SampleGeneral Mathematics Skills Test Answers
1. 0.035 = ?
(A) 7/20
(B) 35/100
(C) 7/1000
(D) 7/200
=35/1000. Divide top and bottom by 5 = 7/200 (Answer Option D)
2. if 4x < 0 then?
(A) 4x > x
(B) -x < 0
(C) x < -x
(D) None of these
Divide both sides by 4 so x < 0
Take any number for x less than zero say, x = -1 and apply to all four options
(A) 4x > x
(B) -x < 0
(C) x < -x
(D) None of these
4(-1) > -1
-1(-1) < 0
-1 <-(-1)
-4 > -1
1<0
-1<1
Which is incorrect
Which is incorrect
Which is correct
(B) –x < 0
(C) -3 = -x
(Answer Option C)
3. If 3 < x then?
(A) -3 < -x
(D) None of these
3<x so x > 3 Try x = 4 and apply to the options
-3 < -4
-4 > 3
-3 - =4
Which is incorrect
Which is incorrectWhich is incorrect (Answer Option D)
4. Tomtakes20coinsfrom abox,andshegets12redcoinsand
8blackcoins.Ifthewholeboxcontains10000coins,abouthowmanyofthemareblack?
(A)8000
(B)4000
(C)400
(D)6000
This is a question about ratios. The ratio of red to black is 12 : 8 giving us 12 + 8 = 20 parts
There are 10,000 coins so each part is 10,000/ 20 = 500 coins
The number of black coins is therefore 500 x 8 = 4,000
(Answer Option B)
5.
Rogerislookingatamapwherethescaleis2km=4.5cm.Ifhemeasuresthedistancefromhishousetothecenteroftownonthem
apas12.6cm,howmanykilometersfromthecenter?
(A) 2.8
(B) 5.6
(C) 6
(D) 7.6
Another question about ratios.
4.5 cm represents 2 Km.
1 cm. represents 2/4.5 Km.
So, 12.6 cm represents12.6 x 2/4.5 Km. = 5.6 Km.
(Answer Option B)
6. Forwhichofthefollowinginequalitiesisthepoint(-7,3)asolution?
(I) x – 3 ≤ 4y
(II) -3x > 15 + 2y
(A)Ionly
(B) IIonly
(III) –x – 4 ≥ 3y
(C)Iand II only
(D) IIand IIIonly
For each of the three options we insert -7 every time we see an x and 3 every time we see a y
x – 3 ≤ 4y
-3x > 15 + 2y
–x – 4 ≥ 3y
-7 – 3 ≤ 4 x 3
-3(-7) > 15 + 2(3)
-(-7) – 4 ≥ 3(3)
-10 ≤ 12
21 > 15 + 6
7–4≥9
-10 ≤ 12
21 > 21
3≥9
Which is correct
Which is incorrect
Which is incorrect
7. (x + 2y)2 = ?
(A)2x2+y2
(B)4x2+y2
(x + 2y) = (x + 2y)(x + 2y)
(C)4x2+4xy+y2
(D)x2+4xy+4y2
= x(x + 2y) + 2y(x + 2y)
= x2 + 2xy + 2yx + 4y2
= x2 + 4xy + 4y2
(Answer Option D)
2
8. Ify=x -3x+8,whatisthevalueofywhenx=2
(A)6
(B)8
(C)10
(D)12
Here we replace x with 2
y = x2 – 3x + 8 = (2)2 – 3(2) + 8 = 4 – 6 + 8 = 6
9. Whatistheequationofthelinethatpassesthroughthepoints(5,1)and(3,5)?
(Answer Option A)
(Answer Option A)
(A)2x+ y=22
(B)2x+y=11
(C)x+2y=22
(D)x+2y=11
To find the equation of a line we need to find the slope (Gradient)
Slope m = (y2 – y1)/(x2 – x1) = (5 -1)/(3 -5) = 4/-2 = -2
The equation of the line is y – y1 = m(x – x1) (We can use either of the two points)
So y – 1 = -2(x – 5)
y -1 = -2x + 10 or y + 2x = 11
(Answer Option B)
10. IfJohncanrun9kminyminutes,howmanykmcanherunin10 minutes?
(A) 9y/10
(B)90y
(C)1/90y
(D)90/y
In y minutes John can run 9 Km.
In 1 minute John can run 9/y Km.
So in 10 minutes John can run 9 x 10/Y Km. = 90/y Km.
(Answer Option D)
11.1y/(1+1/x)=?
(A)x/(1+1/y)
(B)y/(x+y)
(C)xy/(x+1)
(D)(x+y)/xy
We first of all need to work out top and bottom lines separately. There is a fraction on the bottom line so we need
to find the Lowest Common Denominator.
The question becomes
___y__
1/1 + 1/x
=
__ y__
x+1
x
The x now comes up to the top line so we have xy/(x + 1)
(Answer Option C)
12..Atwhichpointsdoesthe graphofy=x2–6x+8 crossthex-axis?
