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1. If s = 2, then the value of (s +1) (s – 6) is:
0
1
7
4
8
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Correct answer is option  5 Explanation:
Since its gives s = 2, substitute its value in the given expression: (2 + 1) (2 – 6).
This gives: (1) * (8) = 8.
2. What is the simplified form of the expression, (p + q + 3) (p + q – 3)?
Correct answer is option  3 Explanation:
According to the ‘Difference of the squares’ formula: (a + b) (a b) = a^{2} – b^{2}.
Here we can group (p + q) together and treat as a single term and consider ‘3’ as the other term.
This gives: [(p + q) + 3] [(p + q) – 3] and this is in the form of the above formula.
Hence we get [(p + q) + 3] [(p + q) – 3] = (p + q)^{2} – 3^{2} = (p + q)^{2} – 9.
3. If two lines, y = 5x – 1 and y = 3x + 7 intersect each other at point P, then the coordinates of the point of intersection in an X – Y plane is:
(3, 11)
(4, 19)
(2, 8)
(4, 10)
(8, 6)
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Correct answer is option  2 Explanation: Since the two lines intersect each other, hence in order to find their point of intersection we can equate or solve for the given two line equations.
This gives: 5x – 1 = 3x + 7 ==> 5x – 3x = 7 + 1.
This implies: 2x = 8 ==> x = 8/2 = 4.
When x = 4, to find ‘y’ substitute the ‘x’ value in any of the two given equations.
y = 5x – 1 ==> y = 5(4) – 1 = 20 – 1 = 19.
Therefore the point of intersection, P = (4, 19).
4. The product of the solutions of the quadratic equation, x^{2} – 9x + 20 = 0 is?
20
20
9
9
12
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Correct answer is option  1 Explanation: The given quadratic equation,x^{2} – 9x + 20 = 0 can be factored as: (x – 4) (x – 5) = 0.
This gives the solutions as: x  4 = 0 ==> x = 4 and x  5 = 0 ==> x = 5.
Hence the product of the solutions is 4 * 5 = 20.
5. Andy wants to buy a jacket which costs $60. If there is a discount of 30% on the jacket, then how much would the jacket cost?
$60
$54
$42
$36
$30
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Correct answer is option  3 Explanation: The discount on the jacket = 30%. So the price which is off on the jacket is 30% of $60.
This gives: (30/100) * $60 = $18.Hence on the jacket there is $18 off.
This makes the new cost of the jacket= $60  $18 = $42.
6. The midpoint of a horizontal line segment AB is (5, 3). If the length of the segment AB is 6, then the endpoints A and Brespectively of this line are:
(2, 3) and (8, 3)
(3, 3) and (7, 3)
(2, 6) and (8, 0)
(0, 3) and (6, 3)
(5, 0) and (5, 6).
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Correct answer is option  1 Explanation:
Since the line segment AB is a horizontal line, hence we can say that the ‘y’ coordinate of the endpoints will remain the same.
In order to find the ‘x’ coordinates of the endpoints, we should consider the fact that the length of AB is 6.
This implies that the length from the midpoint to the one of its endpoints is 6/2= 3.
Therefore, taking ‘x’ values 3 units to the left and 3 units to the right of ‘5’ respectively give:(5 – 3) = 2 and (5 + 3) = 8.
Hence the point A = (2, 3) and B = (8, 3).
7. In triangle PQR, PQ = PR. If the measure of the angle PQR is 65° as shown in the figure, then the measure of the angle QPR is:
35°
50°
65°
70°
80°
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Correct answer is option  2 Explanation:
In the given triangle PQR, side PQ = side PR. One of the triangle properties says that the angles opposite to equal sides are also equal to each other.
This gives angle PQR = angle PRQ = 65°.
Sum of the angles in a triangle = 180°.
Therefore, angle PQR + angle PRQ + angle QPR = 180°.
This implies: 65° + 65° + angle QPR = 180° ==> 130° + angle QPR = 180°.
Hence angle QPR = 180°  130° = 50°.
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