Mixed revision tests

Attempt these only after completing the chapters. Cover the explanation column, set a timer, and mark guessed answers separately. Analyse every error by chapter.

Mixed Test 1

Choose one answer. Target: 8/10 accurately before reducing time.

1. HCF of 84 and 126 is:

(A) 14 (B) 21 (C) 42 (D) 63

Key: C — 84=2²×3×7 and 126=2×3²×7; common minimum product is 42.

2. LCM is used when events must occur:

(A) At the same first future time (B) In the greatest possible size (C) Only once (D) With no common multiple

Key: A — LCM gives the first common multiple.

3. Which number is divisible by 9?

(A) 734 (B) 729 (C) 721 (D) 725

Key: B — 7+2+9=18, divisible by 9.

4. 0.125 equals:

(A) 1/4 (B) 1/8 (C) 3/8 (D) 5/8

Key: B — 0.125=125/1000=1/8.

5. √72 simplifies to:

(A) 3√8 (B) 6√2 (C) 8√2 (D) 9√2

Key: B — √72=√36×√2=6√2.

6. A terminating decimal has reduced denominator made of:

(A) 2 and 3 only (B) 2 and/or 5 (C) 3 and 7 only (D) Any prime

Key: B — Only factors 2 and 5 permit termination.

7. A value rises 20% and falls 20%. Net change is:

(A) 0% (B) 2% decrease (C) 4% decrease (D) 4% increase

Key: C — The multiplier is 1.2×0.8=0.96.

8. After a 25% increase a value is 500. Original value:

(A) 375 (B) 400 (C) 425 (D) 625

Key: B — 500/1.25=400.

9. From 40% to 50%, the percentage-point increase is:

(A) 10 (B) 20 (C) 25 (D) 90

Key: A — 50−40=10 percentage points.

10. Divide 720 in ratio 5:7. Larger share:

(A) 300 (B) 360 (C) 420 (D) 480

Key: C — Larger share=720×7/12=420.

Score: ______ / 10 Time: ______ minutes Re-test date: __________

Mixed Test 2

Choose one answer. Target: 8/10 accurately before reducing time.

1. If x:y=4:9 and x=20, y is:

(A) 36 (B) 45 (C) 54 (D) 60

Key: B — Scale factor is 5, so y=45.

2. For inverse variation, which remains constant?

(A) x+y (B) x−y (C) xy (D) x/y

Key: C — The product remains constant.

3. Average of 8 numbers is 24. Sum:

(A) 32 (B) 192 (C) 216 (D) 240

Key: B — Sum=8×24=192.

4. Groups of 5 and 3 have averages 42 and 58. Combined average:

(A) 46 (B) 48 (C) 48.5 (D) 50

Key: B — (5×42+3×58)/8=384/8=48. The group sizes must weight the two averages.

5. Average of 7 consecutive integers is 31. Largest:

(A) 33 (B) 34 (C) 35 (D) 37

Key: B — The middle is 31; numbers run 28 to 34.

6. CP=800, profit 15%. SP:

(A) 880 (B) 900 (C) 920 (D) 940

Key: C — 800×1.15=920.

7. MP=1000, discounts 10% and 20%. SP:

(A) 700 (B) 720 (C) 800 (D) 820

Key: B — 1000×0.9×0.8=720.

8. Profit percentage is normally calculated on:

(A) SP (B) CP (C) MP (D) Tax

Key: B — Unless stated otherwise, the base is cost price.

9. SI on 5000 at 8% for 2 years:

(A) 400 (B) 800 (C) 900 (D) 1000

Key: B — 5000×8×2/100=800.

10. CI on 10000 at 10% for 2 years:

(A) 2000 (B) 2100 (C) 2200 (D) 2400

Key: B — Amount=12100, so CI=2100.

Score: ______ / 10 Time: ______ minutes Re-test date: __________

Mixed Test 3

Choose one answer. Target: 8/10 accurately before reducing time.

1. For half-yearly compounding, rate per period is:

(A) r (B) 2r (C) r/2 (D) r²

Key: C — There are two periods per year.

2. A invests 5000 for 12 months, B 8000 for 6 months. Ratio:

(A) 5:4 (B) 4:5 (C) 5:8 (D) 8:5

Key: A — Products are 60000:48000=5:4.

3. Profit 9000 in ratio 2:1. First share:

(A) 3000 (B) 4500 (C) 6000 (D) 7500

Key: C — First share=9000×2/3=6000.

4. A partner’s capital-time product is used to find:

(A) Average (B) Profit share (C) Discount (D) Speed

Key: B — It determines proportional partnership share.

5. Mix ₹20 and ₹50 items to get ₹30 mean. Quantity ratio:

(A) 1:2 (B) 2:1 (C) 3:1 (D) 1:3

Key: B — (50−30):(30−20)=20:10=2:1.

6. A mixture has 30% milk. If 10 L mixture, milk is:

(A) 2 L (B) 3 L (C) 4 L (D) 7 L

Key: B — 30% of 10=3 L.

7. Alligation cross-differences represent:

(A) Quantities ratio (B) Final prices (C) Discounts (D) Time ratio

Key: A — They give the quantity ratio.

8. A takes 12 days and B 18 days. Together:

(A) 6 days (B) 7.2 days (C) 8 days (D) 9 days

Key: B — Combined rate=5/36, so time=36/5=7.2 days.

