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Full Grade 7 test

Full Grade 7 mathematics test with mixed topics, dynamically selected questions and a choice of duration. Practise before an assessment or review the whole course at your own pace.

Questions: 32Estimated time: 60 minutes

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Question 1out of 32

Three angles of a quadrilateral are 93°, 92° and 112°. Find the fourth angle.

63°

81°

87°

92°

35°

Question 2out of 32

Simplify: (2³)².

2⁵

2⁶

2¹

4⁶

Question 3out of 32

Write 300 000 in scientific notation. Note: the first factor must be at least 1 and less than 10.

30 · 10⁵

10 · 3⁵

3 · 10⁵

3 · 10⁴

Question 4out of 32

An item cost 1000 €. Its price increased by 10% in each of two consecutive years. What was the price after the second increase?

1100 €

1200 €

1000 €

1210 €

The price increases twice in succession, so the percentage is not calculated from the original price both times. The second increase is calculated from the price obtained after the first year.

Convert the percentage to a multiplier: 1 + p/100.
Multiply the original price by this multiplier to find the price after the first year.
Multiply that result by the same multiplier once more.

Formula: final price = original price × (1 + p/100)².

Question 5out of 32

Which pair of ordered pairs can belong to the same inverse-proportion relationship?

(2; 90) and (3; 91)

(2; 90) and (4; 180)

(2; 90) and (4; 45)

(2; 90) and (1; 45)

Two ordered pairs can belong to the same inverse-proportion relationship only when the product of x and y is equal in both pairs.

Multiply x and y in the first pair.
Do the same for the second pair.
Compare the two products.

Rule: choose the option for which x₁ × y₁ = x₂ × y₂. If the products are different, the pairs do not belong to the same relationship.

Question 6out of 32

A school wants to learn the opinion of all its students about the cafeteria. Which sampling method would be most representative?

Survey only seventh-grade students

Survey only the basketball team

Ask only the first ten students entering school

Randomly select students from every grade

Question 7out of 32

A closed cylinder has radius 8 cm and height 6 cm. Calculate its total surface area using π ≈ 3.14.

703.36 cm²

697.13 cm²

716.74 cm²

709.55 cm²

695.07 cm²

Question 8out of 32

Calculate using the correct order of operations: 4² + 5.

16384

Question 9out of 32

Same-side interior angles are (x + 4)° and x°. Their total measure is 180°. Find x.

Question 10out of 32

Simplify: 4⁵ ÷ 4².

16³

1³

4³

4⁷

Question 11out of 32

One angle of an isosceles trapezoid is 36°. Find the angle on the same leg.

115°

124°

136°

144°

142°

Question 12out of 32

A rate increased from 27% to 29%. By how many percentage points did it increase?

7 percentage points

2 percent

2 percentage points

29 percentage points

Question 13out of 32

After a 20% discount, an item costs 208 €. What was its original price?

228 €

249.6 €

41.6 €

260 €

After a 20% discount, the item costs not 100% but 100 − 20% of its original price.

Find the percentage of the price that remains: 100 − 20.
Divide the current price 208 € by that percentage.
Multiply the result by 100.

Formula: original price = 208 € × 100 ÷ (100 − 20).

Question 14out of 32

A semicircle has radius 6 cm. Calculate the area of the semicircle using π ≈ 3.14.

56.52 cm²

57.72 cm²

51.5 cm²

61.79 cm²

49.22 cm²

Question 15out of 32

A sector of a pie chart has angle 54°. What percentage of all data does it represent?

96 %

54 %

15 %

72 %

40 %

Question 16out of 32

The radius is 8 cm. Calculate the circumference using π ≈ 3.14.

52.14 cm

53.6 cm

50.24 cm

50.35 cm

51.2 cm

Question 17out of 32

One same-side interior angle is 111°. Find the other same-side interior angle.

63°

98°

56°

78°

69°

Question 18out of 32

A student is saving for a purchase costing 1400 €. The student has already saved 27% of the required amount. How much more is needed?

1400 €

1778 €

378 €

1022 €

Question 19out of 32

A transversal crosses two lines. Corresponding angles are 47° and 47°. What can be concluded?

The lines are perpendicular

The lines are parallel

The lines must intersect at 45°

No conclusion is possible

Question 20out of 32

One angle of a parallelogram is 130°. Find an adjacent angle.

38°

27°

50°

37°

23°

Question 21out of 32

What does the height mean in the trapezoid area formula?

Either sloping side

Half the perimeter

The perpendicular distance between the bases

The longer base

Question 22out of 32

If speed over the same distance becomes 3 times greater, how does travel time change? Choose the statement that uses “times” precisely.

3 times shorter

3 hours shorter

3 times longer

It does not change

Question 23out of 32

The quantities x and y are inversely proportional. When x = 4, y = 12. Find y when x = 8.

When x and y are inversely proportional, their product is always the same: x × y = k.

Multiply the original x- and y-values to find the constant product k.
To find the new y-value, divide k by the new x-value.
Choose the result that satisfies y = k ÷ x.

As x increases, y must decrease by the corresponding factor so that their product does not change.

Question 24out of 32

If every length of similar solids is multiplied by 2, by what factor does the volume increase?

8 times greater

2 times greater

4 times greater

It stays unchanged

Question 25out of 32

A ticket costs €3. A student has at most €110. What is the greatest number of tickets the student can buy?

Question 26out of 32

The price was 700 €. It was first increased by 10% and then decreased by 10%. What is the final price?

700 €

770 €

693 €

630 €

Question 27out of 32

A parallelogram has base 4 cm and height 12 cm. Calculate its area.

77 cm²

22 cm²

49 cm²

48 cm²

78 cm²

Question 28out of 32

Point A(2, -6) is rotated 180° about the origin. Find its new coordinates.

(9, -10)

(-5, -10)

(-9, 11)

(-2, 6)

(-6, 11)

Question 29out of 32

Does -4 belong to the interval (-5, 2]?

Yes

Question 30out of 32

Which statement about corresponding angles formed by parallel lines is always true?

Their measures are equal

Their sum is always 90°

Their sum is always 180°

One angle is twice the other

Question 31out of 32

A survey included 300 students. In the pie chart, 50% chose answer A. How many students chose A?

133

137

158

150

120

Question 32out of 32

A rhombus has side length 9 cm. Calculate its perimeter.

52 cm

32 cm

36 cm

47 cm

27 cm

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Full Grade 7 mathematics test

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