MATHEMATICS A - Jan 2009
1. Given the true statements:
“Rob plays basketball or tennis.”
“Rob does not play tennis.”
Which statement must also be true?
(1) Rob plays basketball.
(2) Rob does not play basketball.
(3) Rob does not play basketball, and he does not play tennis.
(4) Rob plays football.
The 2nd statement makes it clear that Rob doesnt play Tennis. The first statement says that Rob definitely plays either basketball or Tennis. Since we know that he doesnt play Tennis, he has to play basketball.
So the
answer is (1)
Cost of 1 Granol bar = $0.55
Therfore,
Cost of 0 Granol bar = $0.55 * 0 = $0.00
Cost of 2 Granol bars = $0.55 * 2 = $1.10
Cost of 4 Granol bars = $0.55 * 4 = $2.20
So the
answer is (2)3 A ship sailed t miles on Tuesday and w miles on Wednesday. Which
expression represents the average distance per day traveled by the ship?
(1) 2(t + w) (3) (t+w)/2
(2) t + w/2 (4) t − w
Miles traveled by the ship on Tuesday = t
Miles traveled by the ship on Wednesday = w
Total miles traveled by the ship in 2 days (Tuesday and Wednesday) = t + w
Average miles traveled by the ship per day = Total miles / Number of days
= (t+w)/2
So the
answer is (3)4 What is the value of x in the equation 2(x − 3) + 1 = 19?
(1) 6 (3) 10.5
(2) 9 (4) 12
2(x − 3) + 1 = 19
2x - 2*3 + 1 = 19
2x - 6 + 1 = 19
2x - 5 = 19
2x = 19 + 5
2x = 24
x = 12
So the
answer is (4)5. Which equation represents the line whose slope is 2 and whose
y-intercept is 6?
(1) y = 2x +6 (3) 2y + 6x = 0
(2) y = 6x +2 (4) y + 2x = 6
Equation of a line with a slope of m is given by
y = mx + c , where c is the y-intercept.
So it is given that the slope is 2 and the y-intercept is 6
ie, m = 2 and c = 6
Substituting the above values in the first equation, we get
y = 2x + 6
So the
answer is (1)6. If 0.02x + 0.7 = 0.8, then x is equal to
(1) 0.5 (3) 5
(2) 2 (4) 50
0.02x + 0.7 = 0.8
0.02x = 0.8 - 0.7
0.02x = 0.1
Multiplying both sides of the above equation with 100 we get
0.02x * 100 = 0.1*100
2x = 10
x = 10/2 = 5
So the
answer is (3)7. If the probability of a spinner landing on red in a game is 1/5, what is the probability of it not landing on red?
(1) 20% (3) 50%
(2) 25% (4) 80%
probability of a spinner landing on red in a game = 1 - probability of it not landing on red
ie. 1/5 = 1 - probability of it not landing on red
therefore,
probability of it not landing on red = 1- 1/5 = 4/5 = (4/5)*100 %
= 80%
So the
answer is (4) 8. What is the solution for the equation x + 1 = x + 2?
(1) −1 (3) all real numbers
(2) (4) There is no solution.
x + 1 = x + 2
Canceling x on both sides we get
1 = 2, which is never true.
So the above equation can never be true for any value of x. So there is no solution for this equation.
So the
answer is (4).
9. If five times the measure of an angle is decreased by 30°, the result is
the same as when two times the measure of the angle is increased by
18°. What is the measure of the angle?
(1) −16° (3) 16°
(2) −4° (4) 4°
Let the measure of the angle be x.
So, 5x - 30 = 2x + 18
5x-2x = 18+30
3x = 48
x = 16
So the
answer is (3) 10. The expression (−2a2b3)(4ab5)(6a3b2) is equivalent to
(1) 8a6b30 (3) −48a6b10
(2) 48a5b10 (4) −48a5b10
(−2a2b3)(4ab5)(6a3b2) = (-2*4*6)(a2*a*a3)(b3*b5*b2)
= -48a6b10
So the
answer is (3) 11. What is the value of n if the number 0.0000082 is written in the form 8.2 × 10^n?
(1) −6 (3) 5
(2) −5 (4) 6
.0000082 has 5 zeroes before the digit 8. So to get to 8.2 we need to move the decimal point 6 times to the right which means
.0000082 = 8.2 * 10^-6
So n = -6
So the
answer is (1)
Square Root (27) = Square root (9*3)
= Square root (9) * Square root (3)
= 3 * Square root (3)
Square Root (108) = Square root (36*3)
= Square root (36) * Square root (3)
= 6 * Square root (3)
Therefore,
Square Root (27) + Square Root (108) = 3 * Square root (3) + 6 * Square root (3)
= 9 * Square root (3)
So the
answer is (2) 13 Which equation has the solution set {1,3}?
(1) x2 − 4x + 3 =0 (3) x2 + 4x + 3 = 0
(2) x2 − 4x − 3 =0 (4) x2 + 4x − 3 = 0
To check which of the equations have the solution set {1,3} substitute the values 1 & 3 for x in the equations given and see which of them satisfies the equation.
This way we can find that only Equation (1) satisfies for both x = 1 & 3.
So the
answer is (1)14 The midpoint of AB has coordinates of (5,−1). If the coordinates of A are (2,−3), what are the coordinates of B?
(1) (8,1) (3) (7,0)
(2) (8,−5) (4) (3.5,−2)
Let the co-ordinates of B be (x,y)
So the midpoint of AB has co-ordinates (2+x)/2 , (-3+y)/2
ie, (2+x)/2 = 5
2 + x = 5*2 = 10
x = 10 - 2 = 8
and, (-3+y)/2 = -1
-3+y = -1*2 = -2
y = -2 + 3 = 1
So the co-ordinates of B are (8,1)
So the
answer is (1)15 If x = 2 and y = −3, what is the value of 2x2 − 3xy − 2y2?
(1) −20 (3) 8
(2) −2 (4) 16
Substituting the values of x and y in the equation we get
2(2)^2 - 3(2)(-3) - 2(-3)^2
= 2*4 - 3*(-6) - 2*9
= 8 + 18 - 18
= 8
So the
answer is (3)16 . Will be posted soon .....
17 For which value of m is the expression
undefined?
(1) 1 (3) 3
(2) 0 (4) −3
A fraction becomes undefined when the denominator becomes zero
So for the above fraction to be become undefined 3 - m must be zero
ie, 3 - m = 0
m = 3
So the
answer is (3)