9. If A is 3 times as efficient as B, time ratio A:B:

(A) 3:1 (B) 1:3 (C) 2:3 (D) 3:2

Key: B — Time is inverse to efficiency.

10. Two workers’ rates should be:

(A) Added (B) Multiplied (C) Subtracted always (D) Ignored

Key: A — Combined work rates are added.

Score: ______ / 10 Time: ______ minutes Re-test date: __________

Mixed Test 4

Choose one answer. Target: 8/10 accurately before reducing time.

1. Inlet fills in 6 h, leak empties in 12 h. Net time:

(A) 6 h (B) 8 h (C) 12 h (D) 18 h

Key: C — Net rate is 1/12 tank per hour.

2. An outlet is represented by a:

(A) Positive rate (B) Negative rate (C) Zero rate always (D) Percentage

Key: B — It removes water.

3. Two inlets fill in 10 h and 15 h. Together time:

(A) 5 h (B) 6 h (C) 7.5 h (D) 25 h

Key: B — Rate=1/10+1/15=1/6.

4. 72 km/h equals:

(A) 15 m/s (B) 20 m/s (C) 25 m/s (D) 30 m/s

Key: B — 72×5/18=20.

5. Equal distances at 30 and 60 km/h average:

(A) 35 (B) 40 (C) 45 (D) 50

Key: B — 2×30×60/90=40.

6. For opposite directions, relative speed is:

(A) Difference (B) Sum (C) Product (D) Average

Key: B — The separation changes at the sum.

7. A 180 m train at 54 km/h crosses a pole in:

(A) 10 s (B) 12 s (C) 15 s (D) 18 s

Key: B — 54 km/h=15 m/s; 180/15=12 s.

8. A 180 m train crosses a 120 m platform at 15 m/s. Time:

(A) 12 s (B) 15 s (C) 20 s (D) 24 s

Key: C — Distance=300 m; time=20 s.

9. Same-direction relative speed is:

(A) u+v (B) u−v (C) uv (D) u/v

Key: B — Subtract the lower speed from the higher.

10. D=18, U=10. Still-water speed:

(A) 4 (B) 8 (C) 14 (D) 28

Key: C — (18+10)/2=14.

Score: ______ / 10 Time: ______ minutes Re-test date: __________

Mixed Test 5

Choose one answer. Target: 8/10 accurately before reducing time.

1. For the same values, stream speed:

(A) 2 (B) 4 (C) 8 (D) 14

Key: B — (18−10)/2=4.

2. Upstream speed equals:

(A) b+s (B) b−s (C) s−b (D) b×s

Key: B — Current opposes the boat.

3. 103² is:

(A) 10509 (B) 10609 (C) 10709 (D) 10809

Key: B — Use (100+3)².

4. a²−b² factors as:

(A) (a−b)² (B) (a+b)² (C) (a−b)(a+b) (D) a²+b²

Key: C — Difference of squares is a product.

5. Middle term in (a−b)² is:

(A) +2ab (B) −2ab (C) 0 (D) ab²

Key: B — The sign is negative.

6. For 3x+7=25, x:

(A) 4 (B) 5 (C) 6 (D) 7

Key: C — 3x=18, so x=6.

7. The graph of y=2x+1 has slope:

(A) −2 (B) −1 (C) 1 (D) 2

Key: D — The coefficient of x is the slope.

8. In elimination, equations are combined to remove:

(A) A variable (B) All constants (C) The graph (D) Units

Key: A — The goal is one equation in one variable.

9. A triangle’s interior angles sum to:

(A) 90° (B) 180° (C) 270° (D) 360°

Key: B — Basic triangle angle sum is 180°.

10. A 3–4 right triangle has hypotenuse:

(A) 5 (B) 6 (C) 7 (D) 12

Key: A — 3²+4²=25.

Score: ______ / 10 Time: ______ minutes Re-test date: __________

Mixed Test 6

Choose one answer. Target: 8/10 accurately before reducing time.

1. If side ratio of similar triangles is 2:3, area ratio:

(A) 2:3 (B) 3:2 (C) 4:9 (D) 8:27

Key: C — Areas scale as the square.

2. Interior sum of a pentagon:

(A) 360° (B) 540° (C) 720° (D) 900°

Key: B — (5−2)×180=540°.

3. Each exterior angle of a regular octagon:

(A) 30° (B) 40° (C) 45° (D) 60°

Key: C — 360/8=45°.

4. Area of parallelogram is:

(A) base×height (B) side² only (C) diagonal×2 (D) perimeter/2

Key: A — Perpendicular height is required.

5. For r=7, circumference using 22/7:

(A) 22 (B) 44 (C) 88 (D) 154

Key: B — 2×22/7×7=44.

6. For r=7, area:

(A) 44 (B) 77 (C) 154 (D) 308

Key: C — 22/7×49=154.

7. Angle in a semicircle is:

(A) 45° (B) 60° (C) 90° (D) 180°

Key: C — Thales’ theorem.

8. Triangle base 10, height 8. Area:

(A) 18 (B) 40 (C) 80 (D) 160

Key: B — 1/2×10×8=40.

9. Rectangle 12×7 perimeter:

(A) 19 (B) 38 (C) 84 (D) 168

Key: B — 2(12+7)=38.

10. Area units are:

(A) Linear (B) Square (C) Cubic (D) No unit

Key: B — Area is measured in square units.

Score: ______ / 10 Time: ______ minutes Re-test date: __________