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Full Grade 8 test

Full Grade 8 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: 31Estimated time: 60 minutes

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Question 1out of 31

A total of 20 type A and B tickets were sold. An A ticket costs €2, a B ticket costs €3, and revenue was €49. How many A and B tickets were sold? Give A first.

(9, 11)

(12, 9)

(-11, 9)

(11, 9)

(11, -9)

(11, 10)

Question 2out of 31

Evaluate P(x) = 1x² + (-3) when x = 0.

-10

-3

Question 3out of 31

Which interval has the greatest frequency?

0–10

10–20

20–30

30–40

10–20

20–30

0–10

30–40

Question 4out of 31

How many solutions does the system 5x + 2y = 7 and 15x + 6y = 21 have?

Infinitely many solutions

One solution

Exactly two solutions

No solutions

Question 5out of 31

A triangle midline is 20 cm. Find the parallel side length.

37 cm

36 cm

25 cm

40 cm

2 cm

Question 6out of 31

A rectangular prism measures 16 cm, 16 cm and 28 cm. Find its space diagonal.

36 cm

26 cm

49 cm

48 cm

21 cm

Question 7out of 31

The solution of a system is written as the pair (12, 10). What exactly does this mean?

The pair gives the number of equations

x and y must be equal

Both equations are true for this pair

Only the first equation must be true

Question 8out of 31

Calculate the magnitude of vector (8, 15).

Question 9out of 31

What is the degree of the monomial 7x⁷?

Question 10out of 31

Which statement about number sets is always true?

Every integer is rational

Every rational number is an integer

Every real number is rational

No natural number is an integer

Question 11out of 31

A cylinder’s axial section is a rectangle of diameter based on radius 10 cm and height 48 cm. Find its diagonal.

21 cm

52 cm

35 cm

34 cm

26 cm

Question 12out of 31

Solve the system: x + y = 0 and x − y = -12.

(6, -6)

(-6, 7)

(6, 6)

(-6, -6)

(-5, 6)

(-6, 6)

Question 13out of 31

Which inclusion relationship between number sets is correct?

Q ⊂ Z

N ⊂ Z ⊂ Q ⊂ R

R ⊂ Q ⊂ Z ⊂ N

I ⊂ Q

Question 14out of 31

How is 2x² + 3x + 3 classified by its number of terms?

Not a polynomial

A monomial

A trinomial

A binomial

Question 15out of 31

Factorise: x² − 3².

(x − 3)(x + 3)

(x + 3)²

(x − 9)(x + 1)

(x − 3)²

Question 16out of 31

In (x + 7)² = x² + kx + 49, find coefficient k.

Question 17out of 31

A regular square pyramid has base side 64 cm and height 60 cm. Find the slant height of a face.

72 cm

86 cm

68 cm

57 cm

7 cm

Question 18out of 31

When exchanging €130 for dollars, offer A gives 1.18 USD per euro and offer B gives 1.20. Which gives more dollars?

Offer A

There is not enough information

Both give the same amount

Offer B

Question 19out of 31

Four interval frequencies are 3, 7, 3 and x, with total frequency 20. Find x.

Question 20out of 31

Multiply vector (-4, 0) by 3.

(0, -12)

(-12, 0)

(12, 0)

(-12, 1)

(-11, 0)

Question 21out of 31

Solve the system: 5x + 3y = 21 and 5x − 3y = 39.

(6, -3)

(6, -2)

(7, -3)

(-6, -3)

(-3, 6)

(6, 3)

Question 22out of 31

Which statement about the principal square root is correct?

The principal square root is non-negative

√a always equals a/2

√a is defined only when a is a perfect square

Every square root is negative

Question 23out of 31

€1 = 2.00 USD. How many euros are needed to receive $380.00?

113 €

190 €

206 €

215 €

123 €

Question 24out of 31

Which set of three side lengths can form a right triangle?

20, 48 and 52

20, 48 and 53

20, 49 and 52

21, 48 and 52

Question 25out of 31

Between which two consecutive integers does √226 lie?

√226 = 15

15 < √226 < 16

14 < √226 < 15

16 < √226 < 17

Question 26out of 31

Approximately what percentage of data lies between the first and third quartiles?

100 %

25 %

50 %

75 %

Question 27out of 31

Calculate: √324 ÷ √9.

Question 28out of 31

A triangle side is 32 cm. Find the length of the parallel midline.

31 cm

16 cm

11 cm

8 cm

9 cm

Question 29out of 31

An interval contains 8 of 20 values. What is its relative frequency as a percentage?

38 %

7 %

8 %

93 %

40 %

Question 30out of 31

Simplify by taking the greatest possible factor outside the radical: √490.

49√10

7√10

7√100

√70

Question 31out of 31

The foot of a ladder is 12 m from a wall and its top reaches 16 m high. How long is the ladder?

20 m

10 m

36 m

40 m

26 m

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Full Grade 8 mathematics test

This complete Grade 8 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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