Table of contents | |
Logical Reasoning | |
Mathematical Reasoning | |
Everyday Mathematics | |
Achievers Section |
Note: The questions provided in this document are similar to the questions that were asked in the actual Olympiad exam. So, we recommend you study these for your Olympiad preparation
Q1: The number of measurements required to construct a quadrilateral is:
(a) 5
(b) 4
(c) 3
(d) 2
Ans: (a)
Minimum number of measurement required to construct a unique quadrilateral.
Q2: Which of the following is true for constructing a quadrilateral?
(a) 5 sides and 3 diagonals
(b) 3 sides only
(c) 3 angles and their 2 included sides
(d) 2 diagonals only
Ans: (c)
3 angles and their 2 included sides. There is only 4 sides and 2 diagonals. So option (a) is not valid. Only 3 sides are not sufficient to draw a quadrilateral. So, option (b) is also invalid. Only 2 diagonals are not sufficient to draw a quadrilateral. So, option (c) is also not valid.
Q3: To construct a convex quadrilateral, which of the following cases is not correct?
(a) When the lengths of four sides and one diagonal are given.
(b) When the lengths of three sides and the two diagonals are given.
(c) When the lengths of four sides and one angle are given.
(d) When the lengths of two sides and two included angles are given.
Ans: (d)
Only four measurements are given, which are not sufficient to construct a convex quadrilateral.
Q4: To construct a parallelogram, the minimum number of measurements required is:
(a) 2
(b) 3
(c) 4
(d) 1
Ans: (b)
To construct a parallelogram minimum 3 measurements are required.
Q5: The minimum number of dimensions needed to construct a rectangle is:
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (b)
Two dimensions are sufficient to construct a rectangle.
Q6: The minimum number of measurements needed to construct a square is:
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (a)
Only 1 measurement is sufficient to construct a square.
Q7: According to the construction shown in the diagram below, what do we call segment CD?
(a) Bisector of angle C
(b) Median to side AB
(c) Perpendicular bisector of segment AB
(d) Altitude to side AB
Ans: (d)
Altitude to side AB.
Q8: The point where the medians of a triangle are concurrent is called the:
(a) Centroid
(b) Orthocenter
(c) Incenter
(d) Circumcenter
Ans: (a)
Centroid.
Q9: The centroid of a triangle divides the medians into ratios from the vertex, of:
(a) 2 : 1
(b) 3 : 1
(c) 4 : 1
(d) 5 : 1
Ans: (a)
2 : 1.
Q10: In relation to constructions, a straightedge is
(a) a clear plastic device devoid of markings.
(b) often shaped like a triangle.
(c) used for drawing straight lines or segments, but not for measuring.
(d) all of the above.
Ans: (c)
Used for drawing straight lines or segments but not for measuring.
Q11: Which construction is shown in the accompanying diagram?
(a) the bisector of ∠ACD
(b) the midpoint of DF
(c) the perpendicular bisector of AB
(d) a perpendicular line to AB from point D
Ans: (c)
The perpendicular bisector of AB.
Q12: Which diagram below shows a correct mathematical construction using only a compass and a straightedge to bisect an angle?
(a)
(b)
(c)
(d)
View AnswerAns: (d)
Q13: How many pairs of letters can be found in the word ORDINAL, where the number of letters between them matches their positions in the English alphabet?
(a) One
(b) Two
(c) Three
(d) None
Ans: (c)
Q14: If ‘–’ stands for division, ‘+’ stands for multiplication, ‘÷’ stands for subtraction, and ‘×’ stands for addition, find the value of 75 × 5 ÷ 80 – 16 + 3.
(a) 60
(b) 70
(c) 80
(d) 65
Ans: (d)
Q15: Select the odd one out.
(a) 43
(b) 80
(c) 15
(d) 90
Ans: (a)
Q16: How many 2’s are present in the provided sequence, each of which is directly preceded by an odd number but not directly followed by 4?
(a) None
(b) One
(c) Two
(d) More than two
Ans: (c)
Q17: Pointing towards Shikha, Vansh said, “She is the daughter of the only child of my grandfather.” How is Shikha related to Vansh?
(a) Daughter
(b) Mother
(c) Sister
(d) Aunt
Ans: (c)
Q18: Which of the following value will replace X in the given expression? (–91) ÷ X + 68 ÷ (–17) = –11
(a) 13
(b) 7
(c) 12
(d) 9
Ans: (a)
Q19: The sum of the digits of a two-digit number is 10. If the ten’s digit is one more than two times the unit’s digit, then find the number.
(a) 82
(b) 73
(c) 64
(d) 91
Ans: (b)
Q20: If two supplementary angles are in the ratio 4:5, then find the difference between the angles.
(a) 78°
(b) 54°
(c) 126°
(d) 20°
Ans: (d)
Q21: Find the value of ( 2a x 2 + b x b + 5ab + 9 ), when ( a = -3 ) and ( b = -2 ).
