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Full Grade 10 test

Full Grade 10 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: 24Estimated time: 45 minutes

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Question 1out of 24

An angle bisector divides the opposite side into 6 cm and X cm. The adjacent sides are 5 cm and 25 cm. Find X.

3 cm

48 cm

21 cm

30 cm

23 cm

Question 2out of 24

The variance is 25. Find the standard deviation.

Question 3out of 24

How do sample size and sampling method affect reliability?

A smaller biased sample is always better

A larger random sample usually gives a more reliable estimate

Sample size never matters

Only the largest values should be sampled

Question 4out of 24

A 90 kg product contains 70% water. How many kilograms are dry matter?

34 kg

23 kg

27 kg

67 kg

71 kg

Question 5out of 24

Mix 30 g of a 30% solution and 50 g of an 80% solution. What is the concentration of the mixture?

91.44

71.38

78.58

61.25

49.73

Question 6out of 24

A box has 8 red and 8 blue balls. Two are drawn without replacement. What is the probability both are red?

7/15

8/16

7/30

Question 7out of 24

A triangle has area 56 cm² and semiperimeter 8 cm. Find its inradius.

7 cm

13 cm

10 cm

17 cm

4 cm

Question 8out of 24

Two triangle sides are 12 cm and 7 cm, and the sine of their included angle is 1.00. Find the area.

70.52

67.93

19.82

26.28

Question 9out of 24

Find the midpoint of the segment with endpoints (-7, 0) and (1, 5).

(11, -3)

(-3, 2.5)

(7, -6)

(3, -10)

(12, -16)

Question 10out of 24

Solve x² > 36.

x > -6

x < -6 arba x > 6

x < 6

-6 < x < 6

Question 11out of 24

The probability of A is 90%. What is the probability of its complement?

10 %

67 %

23 %

70 %

30 %

Question 12out of 24

When does order matter in a counting problem?

Order matters for a code, but not for choosing an unordered group

A code and a group are counted identically

Order always matters

Order never matters

Question 13out of 24

One equation is already y = x² + 1. Which method is most convenient to start with?

Multiply equations

Set right sides to zero

Only graphical estimation

Substitution, because one variable is isolated

Question 14out of 24

Three consecutive sides of a tangential quadrilateral are 6 cm, 9 cm and 10 cm. Find the fourth.

7 cm

35 cm

18 cm

6 cm

20 cm

Question 15out of 24

A fair coin is tossed 4 times. What is the probability of heads every time?

1/8

1/16

4/2

3/4

Question 16out of 24

Triangle sides are 6 cm, 8 cm and 10 cm. Find the angle between the first two sides.

60°

90°

45°

30°

Question 17out of 24

When a solution is diluted only with water, which quantity stays unchanged?

The amount of pure substance stays unchanged

Water amount stays unchanged

Total mass stays unchanged

Concentration stays unchanged

Question 18out of 24

Does (-1, -2) satisfy x + y = -4 and xy = 4?

Yes

Question 19out of 24

In a triangle, a = 8 cm, b = 7 cm and sin A = 0.60. Find sin B.

0.69

0.53

0.60

Question 20out of 24

The larger area is 44 cm² and the area ratio is 4. Find the smaller area.

6 cm²

26 cm²

5 cm²

11 cm²

27 cm²

Question 21out of 24

Divide 48 in the ratio 3 and 3. Find the first share.

Question 22out of 24

How are unit-circle point coordinates related to angle α?

The x-coordinate is cosine and the y-coordinate is sine

x is sine and y is cosine

Coordinates do not depend on the angle

Both coordinates are tangent

Question 23out of 24

Give the unit-circle point coordinates for angle 0°.

(−1; 0)

(0; 1)

(1; 0)

(0; −1)

Question 24out of 24

How many integers satisfy -5 < x < 2?

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Full Grade 10 mathematics test

This complete Grade 10 mathematics test helps students review the main school topics in one mixed set of tasks. Questions are selected from different tests for this grade, so each attempt can be different.

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Choose a 15, 30, 45 or 60 minute test. A longer duration creates a larger task set covering calculation, word problems, geometry and other topics studied in the grade.

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A full grade test is useful for independent checking, revision before a class assessment or mathematics exam preparation. Work at your own pace, review the result and try again: dynamic questions help students learn methods instead of memorising previous answers.

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