Year 7 maths test: free practice questions with answers

Year 7 sample test

10 questions, one from each of 10 topics. Work them out on paper, then open each answer to mark it.

1. Question 1Angles in triangles and quadrilaterals

   A triangle has interior angles of $47°$ and $86°$. Find the third interior angle.

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   Answer:

   $47°$

   Key idea: The interior angles of any triangle add to $180°$.

   1. Write the angle sum equation: $47 + 86 + x = 180$
   2. Add the known angles: $133 + x = 180$
   3. Subtract $133$ from both sides: $x = 180 - 133 = 47$

   Answer: The third angle is $47°$.

   More angles in triangles and quadrilaterals practice →

2. Question 2Probability

   A standard six-sided die has faces numbered 1 to 6. List the sample space for one roll of the die, then find the probability of rolling a number greater than 4. Write your answer as a fraction, a decimal and a percentage.

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   Answer:

   $\frac{1}{3}$, approximately $0.\overline{3}$, approximately $33.3\%$

   Key idea: The sample space is the list of all possible outcomes. Probability = $\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

   1. List the sample space: $\{1, 2, 3, 4, 5, 6\}$. There are 6 equally likely outcomes.
   2. Identify the favourable outcomes (greater than 4): $\{5, 6\}$. There are 2 favourable outcomes.
   3. Write the probability as a fraction: $P(\text{greater than 4}) = \frac{2}{6} = \frac{1}{3}$
   4. Convert to a decimal: $\frac{1}{3} \approx 0.\overline{3}$
   5. Convert to a percentage: $\frac{1}{3} \times 100 \approx 33.3\%$

   Answer: $\dfrac{1}{3}$, approximately $0.\overline{3}$, approximately $33.3\%$

   More probability practice →

3. Question 3Fraction operations

   Calculate $\dfrac{5}{6} \div \dfrac{1}{4}$. Give your answer as a decimal correct to 2 decimal places.

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   Answer:

   $3.33$

   Key idea: Dividing by a fraction is the same as multiplying by its reciprocal.

   1. Keep the first fraction: $\dfrac{5}{6}$
   2. Change $\div$ to $\times$ and flip the second fraction: $\dfrac{5}{6} \times \dfrac{4}{1}$
   3. Multiply numerators and denominators: $\dfrac{5 \times 4}{6 \times 1} = \dfrac{20}{6}$
   4. Simplify: $\dfrac{20}{6} = \dfrac{10}{3}$
   5. Convert to a decimal: $10 \div 3 = 3.3333\ldots \approx 3.33$

   Answer: $3.33$

   More fraction operations practice →

4. Question 4Statistics

   Find the median, mode and range of this data set: $4, 7, 2, 7, 9, 1, 4, 7, 3.$

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   Answer:

   Median $= 4$, Mode $= 7$, Range $= 8$

   Key idea: Sort the data first, then apply each definition.

   1. Sort the values in ascending order: $1, 2, 3, 4, 4, 7, 7, 7, 9$
   2. Median: There are $9$ values (odd count), so the median is the $5$th value: $\text{Median} = 4.$
   3. Mode: The value that appears most often is $7$ (appears $3$ times): $\text{Mode} = 7.$
   4. Range: $\text{Range} = 9 - 1 = 8$

   Answer: Median $= 4$, Mode $= 7$, Range $= 8.$

   More statistics practice →

5. Question 5Tables of values and plotting points

   Mia is saving money. She starts with $5 and earns $3 for each chore she completes. The rule for her total savings $y$ (in dollars) after completing $x$ chores is $y = 3x + 5$. Complete the table of values for $x = 0, 1, 2, 3, 4$, write each result as an ordered pair, and describe how her savings change.

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   Answer:

   $(0, 5),\ (1, 8),\ (2, 11),\ (3, 14),\ (4, 17)$; savings increase by $3 per chore.

   Key idea: Substitute each $x$ value into $y = 3x + 5$ to find Mia's savings after that many chores.