(A)(6,0)&(2,0)
(B)(-4,0)&(-2,0)
(C)(4,0)&(2,0)
(D)(-6,0)&(-2,0)
A graph will always cross the x axis when y = 0 so we need to solve the equation
x2 – 6x + 8 = 0
(x – 4)(x - 2) =0
First we need to factorize the left side
If either of these two brackets 0 then the whole left side becomes 0. This happens when x = 2 or x = 4
Our solution is therefore (2,0) and (4,0) as y = 0
(Answer Option C)
13. Atwhichpointdoesthegraphofy=(x-3)5+60crossesthey-axis?
(A)(0,60)
(B)(0,303)
(C)(0,-183) (D)(0,57)
Same as last question only this time x = 0 so,
y = (0 – 3)5 + 60 = (-3)5 + 60 = - 243 + 60 = -183
(Answer Option C)
14. Findthesolutionsofthefollowingquadraticequationx2 – x – 10 = 2
(A) 4 and -3
(B) -4 and 3
(C) 1 and -12
(D) -1 and 12
Here we have two constant terms which we need to combine
x2 – x -12 = 0
Now we need to factorize
(x -4)(x + 3) =0
As before if either bracket is 0 then the whole left side becomes 0. This happens when x = 4 or -3 (Answer Option A)
15 Findthesolutionsofthefollowingequation-3x2 + 12x = 0
(A)4
(B)0
(C)0and4
(D)no solution
We can simplify this equation by dividing through by -3 giving us x2 – 4x = 0. Now we need to factorize
x(x – 4) =0 and as before this can happen when x = 0 and x = 4
(Answer Option C)
16.Findthesolutionsofthefollowingquadraticequationx2 = 36
(A)6
(B)-6
(C)36
(D)6and-6
This is known as the difference of two squares
x2 – 36 = 0
Now we factorize as before (x + 6)(x – 6) = 0 so x - +6 or -6
(Answer Option D)
17. Findthesolutionsofthefollowingequationx3 = -8
(A)8
(B)-8
(C)2
(D)-2
Here we are looking for a number multiplied by itself and multiplied by itself again which will give us -8. In this case it is
-2 because -2 x -2 x -2 = -8
(Answer Option D)
18.Findthesolutionofthefollowingequation. (x – 4)(x + 3)(x + 1) = 0
(A)1,3,-4
(B)-1,-3,4
(C)-1,3,-4
(D)1,-3,4
This is the same as question 14 after it has been factorized. if any of the three brackets is 0 then the whole left side
becomes 0. This happens when x = 4 or -3 or -1
(Answer Option B)
19. Findthesolutionofthefollowingequation 3(x + 10)2 = 0
(A)3,10
(B)3,-10
Divide both sides by 3
(C)10
(D)-10
(x + 10)2 =0
Take the square root of both sides
x + 10 = 0
x = -10
(Answer Option D)
20. Let a = 5/6 and b = -3/5.Thencompute ab + 1
(A) 2
(B) ½ (C) -1/2
(D) 2
ab + 1 = 5 x -3 + 1 = -15/30 + 1= -1/2+ 1 = 1/2
5x6
21.Let a = 1/4 and b = -1/3. Thencompute
(A) 12
(B) 1/12 (C)-12
(Answer Option C)
1/(a + b)
(D)-1/12
1/(a + b) = 1/(1/4 – 1/3)
Again we need to find the lowest Common Denominator.
1/(a + b) =1/(3 – 4)/12 = 1/-1/12 = 12/-1 ==-12
(Answer Option C)
22. Thesumofanglesinatriangle
is180o.Ifthefirstangleis80oandthesecondangleisthreetimesthethirdangle,findthesecondangle.
(A)100o
(B)75o
(C)50o
(D)25o
If the first angle is 80o then the other two angles add up to 100o
These two angles are in the ratio of 1:3 (4 parts)
1 part = 100/4 = 25o and so the larger one is 100o – 25o i.e. 75o`
(Answer Option B)
23. A new Company is formed by Paul and Jane. The total investment by them is AED 60,000. It is known that Paul’s
investment is twice as much as Jane’s. What is Jane’s investment in AED?
(A) 20,000
(B) 30,000
(C)40000
(D) 15,000
Here is another ratio question. Investments are in the ratio 1:2 giving us 3 parts
Jane’s investment is 60,000/3 = AED 20,000
(Answer Option A)
24. Theedge ofsquareAisthree timesthatofsquareB.ThentheareaofsquareAishowmanytimestheareaofsquareB?
(A)threetimes
(B)ninetimes
(C)one-third
(D)one-ninth
This is a slightly different version of ratios. If side B is 1 unit long then side A is 3 units long. The area of A is 9 square
units and area of B is one square unit so square A is nine times the size of square B
(Answer Option B)
25.Inthesystemofequations3x+y=5 and -6x –5y= -17, thevalueof xwhichsatisfiesbothequations is:
(A)0
(B)1
(C)2
(D)noneoftheabove
We solve this problem using simultaneous equations:
-6x – 5y = -17
3x + 5y = 5
Add the two equations together
-3x = -17 + 5
-3x = -12
x=4
26. Determine the domain of the function
√(x + 1)
(Answer Option D)
__1__
(A) (∞,-1) U(1 ,∞) (B) [-1, ∞) (C) (∞,-1] U[1, ∞) (D) (-1, ∞)
Bottom line of this problem needs to be positive and so x must be greater that -1
Which is (-1, , ∞)
(Answer Option D)
27. If f(x) = 1/(x + 4)and g(x) = x2 - 4 , then what is f(g( -2))?
(A)1 (B) 4
(C) 1/4
(D) 1/8
To find first of all f(g(x)) we substitute the value of g(x) into f(x)
f((g(x)) =1/(x2 + 4 – 4)
=1/x2
Then to find f(g(-2) we now substitute -2 for x
f(g(-2) = 1/22=1/4
(Answer Option C)
28. If f(x) = x2 +kx – 5, and f (3) = 10, then k = ?
(A)-2
(B)-4
(C)2
If f(x) = x2 + kx -5 then
f(3) = 10 = 32 + 3k – 5
So 10 = 9 + 3k – 5
Therefore 3k + 4 = 10
3k = 6
k=2
(D)4
(Answer Option C)