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Full Grade 9 test

Full Grade 9 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: 30Estimated time: 60 minutes

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Question 1out of 30

A central angle over the same arc is 30°. Find the inscribed angle.

147°

15°

45°

68°

97°

A central angle and an inscribed angle intercept the same arc. Their measures are related by:

inscribed angle = central angle / 2.

Divide the given central angle by 2. Before calculating, make sure that both angles really intercept the same arc.

Question 2out of 30

What does a positive discriminant of a quadratic trinomial mean?

It cannot be a quadratic trinomial

It has no real roots

It has two real roots and can be factored into two linear factors

It has exactly one root

Question 3out of 30

Solve x + y = 11 and xy = 28. Give the pair where x < y.

(4, 8)

(4, 7)

(5, 7)

(7, 4)

(-4, 7)

(4, -7)

Question 4out of 30

Simplify (x² − 4²)/(x − 4), where x ≠ 4.

x − 4

x² + 4

x + 4

Question 5out of 30

A plane travels 100 m along a path whose angle has sine 0.80. How high does it climb?

20 m

80 m

12 m

75 m

63 m

Question 6out of 30

What angle is formed by a tangent and the radius to the point of tangency?

90°

180°

45°

60°

A tangent is a line that has exactly one common point with a circle. This point is called the point of tangency.

A radius drawn from the centre to the point of tangency is always perpendicular to the tangent. Therefore, the angle between them is a right angle.

Question 7out of 30

Given f(x) = -3x + (5), find f(-2).

-3

The notation f(x) represents the function value obtained for a particular value of x.

Substitute the given number for every x.
Perform the multiplication first.
Then add the constant term.

If x or the constant term is negative, use brackets during substitution so that its sign is preserved.

Question 8out of 30

On which interval is f(x) = (x − (-1))(x − 1) negative?

(-1; 1)

[-1; 1]

(−∞; -1) ∪ (1; +∞)

Question 9out of 30

Solve x² + (-3)x + (-40) = 0.

-5 and -8

5 and 8

-5 and 8

Only -5

-4 and 9

Question 10out of 30

A line passes through (-3, 13) and (-1, 3). Which equation represents it?

y = -5x − 2

y = -5x + 2

y = -2x − 5

y = 5x − 2

Question 11out of 30

State the restrictions for 1/((x − (-8))(x − 8)).

x = -8 and x = 8

All real numbers

x ≠ -8 and x ≠ 8

x ≠ 0

Question 12out of 30

Continue the arithmetic sequence: 0, 2, 4, 6, 8

Question 13out of 30

Which statement correctly describes a tangent to a circle?

A chord never meets the circle

A tangent touches the circle at exactly one point

A secant touches at one point only

Every radius is a tangent

Question 14out of 30

What does coefficient b mean in y = kx + b?

It is the value of x when y = 0

It is the value of y when x = 0

It determines whether the graph is a parabola

It is always the slope

Question 15out of 30

Which line is parallel to y = 2x + (-8)?

y = -2x − 8

y = 3x − 8

y = 0 − 8

y = 2x − 5

Question 16out of 30

Find the zeros of y = (x − (-7))(x − 4).

Only -7

-6 and 5

-7 and 4

7 and 4

-7 and -4

The zeros of a function are the x-values for which y = 0.

When the function is already factorised, use the zero-product rule:

(x − x₁)(x − x₂) = 0.

A product equals zero when at least one factor equals zero. Therefore solve x − x₁ = 0 and x − x₂ = 0 separately.

Question 17out of 30

A geometric sequence has first term 3 and ratio 3. Find term 6.

768

748

729

735

654

Question 18out of 30

Factorise x² + 13x + 40.

(x − 8)(x + 5)

(x − 8)(x − 5)

(x + 13)(x + 40)

(x + 8)(x + 5)

Question 19out of 30

A conclusion about all students is based on five members of one team. What is the main problem?

The sample may be biased and too small

A non-random sample is always better

Sample size never matters

The result certainly represents everyone

Question 20out of 30

Expand (x − (-6))(x − (-1)).

x² + (-7)x + (6)

x² + (7)x + (6)

x² + (7)x + (-6)

x² + (6)x + (7)

To expand the brackets, multiply each term in the first pair of brackets by each term in the second:

(x − a)(x − b) = x² − bx − ax + ab.

Combine the like terms:

(x − a)(x − b) = x² − (a + b)x + ab.

Multiply x · x.
Combine the two terms containing x: −bx − ax.
Multiply the constant terms: (−a)(−b) = ab.

Pay close attention to the signs. If a negative number appears in brackets, for example x − (−3), the expression is equal to x + 3.

Question 21out of 30

Intersecting chord segments are 6 cm and 8 cm, and the other chord has segments 2 cm and y. Find y.

15 cm

31 cm

38 cm

24 cm

32 cm

Question 22out of 30

sin α = 0.80 and α is acute. Use sin²α + cos²α = 1 to find cos α.

0.80

0.60

Question 23out of 30

Which statement correctly describes an arithmetic sequence?

The ratio is always 2

All terms are equal

The difference between consecutive terms is constant

Every term is positive

Question 24out of 30

A rectangle has perimeter 44 and area 112. Find its side lengths.

9 and 15

8 and -14

Only 8

8 and 14

-8 and 14

Question 25out of 30

A ball’s height is modelled by a downward-opening parabola with coefficient −1. What does its vertex represent?

The graph has no maximum

The vertex represents the starting height only

The vertex represents a maximum height

Every point has the same height

Question 26out of 30

How does increasing |a| affect the width of y = ax²?

Coefficient a changes only the y-intercept

The value of a has no effect

A larger |a| always moves the vertex right

A larger |a| makes the parabola narrower

The graph of y = ax² is a parabola. The value |a| shows how strongly the parabola is horizontally compressed or stretched.

The larger |a| is, the narrower the parabola becomes.
The closer |a| is to zero, the wider the parabola becomes.

The sign of a determines its direction: when a > 0, the parabola opens upwards; when a < 0, it opens downwards.

Question 27out of 30

Which special angle has sine approximately 0.50?

60°

30°

90°

45°

Question 28out of 30

An observer is 70 m from a building. The tangent of the elevation angle is 0.50. Find the height.

5 m

2 m

9 m

7 m

35 m

Question 29out of 30

What relates central and inscribed angles over the same arc?

Their sum is always 90°

The inscribed angle is half the central angle over the same arc

The two angles are always equal

The central angle is half the inscribed angle

Question 30out of 30

For y = (x − (-5))² + (4), give the vertex.

(5, 4)

(-5, 4)

(4, -5)

(-5, 5)

(-4, 4)

(-5, -4)

The vertex form of a parabola is y = a(x − m)² + n.

Its vertex coordinates can be read directly:

V(m, n).

Pay close attention to the sign inside the brackets. For example, if the expression is x − (−3), the x-coordinate of the vertex is −3, not 3.

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Full Grade 9 mathematics test

This complete Grade 9 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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