   1. $x = 0$: $y = 3(0) + 5 = 5$, giving $(0, 5)$
   2. $x = 1$: $y = 3(1) + 5 = 8$, giving $(1, 8)$
   3. $x = 2$: $y = 3(2) + 5 = 11$, giving $(2, 11)$
   4. $x = 3$: $y = 3(3) + 5 = 14$, giving $(3, 14)$
   5. $x = 4$: $y = 3(4) + 5 = 17$, giving $(4, 17)$
   6. Mia's savings increase by $3 for each extra chore completed.

   Answer: $(0, 5),\ (1, 8),\ (2, 11),\ (3, 14),\ (4, 17)$; savings increase by $3 per chore.

   More tables of values and plotting points practice →

6. Question 6Circles

   Aisha rides her bike to school. Each wheel on her bike has a diameter of $60$ cm. The school is $1{,}884$ m away. How many full rotations does each wheel make on the trip to school? Use $\pi \approx 3.14$.

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   Answer:

   $1{,}000$ rotations

   Key idea: Each time a wheel makes one full rotation, it travels a distance equal to its circumference. Divide the total distance by the circumference to find the number of rotations.

   1. Find the circumference of the wheel:
      $C = \pi d = 3.14 \times 60 = 188.4 \text{ cm}$
   2. Convert the distance to school into centimetres:
      $1{,}884 \text{ m} = 188{,}400 \text{ cm}$
   3. Divide the total distance by the circumference:
      $\text{Rotations} = \frac{188{,}400}{188.4} = 1{,}000$

   Answer: Each wheel makes $1{,}000$ full rotations.

   More circles practice →

7. Question 7Angles

   Two parallel lines are crossed by a transversal. One co-interior angle is $74°$. Find the other co-interior angle, giving a reason.

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   Answer:

   $106°$

   Key idea: Co-interior angles (also called C-angles) are between the parallel lines on the same side of the transversal, and they add to $180°$.

   1. Write the co-interior angle relationship: $74° + x = 180°$
   2. Solve for $x$: $x = 180° - 74° = 106°$
   3. State the reason: co-interior angles on parallel lines are supplementary.

   Answer: The other co-interior angle is $106°$.

   More angles practice →

8. Question 8Area and perimeter

   A rectangular room is 7 m long and 4 m wide. What is the area of the room in square metres?

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   Answer:

   $28 \text{ m}^2$

   Key idea: Area of a rectangle = length × width

   1. Write the formula: $A = l \times w$
   2. Substitute the values: $A = 7 \times 4$
   3. Calculate: $A = 28$

   Answer: $28 \text{ m}^2$

   More area and perimeter practice →

9. Question 9Powers and prime factors

   Express $72$ as a product of prime factors using exponent notation.

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   Answer:

   $72 = 2^3 \times 3^2$

   Key idea: A factor tree splits a number into factor pairs, working down until every branch ends in a prime number. Collect repeated primes using exponent notation.

   1. Split $72$ into $8 \times 9$.
   2. Split $8$ into $2 \times 4$, then $4$ into $2 \times 2$. So $8 = 2 \times 2 \times 2$.
   3. Split $9$ into $3 \times 3$.
   4. Collect all prime factors: 2, 2, 2, 3, 3.
   5. Write using exponents:
      $72 = 2^3 \times 3^2$ Answer: $72 = 2^3 \times 3^2$

   More powers and prime factors practice →

10. Question 10Ratios

    A recipe uses flour and sugar in the ratio $3:2$. If you use $360\text{ g}$ of flour, how many grams of sugar do you need?

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    Answer:

    $240$

    Key idea: Scale the ratio so that the flour part equals 360 g.

    1. The ratio of flour to sugar is $3:2$.
    2. Find the value of one part: $360 \div 3 = 120$ g per part.
    3. Sugar is $2$ parts: $2 \times 120 = 240$ g.
    4. Check: flour to sugar is $360:240 = 3:2$ ✓

    Answer: $240$ g

    More ratios practice →