(a) 14
(b) 61
(c) 74
(d) 45
Ans: (b)
Q22: The average weight of 10 students of class 7 is 36 kg. If the average weight of 8 of them is 34 kg, then find the sum of weights of the remaining two students.
(a) 88 kg
(b) 45 kg
(c) 70 kg
(d) None of these
Ans: (a)
Q23: If 3/7 of a certain number equals 33.75, what is the value of 5/7 of that number?
(a) 78.50
(b) 65.75
(c) 68.25
(d) 56.25
Ans: (d)
Q24: Which of the following options shows the integers arranged in descending order?
(a) –43, –37, –12, 0, 6, 18
(b) –43, –12, –37, 0, 6, 18
(c) 18, 6, 0, –12, –37, –43
(d) 18, 6, 0, –43, –37, –12
Ans: (c)
Q25: Which of the following numbers is not divisible by 8?
(a) 765176
(b) 556764
(c) 772648
(d) 555112
Ans: (b)
Q26: Find the difference between the place values of the two 7’s in 476785.
(a) 9300
(b) 67400
(c) 25700
(d) 69300
Ans: (d)
Q27: For which value of x, the given ratios will form a proportion? 35 : 65 :: 56 : x
(a) 91
(b) 78
(c) 117
(d) 104
Ans: (d)
Q28: The given observations show the number of masks sold by a shopkeeper on different days of a week: 37, 57, 48, 33, 39, 64, 86. Find the average sale of masks sold.
(a) 54
(b) 47
(c) 49
(d) 52
Ans: (d)
Q29: Aayush purchased a school bag for ₹736.45 and a belt for ₹384.85. He paid the shopkeeper with a ₹2000 note. What will be the change he receives from the shopkeeper?
(a) ₹878.70
(b) ₹935.35
(c) ₹694.75
(d) ₹782.65
Ans: (a)
Q30: Samar divides his wealth among his three sons Sahil, Varun, and Amit in the ratio of 5:3:7. If Varun gets ₹73,125, then find the total wealth of Samar.
(a) ₹2,75,875
(b) ₹3,65,625
(c) ₹3,75,825
(d) ₹2,65,675
Ans: (b)
Q31: On his birthday, Ankush received ₹500. The following day, he was given ₹350 as pocket money by his father and spent ₹275 on cycle repairs. The next day, his sister rewarded him with ₹170. What is the total amount of money he has left?
(a) ₹745
(b) ₹650
(c) ₹750
(d) ₹845
Ans: (a)
Q32: In an examination, the highest marks achieved are 3 more than 5 times the lowest marks obtained. If the highest marks obtained are 24, then create the equation to find the lowest marks.
(a) x = 24 + 8
(b) 24 = 5x + 3
(c) 24x + 3 = 5
(d) None of these
Ans: (b)
Q33: The diagram shows the construction of a parallelogram KLMN. The width of the compasses for step I and step II are the same. ∠KLM = _______.
(a) 45°
(b) 60°
(c) 120°
(d) 135°
Ans: (b) 60°
Q34: To construct a kite which of the following is necessary?
(a) Two adjacent unequal sides and included diagonal.
(b) Two adjacent equal sides and included diagonal.
(c) Opposite sides length.
(d) None of these.
Ans: Two adjacent unequal sides and included diagonal means two unequal sides and diagonal from common vertex, i.e., sides AB, AD and diagonal AC are given.
Q35: In the diagram, KLMN is a constructed parallelogram.
Find the value of ∠KLM.
(a) 15°
(b) 30°
(c) 45°
(d) 60°
Ans: (c) ∠KLP = 90°
LM is an angular bisector of ∠KLP
∴ ∠KLM = 1/2 × 90° = 45°
Q36: Given below are the steps of construction to construct a quadrilateral ABCD where AB = 5.6 cm, BC = 4.1 cm, CD = 4.4 cm, AD = 3.3 cm and ∠A = 75°. Which of the following is INCORRECT step?
(P) Step I: Draw AB = 5.6 cm and construct ∠BAX = 75°
(Q) Step II: With A as centre and radius = 3.3 cm, cut off AD = 3.3 cm along AX.
(R) Step III: Join BD. With D as centre and radius = 4.1 cm, draw an arc.
(S) Step IV: With B as centre and radius = 4.1 cm, draw an arc to cut the arc drawn in above step at C. Join BC, CD to obtain the required quadrilateral ABCD.
(a) P
(b) Q
(c) R
(d) S
Ans: (c) R
Q37: If AB = 7.3 cm, one angle is 60° and diagonal bisect each other at 90°, then which of the following figure can be constructed?
