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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: 17Estimated time: 31 minutes

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Question 1out of 17

Compare the slopes of y = -2x and y = 6x.

The second line has the greater slope

The slopes are equal

The first line has the greater slope

Question 2out of 17

Solve x² = 4.

Only -2

-1 and 3

-2 and 2

2 and 2

-2 and -2

Question 3out of 17

Which chart is most suitable for studying the relationship between two numerical variables?

A scatter plot

A single bar

A box plot only

A pie chart

Question 4out of 17

Solve y = x² and y = 16.

(16, -4) and (16, 4)

(4, 16) and (-4, 16)

(-4, 16) and (4, 16)

(-4, -16) and (4, -16)

Question 5out of 17

Expand (x − (-8))(x − (3)).

x² + (-5)x + (-24)

x² + (-24)x + (5)

x² + (5)x + (-24)

x² + (5)x + (24)

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 6out of 17

Find the zeros of y = (x − (-8))(x − 2).

8 and 2

-7 and 3

-8 and -2

Only -8

-8 and 2

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 7out of 17

The opposite side is 24 and adjacent side 45. Find the tangent.

9/15

8/16

15/8

8/15

Question 8out of 17

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

12 cm

45 cm

2 cm

15 cm

7 cm

Question 9out of 17

The trend line y = 5x + b has slope 5. How should it be interpreted?

The variables have no relationship

x increases by 5 when y increases by 1

y always equals 5

When x increases by 1, predicted y increases by 5

Question 10out of 17

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

0.60

0.80

Question 11out of 17

Which quadratic equation has roots -7 and 7?

x² + (-49)x + (0) = 0

x² + (0)x + (49) = 0

x² + (0)x + (-49) = 0

Question 12out of 17

Continue the arithmetic sequence: -1, -8, -15, -22, -29

-29

-30

-26

-36

-46

Question 13out of 17

What exactly does a 8% road slope mean?

The height always equals 108 units

The road length is 8 units

A 8% slope means a rise of 8 units per 100 horizontal units

The road angle is 8°

Question 14out of 17

The first figure has 2 elements and each next figure has 2 more. How many are in figure 8?

Question 15out of 17

When factoring using roots x₁ and x₂, why is the form (x − x₁)(x − x₂) used?

The roots must be multiplied by 2

The factors use the same signs as the roots

The signs in the factors are opposite to the root signs

The constant term is ignored

Question 16out of 17

Which line is parallel to y = -1x + (-6)?

y = x − 6

y = 0 − 6

y = -x − 4

Question 17out of 17

Write x² + 22x + 121 as a perfect square.

(x + 11)²

(x + 22)²

x² + 121

(x − 11)²

Use the perfect-square identity:

(x + a)² = x² + 2ax + a².

Check that the final term is the square of a and that the coefficient of x equals 2a. When both conditions hold, the trinomial can be written as (x + a)².

You can also find a by dividing the coefficient of x by 2.

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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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