# Essentials and Mathematics grade 10 level 4

Subject: ; Class: ; with 30 questions; test in 45 minutes; update 13/07/2018
 Time 45 minutes Time to take the test Start exam Click button start to test. Guide to the test Subjects Gmat test Update 13/07/2018 Class Grade 10 Number of questions 30 View 426 Tested 3

Question 1.

Which factor is common to both of the following polynomials?

 (A) 2x - 1 (B) 2x + 1 (C) 4x - 1 (D) 4x + 1

Question 2.

What value of k will make the following trinomial a perfect square?

x2 + 8x + k

 (A) 4 (B) 16 (C) 32 (D) 64

Question 3.

Expand and simplify (x - 5)(x - 5) . How many terms are in the simplified product?

 (A) 1 (B) 2 (C) 3 (D) 4

Question 4.

Expand and simplify : 3x(2x - 3)2 - (x +4)

 (A) 12x3 -26x - 4 (B) 144x4 - 81x2 - x - 4 (C) 12x3 - 36x2 + 26x - 4 (D) 36x4 + 81x2 - x + 4

Question 5.

Simplify for all permissible values :$$2x^2 + 9x - 5\over 2x^2 - 3x + 1$$

 (A) $$x - 5\over x - 1$$ (B) $$x + 5\over x - 1$$ (C) $$x + 5\over x + 1$$ (D) $$(2x + 1)(x - 5)\over (2x -1)(x - 1)$$

Question 6.

Simplify for all permissible values :$$2x^3 - 5x^2\over 4x^3 - 25x$$

 (A) $$x\over x + 5$$ (B) $$x\over 2x - 5$$ (C) $$2x- 5\over 2x + 5$$ (D) $$2x - 5\over 4x - 25$$

Question 7.

Simplify for all permissible values :$$3\over x + 1$$ + $$x^2\over x^2 + 2x + 1$$ - 1

 (A) $$x + 2\over x^2 + 2x + 1$$ (B) $$5x + 4\over x^2 + 2x + 1$$ (C) $$x^2 + 2\over x^2 + 2x + 1$$ (D) $$x^2 + 3x + 2\over x^2 + 2x + 1$$

Question 8.

Solve for x :$$6\over x + 2$$ = $$4\over x - 4$$

 (A) -8 (B) 3 (C) 13 (D) 16

Question 9.

How many non-permissible values for x are in the following expression?

$$2x\over x + 3$$ + $$1\over x^2 + 6x + 9$$

 (A) 1 (B) 2 (C) 3 (D) 4

Question 10.

For what values of x is the following expression undefined?

$$x^2 + 3x + 2\over x^3 - 4x$$

 (A) -2, 2 (B) 0, 4 (C) -1, 0, 2 (D) -2, 0, 2

Question 11.

What is the quotient when x3 + 3x2 + 2x - 1 is divided by x + 3 ?

 (A) -7 (B) x2 + 2 (C) x2 + 2x - 7 (D) x2 + 6x + 20

Question 12.

What is the remainder when 4x3 - 5x + 2 is divided by 2x - 3?

 (A) -4 (B) 3.5 (C) 4 (D) 8

Question 13.

Determine the length of side PQ.

 (A) 38.06 cm (B) 21.34 cm (C) 21.02 cm (D) 16.47 cm

Question 14.

To display a valuable specimen of moon rock, staff at the Space Centre roped off a triangular area and installed a security camera, as shown below.

The security camera was installed so that it scanned continually between the two longest ropes through the angle C. Determine the measure of $$\measuredangle$$C .

 (A) 32° (B) 42° (C) 48° (D) 58°

Question 15.

Determine the area of the triangle shown below.

 (A) 5 879 m2 (B) 11 758 m2 (C) 13 204 m2 (D) 35 537 m2

Question 16.

Solve for x :

 (A) 2.75 (B) 4.89 (C) 5.17 (D) 6.63

Question 17.

From where she parked her car, Jade observed that the angle of elevation to the top of a building was 25°. When she walked 50 m closer to the building, the angle of elevation became 60°. Determine the distance from the base of the building to her car.

 (A) 18.42 m (B) 36.84 m (C) 68.42 m (D) 75.49 m

Question 18.

The point (7, b) is the midpoint of the line segment JK with J(-5, 2) and K(a, -6) . Determine the value of a - b .

 (A) 7 (B) 11 (C) 17 (D) 21

Question 19.

Which line has a positive slope and a negative x-intercept?

 (A) (B) (C) (D)

Question 20.

A line passes through the points (3n, 4) and (-6, 4n). The slope of the line is -$$2\over 3$$ . Determine the value of n .

 (A) 4 (B) $$5\over 8$$ (C) 0 (D) -26

Question 21.

Determine an equation of a line which has a slope of $$1\over 3$$ and passes through the point (6, 0).

 (A) x + 3y - 6 = 0 (B) x + 3y + 6 = 0 (C) x - 3y - 6 = 0 (D) x - 3y + 6 = 0

Question 22.

Determine an equation of the following line :

 (A) y = -$$4\over 5$$x + 4 (B) y = -$$4\over 5$$x + 5 (C) y = -$$5\over 4$$x + 4 (D) y = $$4\over 5$$x + 4

Question 23.

Which of the following lines passes through the points (3, -1) and (10, -4) ?

 (A) y = $$3\over 7$$x - $$16\over 7$$ (B) y = $$3\over 7$$x - $$58\over 7$$ (C) y = -$$3\over 7$$x - $$16\over 7$$ (D) y = -$$3\over 7$$x + $$2\over 7$$

Question 24.

Which of the following equations represents a line that is perpendicular to the line shown below and passes through the point (-2, -6) ?

 (A) y = $$2\over 3$$x + 2 (B) y = $$2\over 3$$x - $$14\over 3$$ (C) y = - $$3\over 2$$x - 9 (D) y = -$$2\over 3$$x - $$22\over 3$$

Question 25.

The equation of a line is 4x - 3y - 12 = 0 . Determine an equation of a parallel line that intersects the y-axis 6 units above the given line.

 (A) y = -$$3\over4$$x + 2 (B) y = -$$4\over 3$$x + 2 (C) y = $$4\over 3$$x + 10 (D) y = $$4\over 3$$x + 2

Question 26.

Simplify: 7$$\sqrt3$$ - 4$$\sqrt3$$ + 2$$\sqrt3$$

 (A) $$\sqrt3$$ (B) 5$$\sqrt3$$ (C) 9$$\sqrt3$$ (D) 13$$\sqrt3$$

Question 27.

Simplify : $$\sqrt{28} + 3\sqrt{63} - \sqrt7$$

 (A) 30$$\sqrt7$$ (B) 18$$\sqrt7$$ (C) 11$$\sqrt7$$ (D) 10$$\sqrt7$$

Question 28.

Simplify :($$(\sqrt x - \sqrt 5)(\sqrt x + \sqrt5)$$

 (A) x -5 (B) x + 5 (C) 2$$\sqrt x$$ (D) x - 2$$\sqrt{5x}$$ - 5

Question 29.

Simplify : ($$\sqrt{12} + 5\sqrt3$$)2

 (A) 87 (B) 117 (C) 147 (D) 189

Question 30.

Simplify : $$8\sqrt3 \over \sqrt6 + \sqrt5$$

 (A) $$24\sqrt2 - 18\sqrt5$$ (B) $$72\sqrt2 - 18\sqrt5$$ (C) $$72\sqrt2 + 18\sqrt5 \over 11$$ (D) $$24\sqrt2 - 8\sqrt{15} \over 11$$