(a) Rectangle
(b) Square
(c) Trapezium
(d) Rhombus
Ans: (d)
Here, one side, one angle 60° and diagonal bisect each other at 90° is given and we know that diagonals of a rhombus bisect each other at right angle. So, a rhombus can be drawn since one angle is 60°.
Q38: Given below are the steps of construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, ∠A = 75°, ∠B = 105° and ∠C = 120°. Which of the following is a wrong step?
(P) Step I: Draw AB = 3.5 cm.
(Q) Step II: Draw ∠XAB = 75° at A and ∠ABY = 105° at B.
(R) Step III: With B as centre and radius BC = 6.5 cm, draw an arc to intersect BY at C.
(S) Step IV: At C draw ∠ADC = 120° such that CZ meets AX at D.
(a) P
(b) Q
(c) R
(d) S
Ans: (d) S
Q39: Given AB = 3 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following is true about the construction of a quadrilateral?
(a) It is possible to draw the quadrilateral.
(b) It is not possible to draw the quadrilateral since AD + DC > AC.
(c) It is possible to draw the quadrilateral since AD + DC < AC.
(d) None of these
Ans: (b)
Here, it is given that AD + DC < AC which does not satisfy triangle inequality and hence quadrilateral cannot be drawn.
Q40: The construction of which figure is shown in the diagram?
(a) A trapezium
(b) A rhombus
(c) A rectangle
(d) A kite
Ans: (b)
Diagonals and bisecting each other at right angle.
Q41: Where is the circumcenter of a right triangle located in relation to the triangle?
(a) On the triangle
(b) Outside the triangle
(c) Inside the triangle
(d) The location varies
Ans: (a)
On the triangle
Q42: You are looking at a triangle where the orthocenter, the centroid and the circumcenter are all the same point. What type of triangle are you looking at?
(a) Scalene
(b) Isosceles
(c) Equilateral
(d) Right
Ans: (c) Equilateral
Q43: When constructing a line parallel to a given line, you will be
(a) copying a segment.
(b) bisecting a segment.
(c) copying an angle.
(d) constructing a perpendicular.
Ans: (c) Copying an angle
Q44: The centroid of a triangle is located 12 units from one of the vertices of a triangle. Find the length of the median of the triangle drawn from that same vertex.
(a) 16
(b) 18
(c) 24
(d) 36
Ans: (b)
Let AD be the median of △ABC.
Let G be the centroid of △ABC.
Let GD = x unit
∴ Length of median = 12 + x.
Since centroid divides median in 2 : 1 ratio.
∴ 12 : x = 2 : 1
Hence, length of median = 12 + 6 = 18 units.
Q45: The diagram shows the four quadrants P, Q, R, and S on a Cartesian plane.
Which of the following points lie in quadrant S?
I (–1, 2)
II (–1, –2)
III (1, –2)
IV (2, –1)
(a) I and II only
(b) I and IV only
(c) II and III only
(d) III and IV only
Ans: (d)
In S, the abscissa of a point is positive, and the ordinate of a point is negative.
Thus, (1, –2) and (2, –1) will lie in quadrant S.
Achievers Section
Q46: If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then
(Abscissa of P) – (Abscissa of Q) is:
(a) 5
(b) 1
(c) 2
(d) –3
Ans: (b)
(Abscissa of P) – (Abscissa of Q)
= –2 – (–3) = –2 + 3 = 1
Q47: The distance of the point P(4,3) from the origin is:
(a) 5
(b) 4
(c) 7
(d) 3
Ans: (a)
Q48: The diagram shows a straight line MN.
Which of the following coordinates does not lie on the line MN?
(a) (1, 6)
(b) (3, 5)
(c) (4, 5)
(d) (7, 3)
Ans: (c) (4, 5)
Q49: The graph below compares the price (in Rs) and weight of 6 bags (in kg) of sugar of different brands A, B, C, D, E, F.
Which brand(s) costs more than Brand D?
(a) E and F
(b) E and C
(c) F
(d) E
Ans: (a)
We can see that points E and F lie above point D.
So, brands E and F cost more than brand D.
Q50: Observe the adjoining graph and answer the following questions:
(i) Changes in y when x changes from 0 to 2.
(a) 2
(b) 4
(c) 0
(d) –4
(ii) Change in y when x changes from 2 to 4.
(a) 0
(b) 2
(c) 4
(d) 3
Ans:
(i) (d) Graph decreases steadily from 8 to 4.
(ii) (a) There is no change in Y.
24 videos|57 docs|102 tests
|
1. What topics are covered in the Class 7 Mathematics Olympiad Previous Year Papers? |
2. How can students prepare for the Class 7 Mathematics Olympiad effectively? |
3. What is the format of questions in Class 7 Mathematics Olympiad exams? |
4. Are there any specific strategies for solving Logical Reasoning questions in the Olympiad? |
5. How important is time management during the Class 7 Mathematics Olympiad? |
|
Explore Courses for Class 7 exam
|