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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.

Question qty: 32Duration in minutes: 60

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Question Nr. 1out of 32

How do you find the coordinates of a point translated by a given vector?

Change both signs only

Add the vector coordinates to the point coordinates

Swap x and y

Multiply all coordinates

Question Nr. 2out of 32

One base of a trapezoid is 6 cm and its midline is 8 cm. Find the other base.

21 cm

1 cm

17 cm

10 cm

19 cm

Question Nr. 3out of 32

€1 = 2.00 USD. How many euros are needed to receive $240.00?

42 €

144 €

123 €

55 €

120 €

Question Nr. 4out of 32

Calculate ∛1000.

Question Nr. 5out of 32

Which statement about number sets is always true?

Every real number is rational

No natural number is an integer

Every rational number is an integer

Every integer is rational

Question Nr. 6out of 32

A cylinder’s axial section is a rectangle of diameter based on radius 7 cm and height 48 cm. Find its diagonal.

37 cm

40 cm

21 cm

50 cm

65 cm

Question Nr. 7out of 32

Multiply vector (2, 4) by 2.

(5, 8)

(-4, 8)

(8, 4)

(4, -8)

(4, 8)

(4, 9)

Question Nr. 8out of 32

How many solutions does the system 3x + 3y = 4 and 12x + 12y = 21 have?

One solution

Infinitely many solutions

Exactly two solutions

No solutions

Question Nr. 9out of 32

The line has equation y = 8x + (7). At which point does it cross the y-axis?

(0, 7)

(10, -9)

(3, 8)

(4, 2)

(4, 0)

Question Nr. 10out of 32

What median is shown in the box plot?

Question Nr. 11out of 32

A regular square pyramid has base side 16 cm and height 15 cm. Find the slant height of a face.

22 cm

34 cm

17 cm

6 cm

19 cm

Question Nr. 12out of 32

Factor out the common factor: 9x + 9·4.

9(x + 4)

36(x + 1)

9(x + 36)

x(9 + 4)

Question Nr. 13out of 32

Which interval has the greatest frequency?

0–10

10–20

20–30

30–40

30–40

0–10

20–30

10–20

Question Nr. 14out of 32

A loan of 900 € is offered. A: 6% interest plus a fee of 20 €. B: 9% with no fee. Which is cheaper?

Offer A

There is not enough information

Both are equal

Offer B

Question Nr. 15out of 32

Which definition correctly describes a triangle midline?

It divides the triangle into two equal triangles

It joins the midpoints of two sides

It joins a vertex to the opposite midpoint

It is always perpendicular to a side

Question Nr. 16out of 32

What is the degree of the monomial 5x⁶?

Question Nr. 17out of 32

Which inclusion relationship between number sets is correct?

R ⊂ Q ⊂ Z ⊂ N

I ⊂ Q

N ⊂ Z ⊂ Q ⊂ R

Q ⊂ Z

Question Nr. 18out of 32

Subtract vector (1, 4) from (-1, -4).

(-2, -8)

(-1, -8)

(-2, -7)

(-2, 8)

(2, -8)

(-8, -2)

Question Nr. 19out of 32

Using interval midpoints 5, 15 and 25, estimate the data mean.

0–10	10–20	20–30
5	5	2

12.65

12.5

16.9

14.33

16.13

Question Nr. 20out of 32

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

Question Nr. 21out of 32

Which statement correctly explains how compound interest works?

Compound interest can never exceed simple interest

Interest is always calculated only on the initial deposit

Each period, interest is calculated on the current balance

The balance grows by the same fixed amount every period

Question Nr. 22out of 32

Calculate: √81 · √9.

114

Question Nr. 23out of 32

How is 3x² + 6x + 9 classified by its number of terms?

A trinomial

A monomial

A binomial

Not a polynomial

Question Nr. 24out of 32

Factorise: x² − 6².

(x − 6)(x + 6)

(x + 6)²

(x − 6)²

(x − 36)(x + 1)

Question Nr. 25out of 32

A triangle midline is 10 cm. Find the parallel side length.

20 cm

5 cm

24 cm

22 cm

27 cm

Question Nr. 26out of 32

A deposit of 1200 € earns 10% compound interest annually for 3 years. What is the final amount?

1560 €

1597.2 €

1200 €

1320 €

Question Nr. 27out of 32

Use the histogram to find the frequency of interval 0–10.

0–10

10–20

20–30

30–40

Question Nr. 28out of 32

For 14 units, plan A costs 6 + 5x euros and plan B costs 12 + 1x euros. Compare plans A and B.

Both plans cost the same

There is not enough information

Plan A is cheaper

Plan B is cheaper

Question Nr. 29out of 32

Subtract the polynomial (5x + 5) from (11x + 3).

16x − 2

6x − 2

16x + 8

6x + 8

Question Nr. 30out of 32

Which identity correctly represents the difference of two squares?

(a − b)(a + b) = a² + b²

(a − b)(a + b) = a² − b²

(a − b)² = a² − b²

(a + b)² = a² + b²

Question Nr. 31out of 32

The line has equation y = 2x + (-2). What is its slope?

-7

-5

Question Nr. 32out of 32

Which statement correctly describes a histogram?

A histogram is used only for names of categories

A histogram represents numerical intervals with adjacent bars

Bars in every histogram must be separated

A histogram cannot show frequencies

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Full Grade 8 mathematics test

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