GAT: 5 Questions with solutions

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بســم الله الرحمــن الرحيـــم

GAT: Quick Test -1

:: Math Test – 5 Questions with solutions ::

:NOTES

.The use of a calculator is NOT permitted -

.All variables and expressions used represent real numbers unless otherwise indicated -

.Figures provided in this test are drawn to scale unless otherwise indicated -

.All figures lie in a plane unless otherwise indicated -

.Unless otherwise indicated, the domain of a given function f is the set of all real numbers for which f(x) is a real number -


:REFERENCE

.The number of degrees of arc in a circle is 360 -

.The number of radians of arc in a circle is 2π -

.The sum of the measures in degrees of the angles of a triangle is 180 -

:: تنبيه ::
الأسئلة في هذا الموضوع؛ هي أسئلة تدريبية فقط وليست أسئلة الاختبار الفعلي
وضعتها لكم للتدريب والاستفادة

:: Note ::
.All the questions here are for training "only", and not the actual test questions





أ.رحـاب
منتديات اختبارات القدرات والتحصيل

[أ.رحاب]

Questions (1) with solutions

:: Algebra ::

?If 6x + 9 = 30, what is the value of 2x + 3
A) 5
B) 10
C) 15
D) 20

The correct answer is: B
Explanation

6x + 9 = 30

To solve in one step, just divide both sides by 3

2x + 3 = 10

Most students waste time solving for x, which will work, but takes longer

6x + 9 = 30

Subtract 9

6x = 21

Divide by 6

x = 3.5

Evaluate 2x + 3 by

substituting x = 3.5

2x + 3 = 2(3.5) + 3 = 7 + 3 = 10

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Questions (2) with solutions

:: Algebra ::

,A total of 300 tickets were sold for a performance of a school play. The ticket prices were $5 for each adult and $3 for each child
and the total revenue from tickets was $1,400. Solving which of the following systems of equations
?would yield the number of adult tickets sold, a, and the number of children’s tickets sold, c

A) a + c = 1,400
5a + 3c = 300

B) a + c = 300
5a + 3c = 1,400

C) a + c = 300
3a + 5c = 1,400

D) a + c = 300

3a + 5c = 1,400 × 2

The correct answer is: B

:Explanation

:Let a = # of adult tickets sold, and c = # of child tickets sold. If 300 tickets were sold altogether

c + a = 300

The revenue for a adult tickets sold at $5 each is $5a, and the revenue for c child tickets sold at $3 each is $3c
Since the total revenue is $1,400

5a + 3c = 1,400

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Questions (3) with solutions

:: Polynomials ::

?Which of the following expressions is equivalent to 2(x - 4)^2 - 5x
A) 2x^2 - 21x + 32
B) 2x^2 - 21x - 32
C) 2x^2 - 13x + 32
D) 2x^2 - 16x - 21

The correct answer is: A

:Explanation

Expression: 2(x - 4)^2 - 5x

Factor: 2[(x - 4)(x - 4)] - 5x

FOIL: 2[ x^2 - 4x - 4x + 16] - 5x

Simplify: 2[ x^2 - 8x + 16] - 5x

Distribute: 2x^2 - 16x + 32 - 5x

Combine like terms: 2x^2 - 21x + 32

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Questions (4) with solutions

:: Three-Dimensional Geometry ::

.A rectangular solid above has dimensions 3, a, and b, where a and b are integers
?Which of the following CANNOT be the areas of three different faces of this solid

A) 15, 18, and 30
B) 18, 24, and 48
C) 12, 15, and 24
D) 15, 24, and 40

The correct answer is: C

:Explanation

On the drawing, we should first mark the areas of the three faces
The front and back faces both have an area of 3a
The left and right faces both have an area of 3b
The top and bottom faces both have an area of ab
We should now try to find integer values for a and b so that these areas match those given in the choices

A) 15, 18, and 30
This is possible if a = 5 and b = 6

B) 18, 24, and 48
This is possible if a = 6 and b = 8

C) 12, 15, and 24
This cannot work for any integer values of a and b

D) 15, 24, and 40
This is possible if a = 5 and b = 8

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Questions (5) with solutions

:: (Algebra (linear equations ::

A) 30
B) 60
C) 35
D) 65

The correct answer is: A

:Explanation