + 5 x + 1$ by collecting like terms.

[1]

Collect the x terms: $3 x + 5 x = 8 x$ .
Collect the numbers: $7 + 1 = 8$ .
Answer: $8 x + 8$

3 steps · 1 to fill in

Factorise $35 x + 28$ fully.

[1]

The highest common factor of the terms is 7.
Divide each term by 7: $7 (5 x + 4)$ .
Answer: $7 (5 x + 4)$

3 steps

Linear equations, inequalities and formulae2 questions

Solve $4 x + 1 = 41$ .

[1]

Subtract 1 from both sides: $4 x = 40$ .
Divide by 4: $x = 10$ .
Answer: $x = 10$

3 steps · 1 to fill in

Solve $7 x + 3 = 2 x + 33$ .

[2]

Collect the x terms on one side and the numbers on the other.
Divide to find $x = 6$ .
Answer: $x = 6$

3 steps · 1 to fill in

Sequences and general rules2 questions

A sequence starts $5, 9, 13, 17$ . 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 4.
Next terms: $17 + 4 = 21$ and $21 + 4 = 25$ .
Answer: $21, 25$ ; add 4 each time

3 steps · 1 to fill in

Find an expression for the $n$ th term of the sequence $13, 16, 19, 22, 25, \dots$ .

[2]

The common difference is 3, so the rule starts $3 n$ .
When $n = 1$ , $3 n = 3$ , so add 10: $3 n + 10$ .
Answer: $3 n + 10$

3 steps

Angles and polygons2 questions

Three angles lie on a straight line. Two of them are $25^{\circ}$ and $100^{\circ}$ . Find the third angle.

[1]

Angles on a straight line add up to $180^{\circ}$ .
$180 - 25 - 100 = 55$
Answer: $55^{\circ}$

3 steps · 1 to fill in

Work out the sum of the interior angles of a heptagon.

[1]

Split it into 5 triangles from one corner.
$(7 - 2) \times 180 = 900$
Answer: $900^{\circ}$

3 steps · 1 to fill in

Perimeter, area, surface area and volume2 questions

Find the area enclosed by a parallelogram whose base is 5 cm long and whose perpendicular height is 12 cm.

[1]

Area of a parallelogram = base × perpendicular height.
$5 \times 12 = 60$
Answer: 60 cm²

3 steps · 1 to fill in

A cuboid is 15 cm long, 6 cm wide and 10 cm high. Work out its volume.

Volume [1]

Volume = length × width × height = $15 \times 6 \times 10 = 900$ .
Answer: 900 cm³

2 steps

Pythagoras' theorem2 questions

The two sides next to the right angle of a triangle measure 9 cm and 12 cm. How long is the longest side?

[1]

$c^{2} = 9^{2} + 12^{2} = 225$
$c = \sqrt{225} = 15$
Answer: 15 cm

3 steps · 1 to fill in

A right-angled triangle has hypotenuse 25 cm and one shorter side 7 cm. Work out the other side.

[2]

$b^{2} = 25^{2} - 7^{2} = 576$
$b = 24$
Answer: 24 cm

3 steps · 1 to fill in

Transformations, congruence and similarity2 questions

Reflect the point $P (2, - 5)$ in the y-axis. Where does it end up?

[1]

Reflecting in the y-axis keeps y and changes the sign of x.
Answer: $(- 2, - 5)$

2 steps

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

[2]

Multiply every coordinate by 2.
Answer: $(4, 4)$ , $(4, 8)$ , $(2, 4)$

2 steps

Collecting data, sampling and bias2 questions

A class survey asked 30 students one question. The frequencies are: football 5, swimming 15, dance ?, chess 2.

Find the missing frequency. [1]

The frequencies add up to the number of students: $30 - 22 = 8$ .
Answer: 8

2 steps

In a survey of 12 people, 4 chose fish. In a pie chart of the results, what angle is the sector for fish?

[2]

Each person gets $360 \div 12$ .
$\frac{4}{12} \times 360 = 120^{\circ}$
Answer: $120^{\circ}$

3 steps · 1 to fill in

Averages and spread2 questions

Here are some data: $12, 12, 2, 10, 13$ . Find the mean, median, mode and range.

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

Mean: add them up and divide by 5: $49 \div 5 = 9.8$ .
Median: put them in order (2, 10, 12, 12, 13) and take the middle.
Range = largest − smallest.
Answers: (a) $9.8$ ; (b) $12$ ; (c) $12$ ; (d) $11$

4 steps

The mean of 7 numbers is 11. 6 of them are $13, 6, 15, 10, 5, 16$ . Find the missing number.

[2]

Total of all 7 numbers: $11 \times 7 = 77$ .
Subtract the ones you know: $77 - 65 = 12$ .
Answer: $12$

3 steps · 1 to fill in

Probability of single and combined events2 questions

There are 6 yellow, 5 purple, 4 white counters in a bag. Without looking, Zoe pulls one out.

Find the chance that Zoe's counter is white. [1]

There are 15 counters altogether and 4 are white.
P(not A) = 1 − P(A).
Answer: $\frac{4}{15}$

3 steps

The probability that a spinner lands on blue is $\frac{1}{4}$ . It is spun 80 times. How many times would you expect it to land on blue?

[1]

Expected frequency = probability × number of trials: $0.25 \times 80 = 20$ .
Answer: 20

2 steps

Sets and Venn diagrams2 questions

$A$ is the set of multiples of 2 and $B$ the set of multiples of 4, using the whole numbers from 1 to 15.

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

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

3 steps

In a class of 30 students, 8 study French, 10 study Spanish and 2 do both.

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

Fill in the middle of the Venn diagram first: 2.
Then study French only: $8 - 2 = 6$ ; study Spanish only: $10 - 2 = 8$ .
Neither: $30 - 6 - 8 - 2 = 14$ .
Answers: (a) 6; (b) 14

4 steps · 1 to fill in

Algorithms and flowcharts2 questions

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

What number do you finish with? [2]

The numbers are 0, -4, -12.
Answer: -12

2 steps

A flowchart says: start with 27. 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: 111 steps

2 steps

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