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Full Syllabus Mock Test

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Q1 Mathematical Reasoning
Compute 102² using an identity.
(100 + 2)² = 10000 + 400 + 4 = 10404.
Q2 Everyday Mathematics
Compute 103 × 97 using an identity.
(100 + 3)(100 − 3) = 10000 − 9 = 9991.
Q3 Mathematical Reasoning
Decrease 100 by 40%.
40% of 100 = 40, so 100 − 40 = 60.
Q4 Achievers Section
The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The largest is ___ ?
Parts = 10; 360 ÷ 10 = 36, so the largest is 4 × 36 = 144°.
Q5 Logical Reasoning
The exterior angles of any polygon sum to ___ ?
Exterior angles always total 360°.
Q6 Logical Reasoning
A point on the x-axis has y-coordinate ___ ?
On the x-axis y = 0.
Q7 Achievers Section
What is the reciprocal of −¾?
−¾ × (−4/3) = 1, so the reciprocal is −4/3.
Q8 Mathematical Reasoning
What pie-chart angle represents 50% of the data?
(50/100) × 360 = 180°.
Q9 Everyday Mathematics
A square garden has area 169 sq m. What is its side?
√169 = 13 m.
Q10 Mathematical Reasoning
Expand: (x − 4)².
x² − 8x + 16.
Q11 Mathematical Reasoning
3 kg of rice cost ₹90. What do 5 kg cost?
1 kg = ₹30, so 5 kg = ₹150.
Q12 Mathematical Reasoning
Solve: 5x = 2x + 12.
3x = 12, so x = 4.
Q13 Everyday Mathematics
The diagonals of a rectangle are ___ ?
A rectangle has equal diagonals.
Q14 Achievers Section
If A = 1, B = 2, …, Z = 26, what is the sum of the letters in 'CAB'?
C + A + B = 3 + 1 + 2 = 6.
Q15 Mathematical Reasoning
Factorise x² − 16.
Difference of squares: (x + 4)(x − 4).
Q16 Everyday Mathematics
On a distance-time graph, a steeper line shows ___ ?
A steeper distance-time graph means greater speed.
Q17 Achievers Section
A pie-chart sector is 120°. What fraction of the total is it?
120 ÷ 360 = ⅓.
Q18 Logical Reasoning
If each letter moves forward by 1, the code for DOG is ___ ?
D→E, O→P, G→H gives EPH.
Q19 Everyday Mathematics
A stop sign is a regular octagon. Its interior angle sum is ___ ?
(8 − 2) × 180 = 1080°.
Q20 Mathematical Reasoning
A car covers 100 km in 2 hours. How far in 5 hours at the same speed?
50 km/hr × 5 = 250 km.
Q21 Logical Reasoning
Find the next term: 3, 9, 27, ___ ?
Each term is ×3: 27 × 3 = 81.
Q22 Mathematical Reasoning
What is 5⁰?
Any non-zero number to the power 0 is 1.
Q23 Logical Reasoning
aᵐ ÷ aⁿ equals a to the power ___ ?
Dividing powers of the same base subtracts the exponents.
Q24 Logical Reasoning
In inverse proportion, x × y is ___ ?
In inverse proportion the product stays constant.
Q25 Mathematical Reasoning
What is the surface area of a cuboid 5 × 4 × 3?
2(20 + 12 + 15) = 2 × 47 = 94 sq cm.
Q26 Mathematical Reasoning
Write 38 in generalised form.
38 = 30 + 8.
Q27 Logical Reasoning
47 = 10 × 4 + ___ ?
47 = 40 + 7.
Q28 Logical Reasoning
Probability values range from 0 to ___ ?
Probability ranges from 0 to 1.
Q29 Mathematical Reasoning
2000 cm³ equals how many litres?
2000 ÷ 1000 = 2 L.
Q30 Logical Reasoning
a⁰ equals ___ ?
Any non-zero number to the power 0 is 1.
Q31 Logical Reasoning
The surface area of a cube is ___ ?
A cube has 6 square faces, so 6a².
Q32 Everyday Mathematics
A cylindrical tank has radius 7 m and height 10 m. Its volume is (π = 22/7) ___ ?
(22/7) × 49 × 10 = 1540 m³.
Q33 Mathematical Reasoning
Factorise x² + 5x + 6.
2 × 3 = 6 and 2 + 3 = 5.
Q34 Everyday Mathematics
Food lasts 20 people for 6 days. How long for 30 people?
20 × 6 = 120, so 120 ÷ 30 = 4 days.
Q35 Mathematical Reasoning
Solve: 3(x − 2) = 9.
3x − 6 = 9, so x = 5.
Q36 Mathematical Reasoning
What is the mean of ¼ and ¾?
(¼ + ¾) ÷ 2 = 1 ÷ 2 = ½.
Q37 Achievers Section
Factorise x² − x − 6.
−3 × 2 = −6 and −3 + 2 = −1.
Q38 Mathematical Reasoning
Expand: (x + 1)(x + 6).
x² + (1 + 6)x + 6 = x² + 7x + 6.
Q39 Mathematical Reasoning
Solve: 2x + 3 = x + 8.
x = 8 − 3 = 5.
Q40 Logical Reasoning
The probability of a certain event is ___ ?
A certain event has probability 1.
Q41 Logical Reasoning
Your mother's brother is your ___ ?
A mother's brother is an uncle.
Q42 Mathematical Reasoning
Factorise 6x + 9.
HCF is 3: 3(2x + 3).
Q43 Mathematical Reasoning
What is 5³?
5 × 5 × 5 = 125.
Q44 Logical Reasoning
A polygon with 5 sides is a ___ ?
5 sides make a pentagon.
Q45 Logical Reasoning
The interior angle sum is (n − 2) × ___ ?
Interior angle sum = (n − 2) × 180°.
Q46 Logical Reasoning
x² + 2x + 1 factorises as ___ ?
It is a perfect square: (x + 1)².
Q47 Mathematical Reasoning
4 workers finish in 6 days. How long for 8 workers?
4 × 6 = 24, so 24 ÷ 8 = 3 days.
Q48 Everyday Mathematics
A rectangle has area x² + 7x + 12. Its sides could be ___ ?
x² + 7x + 12 = (x + 3)(x + 4).
Q49 Everyday Mathematics
A shirt with MP ₹800 has a 25% discount. The SP is ___ ?
₹200 off ₹800 gives ₹600.
Q50 Everyday Mathematics
3000 cm³ of water equals how many litres?
3000 ÷ 1000 = 3 L.
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