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Essentials and Mathematics grade 10 level 4

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; Subject: ; Class: ; with 30 questions; test in 45 minutes; update 13/07/2018
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Subjects Update 13/07/2018
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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)

\(24\sqrt2 - 8\sqrt{15} \over 11\)

Question 1    Question 2    Question 3    Question 4    Question 5    Question 6    Question 7    Question 8    Question 9    Question 10    Question 11    Question 12    Question 13    Question 14    Question 15    Question 16    Question 17    Question 18    Question 19    Question 20    Question 21    Question 22    Question 23    Question 24    Question 25    Question 26    Question 27    Question 28    Question 29    Question 30   
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