Question 1 :
In a class test containing 15 questions, 4 marks are given for each correct answer and -2 marks are given for every incorrect answer. James attempts all the questions but only 9 of his answers are correct. what is his total score?
Question 2 :
A batsman scored the following number of runs in six innings :
36, 35, 50, 46, 60, 55
Calculate the runs scored by him in an inning.
Question 4 :
Solve for x :
-2(x + 3) = 8
Question 5 :
Kevin's father's age is 5 years more than three times Kevin's age.Find Kevin's age, if his father is 44 years old.
Question 6 :
If two lines intersect at a point, and if a pair of vertically opposite angles are acute angles, what will the other pair of vertically opposite angles be?
Question 7 :
In the figure shown below, if the lines L and M are parallel, find the value of x.
Question 8 :
In the figure shown below, find the value of x.
Question 9 :
I have 2 vats each containing 2 mats 2 cats sat on each of the mats each cat wore 2 hats on each hat lay to rats on each rat perched 2 thin bats how many things are there in my vats?
Question 10 :
Express the number 5985.3 in standard form.
1. Answer :
Total number of questions = 15.
Number of questions answered correctly by James = 9.
Number of questions answered incorrectly by him.
= 15 - 9
= 6
For each correct answer he will get +4 marks and for each questions he will get -2 marks.
James' total score :
= 9 ⋅ 4 + 6 ⋅ (-2)
= 36 - 12
= 24
2. Answer :
To find the runs scored in one innings, we have to find the average.
= ⁽³⁶ ⁺ ³⁵ ⁺ ⁵⁰ ⁺ ⁴⁶ ⁺ ⁶⁰ ⁺ ⁵⁵⁾⁄₆
= ²⁸²⁄₆
= 47
Therefore, the batsman scored 47 runs in one innings.
3. Answer :
Number of mangoes in small boxes = m.
Number of magoes in big box = 8m + 4.
Total number of mangoes in big box = 100.
The required equation :
8m + 4 = 100
4. Answer :
-2(x + 3) = 8
Use the distributive property.
-2(x) - 2(3) = 8
-2x - 6 = 8
Add 6 to both sides.
-2x = 14
Divide both sides by -2.
x = -7
5. Answer :
Let x be the age Kevin.
Kevin's father's age = 3x + 5.
Given : Father's age = 44.
3x + 5 = 44
Subtract 5 from both sides.
3x = 39
Divide both sides by 3.
x = 13
Therefore, Kevin's age is 13 years.
6. Answer :
If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertical opposite angles must be obtuse angles.
7. Answer :
In the figure shown above, the lines L and M are parallel and the line t is transversal. 110° and y are linear pair.
110° + y = 180°
Subtract 110° from both sides.
y = 70°
Since x and y are alternate interior angles, they must be equal.
Therefore,
x = 70°
8. Answer :
Exterior Angle Theorem :
In a triangle, the measure of an exterior angle is equal to sum of the measures of two remote interior angles.
In the triangle shown above, 110° is an exterior angle and x and 50° are the two remote interior angles.
By Exterior Angle Theorem,
x + 50° = 110°
Subtract 50° from both sides.
x = 60°
9. Answer :
There are two vats
Number of mats in 1 vat = 2
Number of mats in 2 vats = 2 × 2 = 4
Number of cats on 1 mat = 2
Number of cats on 4 mats = 4 × 2 = 8
Number of funny old hat with 1 cat = 2
Number of funny old hat with 8 cats = 8 × 2 = 16
Number of thin rat on 1 old hat = 2
Number of thin rat on 16 old hats = 16 × 2 = 32
Number of black bats on 1 rat = 2
Number of black bats on 32 rats = 32 × 2 = 64
Number of things in in my vats :
= 64 + 32 + 16 + 8 + 4 + 2
= 126
10. Answer :
5985.3
Here, non zero digit comes first and decimal point comes next.
We have to move the decimal point to the left.
There are three digits between the 1st non zero digit and the decimal point.
So, the decimal point has to be moved three digits to the left and exponent of 10 should be 3 (positive integer).
Therefore, the scientific notation of 5985.3 is
5.9853 x 103
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