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Round 1 — Algebra Gate Takshay Simplify fully: 5 𝑥 + 3 − 2 𝑥 + 9 Aanjaneya Simplify fully: 7 𝑦 − 4 + 3 𝑦 + 11 Answers • Takshay: 3 𝑥 + 12 • Aanjaneya: 10 𝑦 + 7 Round 2 — Equation Strike Takshay Solve: 4 𝑥 + 7 = 31 Aanjaneya Solve: 5 𝑦 − 9 = 26 Answers • Takshay: 4 𝑥 = 24 𝑥 = 6 • Aanjaneya: 5 𝑦 = 35 𝑦 = 7 Round 3 — Percentage Tower Takshay A gaming headset costs £48. It is reduced by 25%. Find the sale price. Aanjaneya A jacket costs £72. It is reduced by 15%. Find the sale price. Answers • Takshay: 25% of 48 = 12 48 − 12 = £36 • Aanjaneya: 15% of 72 = 10 8 72 − 10 8 = £61 20 Round 4 — Ratio Forge Takshay The ratio of blue crystals to red crystals is: 3 : 5 There are 64 crystals altogether. How many are red? Aanjaneya The ratio of attack points to defence points is: 4 : 7 There are 99 points altogether. How many are defence points? Answers • Takshay: 3 + 5 = 8 64 ÷ 8 = 8 5 × 8 = 40 40 red crystals • Aanjaneya: 4 + 7 = 11 99 ÷ 11 = 9 7 × 9 = 63 63 defence points Shop 1 — Equation Armory text TAKSHAY HP: ____ / 45 Gold: ____ Upgrade purchased: ______________________________ AANJANEYA HP: ____ / 45 Gold: ____ Upgrade purchased: ______________________________ Round 5 — Angle Ambush Takshay Angles on a straight line are: ( 3 𝑥 + 15 ) ∘ and ( 5 𝑥 + 5 ) ∘ Find 𝑥 Aanjaneya Angles around a point are: ( 4 𝑦 + 10 ) ∘ , 110 ∘ , 70 ∘ Find 𝑦 Answers • Takshay: 3 𝑥 + 15 + 5 𝑥 + 5 = 180 8 𝑥 + 20 = 180 8 𝑥 = 160 𝑥 = 20 • Aanjaneya: 4 𝑦 + 10 + 110 + 70 = 360 4 𝑦 + 190 = 360 4 𝑦 = 170 𝑦 = 42 5 Round 6 — Coordinate Canyon Takshay Point 𝐴 is at: ( − , 34 ) It is translated by the vector: ( 5 − 6 ) Write the coordinates of the new point. Aanjaneya Point 𝐵 is at: ( 7 , − 2 ) It is translated by the vector: ( − 9 4 ) Write the coordinates of the new point. Answers • Takshay: ( − , 3 + 5 4 − 6 ) = ( 2 , − 2 ) • Aanjaneya: ( 7 , − 9 − 2 + 4 ) = ( − , 22 ) Round 7 — Probability Portal Takshay A bag contains: • 5 red counters • 3 blue counters • 2 green counters One counter is chosen at random. Find the probability of choosing a counter that is not blue Give your answer in its simplest form. Aanjaneya A spinner has 12 equal sections: • 4 yellow • 3 red • 5 blue Find the probability of landing on yellow or red Give your answer in its simplest form. Answers • Takshay: Not blue = 5 + 2 = 7 𝑃 ( not blue ) = 7 10 • Aanjaneya: Yellow or red = 4 + 3 = 7 𝑃 ( yellow or red ) = 7 12 Round 8 — Area Arena Takshay A rectangle has length 12 cm and width 7 cm. A square of side 3 cm is cut out from one corner. Find the remaining area. Aanjaneya A rectangle has length 15 cm and width 9 cm. A smaller rectangle of length 5 cm and width 4 cm is cut out. Find the remaining area. Answers • Takshay: 12 × 7 = 84 3 × 3 = 9 84 − 9 = 75 cm 2 • Aanjaneya: 15 × 9 = 135 5 × 4 = 20 135 − 20 = 115 cm 2 Shop 2 — Equation Armory text TAKSHAY HP: ____ / 45 Gold: ____ Second upgrade purchased: ________________________ AANJANEYA HP: ____ / 45 Gold: ____ Second upgrade purchased: ________________________ Round 9 — Function Fortress Takshay The rule is: 𝑦 = 3 𝑥 − 2 Complete the table. 𝑥 1 4 7 𝑦 ? ? ? Aanjaneya The rule is: 𝑦 = 4 𝑥 + 1 Complete the table. 𝑥 0 3 6 𝑦 ? ? ? Answers • Takshay: 𝑦 = 1 , 10 , 19 • Aanjaneya: 𝑦 = 1 , 13 , 25 Round 10 — Boss Round: Simultaneous Shadows Correct answer gives 5 Gold Winner rolls two damage dice Boss Key may be used here. Takshay Two pens and one notebook cost £11. One pen and one notebook cost £7. Find the cost of one pen. Aanjaneya Three game tokens and one key cost £17. One game token and one key cost £9. Find the cost of one game token. Answers • Takshay: 2 𝑝 + 𝑛 = 11 𝑝 + 𝑛 = 7 Subtract: 𝑝 = 4 One pen costs £4. • Aanjaneya: 3 𝑡 + 𝑘 = 17 𝑡 + 𝑘 = 9 Subtract: 2 𝑡 = 8 𝑡 = 4 One token costs £4. Round 11 — Final Boss: The Equation Titan Correct answer gives 5 Gold Winner rolls two dice This is the final attack round. Takshay A number is multiplied by 6 and then 11 is added. The answer is 53. Find the number. Aanjaneya A number is multiplied by 7 and then 9 is subtracted. The answer is 40. Find the number.